Reconstruction method of a computed tomographic image from a few X-ray projections

• US 4,422,146 A
• Filed: 11/12/1980
• Issued: 12/20/1983
• Est. Priority Date: 11/22/1979
• Status: Expired due to Term

• Current Assignee: President of Tokyio Institute of Technology The A Japanese National Institute
• Original Assignee: President of Tokyo Institute of Technology
• Inventors: Kobayashi, Fujio, Yamaguchi, Shoichiro
• Primary Examiner(s): Chin, Gary
• Application Number:
  US06/205,909
• Time in Patent Office: 1,133 Days
• Field of Search: 364/414, 364/515, 250/445 T, 250/445 R, 250/363 S, 250/363 R, 378/4, 378/901
• US Class Current: 378/22
• CPC Class Codes: G06T 11/006 Inverse problem, transformation from projection-space into object-space, e.g. transform methods, back-projection, algebraic methods
• CPC Class Codes: Y10S 378/901 Computer tomography program or processor

Abstract

A tomographic image of a X-ray tested tissue of body is reconstructed by calculating X-ray absorption coefficients of picture elements constituting a tomographic plane in reference to measured values produced by the first and second projectional distributions of X-ray produced by projecting X-ray. Accordingly, it becomes possible to reconstruct a clear tomographic image of a moving X-ray tested tissue and to make an X-ray exposure level very low by extremely shortening the time of the reconstruction of computed tomographic image. Moreover, a resolving power of measuring is substantially improved, resulting in that an accuracy of reconstructing the tomographic image may also be improved.

Claims

1. A reconstructions method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two desired directions toward tested tissue of a body for producing first and second X-ray projectional distributions of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (k is natural number) of X-ray density on said first X-ray projectional distribution at a plurality of positions spaced apart from each other from one end of said first X-ray projectional distribution toward the other end thereof, and at the same time measuring the values d_k '"'"' (k'"'"' is natural number) of X-ray density on said second X-ray projectional distribution at a plurality of positions spaced apart from each other from one end of said second X-ray projectional distribution toward the other end thereof, where said plurality of positions spaced apart from each other on the first and second X-ray projectional distributions for measurement of the values d_k and d_k, of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions, (ii) that said pseudo-tomographic plane is divided into a first part of a plane constructed collectively by said picture elements with i pieces in a row (i is natural number, i<

m) and n picture elements in a column and a second part of a plane constituted collectively by said picture elements with (m-i) pieces in a row and n pieces in a column, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1,2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1,2, . . . , m;

m+1, m+2, . . . , 2m;

. . . ;

(n-1)m+1, (n-1)m+2, . . . mn from the side of said x-ray source toward the side of said two X-ray projectional distributions in order and that at least mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams passing through respectively the left upper corner of each picture element in said second part of a plane, and said plurality of positions spaced apart from each other on said two X-ray projectional distributions for measurement of the values d_k and d_k'"'"' of X-ray density correspond to the positions on said two X-ray projectional distributions which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane;

(c) calculating the X-ray absorption coefficient μ

_t (t=1,2, . . . , mn and t is a natural number) of each of mn pieces of picture elements based on the X-ray density values d_k and d_k'"'"' measured in step (b) and length of the X-ray beams passing through each of the picture elements;

(d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients μ

₁,μ

₂, . . . , μ

_mn calculated in step (c) are positioned at the locations of said picture elements numbered 1,2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

2. A reconstruction method of a computed tomographic image from a few X-ray projections according to claim 1, wherein neighboring measuring positions on said X-ray projectional distributions are equally spaced apart.

3. A reconstruction method of a computed tomographic image according to claim 1, comprising the step of displaying the m×

n array of picture elements in order to display the internal structure of said tested tissue of a body.

4. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₁, θ

₂) toward tested tissue of a body for producing first and second X-ray projectional distributions D₁, D₂ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (1) (k(1) is a natural number) of X-ray density on said first X-ray projectional distribution D₁ at mn/2 (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D₁ toward the other end thereof, and at the same time measuring the values d_k (2) (k(2) is a natural number) of X-ray density on said second X-ray projectional distribution D₂ at mn/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D₂ toward the other end thereof, where said mn/2 positions spaced apart from each other on the first and second X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₁, D₂ (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m;

m+1, m+2, . . . , 2m . . . ;

(n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₁, D₂ in order and that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₁, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₂ passing through respectively the left upper corner of each picture element in said second part of a plane, and said mn/2 positions spaced apart from each other on said two X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density correspond to the positions on said two X-ray projectional distributions D₁, D₂ which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, θ

₁ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₁ =tan^-1(m/2), and θ

₂ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₂ = -tan^-1(m/2) ;

(c) calculating X-ray absorption coefficient μ

_t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based on the X-ray density values d_k (1) and d_k (2) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU41## L is a square matrix of dimensions mn×

mn, T indicates a matrix transpose and α

is a length of an X-ray beam passing through each picture element from directions of θ

₁ and θ

₂ ;

(d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂, . . . , μ

_mn calculates in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m=n array constitute the reconstructed computed tomographic plane of the tested tissue of a body.

5. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₃, θ

₄) toward tested tissue of a body for producing first and second X-ray projectional distributions D₃, D₄ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (3) (k(3) is a natural number) of X-ray density on said first X-ray projectional distribution D₃ at mn/2 (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D₃ toward the other end thereof, and at the same time measuring the values d_k (4) (k(4) is a natural number) of X-ray density on said second X-ray projectional distribution D₄ at mn/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D₄ toward the other end thereof, where said mn/2 positions spaced apart from each other on the first and second X-ray projectional distributions D₃, D₄ for measurement of the valves d_k (3) and d_k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₃, D₄, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . m;

m+1, m+2, . . . , 2 m;

. . . ;

(n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₃, D₄ in order and that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₃, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₄ passing through respectively the left upper corner of each picture element in said second part of a plane, and said mn/2 positions spaced apart from each other on said two X-ray projectional distributions D₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, θ

₃ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₃ =tan^-1 m and θ

₄ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₄ =-tan^-1 m;

(c) calculating X-ray absorption coefficient μ

_t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based of the X-ray density values d_k (3) and d_k (4) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU42## L is a square matrix of dimension mn×

mn, T indicates a matrix transpose and α

is a length of an X-ray beam passing through each picture element from directions of θ

₃, and θ

₄ ;

(d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂, . . . , μ

_mn calculated in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed computed tomographic plane of the tested tissue of a body.

6. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₁, θ

₂) toward tested tissue of a body for producing first and second X-ray projectional distributions D₁, D₂ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (1) (k(1) is a natural number, k(1)=1, 2, . . . , m/2) of X-ray density on said first X-ray projectional distribution D₁ at m/2 (m is a natural number) positions spaced apart from each other from one end of said first X-ray projectional distribution D₁ toward the other end thereof, and at the same time measuring the values d_k (2) (k(2) is a natural number, k(2)=1, 2, . . . , m/2) of X-ray density on said second X-ray projectional distribution D₂ at m/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D₂ toward the other end thereof, where said m/2 positions spaced apart from each other on the first and second X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₁, D₂, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m;

m+1, m+2, . . . , 2m;

. . . ;

(n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₁, D₂ in order and that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₁, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₂ passing through respectively the left upper corner of each picture element in said second part of a plane, and said m/2 positions spaced apart from each other on said two X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density correspond to the positions on said two X-ray projectional distributions D₁, D₂ which have X-ray density information to be obtained by passing first m/2 X-ray beams through said pseudo-tomographic plane based on the abovementioned criteria, θ

₁ indicates the angle at whih each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₁ -tan^-1 m/2, and θ

₂ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₂ =-tan^-1 m/2;

(c) calculating X-ray absorption coefficient μ

_t (t is a natural number, t=1, 2, . . . , m/2) of each of m/2 pieces of picture elements in the first part of a plane in accordance with the following equations based on the values d_k (1) of X-ray density measured in step (b) and length of the X-ray beams in the direction of θ

₁ passing through each picture element in the first part of a plane, and at the same time calculating X-ray absorption coefficient μ

_t (t is a natural number, t=m/2+1, m/2+2, . . . ,m) of each of m/2 pieces of picture elements in the second part of a plane in accordance with the following equations based on the values d_k (2) of X-ray density measured in step (b) and length of the X-ray beams in the direction of θ

₂ passing through each picture element in the second part of plane, ##EQU43## L is a square matrix of dimension m×

m, T indicates a matrix transpose and α

is a length of an X-ray beam passing through each picture element from directions of θ

₁, θ

₂ ;

(d) memorizing X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c);

(e) measuring each of the values d_k (1) (k(1) is a natural number, k(1)=m/2+1, m/2+2, . . . ,m) of X-ray density on said first X-ray projectional distribution D₁ at the positions numbering m/2 spaced apart from each other from the (m/2+1) position from one end of said first X-ray projectional distribution D₁ toward the other end thereof, and at the same time measuring each of the values d_k (2) (k(2) is a natural number, k(2)=m/2+1, m/2+2, . . . , m) of X-ray density on said second X-ray projectional distribution D₂ at the positions number m/2 spaced apart from each other from the (m/2+1) position from one end of said second X-ray projectional distribution D₂ toward the other end thereof, where said positions numbering m/2 spaced apart from each other on said first X-ray projectional distribution D₁ for measurement of the values d_k (1) (k(1)=m/2+1, m/2+2, . . . ,m) of X-ray density are selected such that said positions number m/2 spaced apart from each other on said first X-ray projectional distribution D₁ for measurement of the values d_k (1) (k(1)=m/2+1, m/2+2, . . . , m) of X-ray density correspond to the positions on said first X-ray projectional distribution D₁ which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left lower corner of each of the respective picture elements number (m+1) to 3m/2 passing through said first part of a plane based on the three criteria in step (b), and said positions numbering m/2 spaced apart from each other on said second X-ray projectional distribution D₂ for measurement of the values d_k (2) (k(2)=m/2+1, m/2+2, . . . , m) of X-ray density are selected such that said positions number m/2 spaced apart from each other on said second X-ray projectional distribution D₂ for measurement of the values d_k (2) (k(2)=m/2+1, m/2, . . . , m) of X-ray density correspond to the positions on said second X-ray projectional distribution D₂ which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left upper corner of each of the respective picture elements numbered ##EQU44## to 2m passing through said second part of a plane based on the three criteria in step (b);

(f) calculating the X-ray absorption coefficients μ

_m+1 ˜

μ

_3m/2 based on the X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c), the values d_k (1) (k(1)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3m/2 from the θ

₁ direction, and at the same time, calculating the X-ray absorption coefficients μ

_3m/2+1 ˜

μ

_2m based on the X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c), the values d_k (2) (k(2)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (3m/2+1) to 2m from the θ

₂ direction,

where the method of calculating the X-ray absorption coefficients μ

_m+1 ˜

μ

_2m is the same as in step (c) and the X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c) are selectively used;

(g) memorizing the X-ray absorption coefficients μ

_m+1 ˜

μ

_2m calculated in step (f);

(h) calculating the X-ray absorption coefficients μ

_2m+1 ˜

μ

_3m , μ

_3m+1 ˜

μ

_4m, . . . , μ

.sub.(n-1)m+1 ˜

μ

_mn repeating substantially the same steps as steps (e), (f) and (g) and memorizing them;

(i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients μ

₁ ˜

μ

_m, μ

_m+1 ˜

μ

_2m, . . . , μ

.sub.(n-1) m+1 ˜

μ

_mn memorized in steps (d), (g) and (h), where the picture elements having respective X-ray absorption coefficcients μ

₁, μ

₂, . . . , μ

_mn calculated in step (c), (f) and (h) are positioned at the locations of said picture elements number 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

7. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₃, θ

₄) toward tested tissue of a body for producing first and second X-ray projectional distributions D₃, D₄ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (3) (k(3) is a natural number, k(3)=1, 2, . . . , m/2) of X-ray density on said first X-ray projectional distribution Dl₃ at m/2 (m is a natural number) positions spaced apart from each other from one end of said first X-ray projectional distribution D₃ toward the other end thereof, and at the same time measuring the values d_k (4) (k(4) is a natural number, k(4)=1, 2, . . . , m/2) of X-ray density on said second X-ray projectional distribution D₄ at m/2 positions spaced apart from each other from one end of said second X-ray projectional distribution D₄ toward the other end thereof, where said m/2 positions spaced apart from each other on the first and second X-ray projectional distributions D₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₃, D₄, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m;

m+1, m+2 , . . . , 2 m;

. . . ;

(n-1)m+1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₃, D₄ in order that mn X-ray beams passing through said pseudo-tomographic plane from two directions comprise the first group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₃, passing through respectively the left lower corner of each picture element in said first part of a plane and the second group of X-ray beams which is constituted by mn/2 X-ray beams in a direction of θ

₄ passing through respectively the left upper corner of each picture element in said second part of a plane, and said m/2 positions spaced apart from each other on said two X-ray projectional distributions D₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions D₃, D₄ which have X-ray density information to be obtained by passing first m/2 X-ray beams through said pseudo-tomographic plane based on the above-mentioned criteria, θ

₃ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₃ =tan^-1 m and θ

₄ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₄ =-tan^-1 m;

(c) calculating X-ray absorption coefficient μ

_t (t is a natural number, t=1, 2, . . . , m/2) of each of m/2 pieces of picture elements in the first part of a plane in accordance with the following equations based on the values d_k (3) of X-ray density measured in step (b) and length of the X-ray beam in the direction of θ

₃ passing through each picture element in the first part of a plane, and at the same time calculating X-ray absorption coefficient μ

_t (t is a natural number, t=m/2+1, m/2+2, . . . , m) of each of m/2 pieces of picture elements in the second part of a plane in accordance with the following equations based on the values d_k (4) of X-ray density measured in step (b) and length of the X-ray beams in the direction of θ

₄ passing through each picture element in the second part of plane, ##EQU45## L is a square matrix of dimension m×

m, T indicates a matrix transpose and α

is a length of an X-ray beam passing through each picture element from directions of θ

₃, θ

₄ ;

(d) memorizing X-ray absorption coefficients μ

₁ ˜

μ

m calculated in step (c);

(e) measuring each of the values d_k (3) (k(3) is a natural number, k(3)=m/2+1, m/2+2, . . . , m) of X-ray density on said first X-ray projectional distribution d₃ at the positions numbering m/2 spaced apart from each other from the (m/2+1)position from one end of said first X-ray projectional distribution D₃ toward the other end thereof, and at the same time measuring each of the values d_k (4) (k(4) is a natural number, k(4)=m/2+1, m/2+2, . . . , m) of X-ray density on said second X-ray projectional distribution D₄ at the positions numbering m/2 spaced apart from each other from the (m/2+1) position from D₄ toward the other end thereof, where said positions numbering m/2 spaced apart from each other on said first X-ray projectional distribution D₃ for measurement of the values d_k (3) (k(3)=m/2+1, m/2+2, . . . , m) of X-ray density are selected such that said positions numbering m/2 spaced apart from each other on said first X-ray projectional distribution D₃ for measurement of the values d_k (3) (k(3)=m/2+1, m/2+2, . . . , m) of X-ray density correspond to the positions on said first X-ray projectional distribution D₃ which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left lower corner of each of the respective picture elements numbered (m+1) to 3 m/2 passing through said first part of a plane based on the three criteria in step (b), and said positions numbering m/2 spaced apart from each other on said second X-ray projectional distribution D₄ for measurement of the values d_k (4) (k(4)=m/2+1, m/2+2, . . . , m) of X-ray density are selected such that said positions numbering m/2 spaced apart from each other on said second X-ray projectional distribution D₄ for measurement of the values d_k (4) (k(4)=m/2+1, m/2+2, . . . , m) of X-ray density correspond to the positions on said second X-ray projectional distribution D₂ which have X-ray density information obtained as a result of the m/2 X-ray beams passing through the left upper corner of each of the respective picture elements numbered (3m/2+1) to 2 m passing through said second part of a plane based on the three criteria in step (b);

(f) calculating the X-ray absorption coefficients μ

_m+1 ˜

μ

_3m/2 based on the X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c), the valuess d_k (3) (k(3)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3 m/2 from the θ

₃ direction, and at the same time, calculating the X-ray absorption coefficients μ

_3m/2+1 18 μ

_2m based on the X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c), the values d_k (4) (k(4)=m/2+1, m/2+2, . . . , m) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (3m/2+1) to 2 m from the θ

₄ direction, where the method of calculating the X-ray absorption coefficients μ

_m+ 1˜

μ

_2m is the same as in step (c) and the X-ray absorption coefficients μ

₁ ˜

μ

_m calculated in step (c) are selectively used;

(g) memorizing the X-ray absorption coefficients μ

_m+1 ˜

μ

_2m calculated in step (f);

(h) calculating the X-ray absorption coefficient μ

_2m+ 1˜

μ

_3m, μ

_3m+ 1˜

μ

_4m, . . . , μ

(n-1)m+1˜

μ

_mn repeating substantially the same steps as steps (e), (f) and (g) and memorizing them;

(i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients μ

₁ ˜

μ

_m, μ

_m+1 ˜

μ

_2m , . . . , μ

.sub.(n-1) m+1 ˜

_mn memorized in steps (d), (g) and (h), where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂, . . . , μ

_mn calculated in step (c), (f) and (h) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed computed tomographic plane of the tested tissue of a body.

8. A reconstruction method of a computed tomographic image from a fiew X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₁, θ

₂) toward tested tissue of a body for producing first and second X-ray projectional distributions D₁, D₂ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (1) (k(1) is a natural number) of X-ray density on said first X-ray projectional distribution D₁ at at least ##EQU46## (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D₁ toward the other end thereof, and at the same time measuring the values d_k (2) (k(2) is a natural number) of X-ray density on said second X-ray projectional distribution D₂ at at least ##EQU47## positions spaced apart from each other from one end of said second X-ray projectional distribution D₂ toward the other end thereof, where each said ##EQU48## positions spaced apart from each other on the first and second X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) are selected according to the three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₁, D₂, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m;

m+1, m+2, . . . , 2 m;

. . . ;

(n-1)m+1, (n-1 ) m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₁, D₂ in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (θ

₁, θ

₂) are constituted by the first group of X-ray beams in a direction of θ

₁ and the second group of X-ray beams in a direction of θ

₂, wherein the first group of X-ray beams comprise mn/2 X-ray beams, each of which passes through the left lower corner of one of the picture elements in the first part of the plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of the plane, and the second group of X-ray beams comprises mn/2 X-ray beams, each of which passes through the left upper part of one of the picture elements in the second part of the plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of the plane, said ##EQU49## positions spaced apart from each other on said two X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density correspond to the positions on said two X-ray projectional distributions D₁, D₂ which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, θ

₁ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₁ =tan^-1 m/2, and θ

₂ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₂ =-tan^-1 m/2;

(c) calculating X-ray absorption coefficient μ

_t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based on the X-ray density values d_k (1) and d_k (2) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU50## L is a band matrix of dimension m(n+1)×

mn, T indicates a matrix transpose and α

is a length of an X-ray beam passing through each picture element from directions of θ

₁, and θ

₂ ;

(d) reconstructing the computed tomographic image of said tested tissue of a body where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂, . . . , μ

_mn calculated in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the completed collection of picture elements located in the m×

n array constitute the reonstructed computed tomographic plane of the tested tissue of a body.

9. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₃, θ

₄) toward tissue of a body for producing first and second X-ray projectional distributions D₃, D₄ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (3) (k(3) is a natural number) of X-ray density on said first X-ray projectional distribution D₃ at at least ##EQU51## (m and n are natural numbers and the product of m and n is an even number) positions spaced apart from each other from one end of said first X-ray projectional distribution D₁ toward the other end thereof, and at the same time measuring the values d_k (4) (k(4) is a natural number) of X-ray density on said second X-ray projectional distribution D₄ at at least ##EQU52## positions spaced apart from each other from one end of said second X-ray projectional distribution D₄ toward the other end thereof, where each said ##EQU53## positions spaced apart from each other on the first and second X-ray projectional distributions d₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₃, D₄, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . , n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m;

m+1, m+2, . . . , 2 m;

. . . ;

(n-b

     1)m-1, (n-1)m+2, . . . mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₃, D₄ in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (θ

₃, θ

₄) are constituted by the first group of X-ray beams in a direction of θ

₃ and the second group of X-ray beams in a direction of θ

₄, wherein the first group of X-ray beams comprises mn/2 X-ray beams, each of which passes through the left lower corner of one of the picture elements in the first part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of a plane, and the second group of X-ray beams comprises mn/2 X-ray beams, each of which passes through the left upper part of one of the picture elements in the second part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of a plane, said ##EQU54## positions spaced apart from each other on said two X-ray projectional distributions D₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions D₃, D₄ which have X-ray density information to be obtained by passing said X-ray beams through said pseudo-tomographic plane, θ

₃ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₃ =tan^-1 m, and θ

₄ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₄ =-tan^-1 m;

(c) calculating X-ray absorption coefficient μ

_t (t=1, 2, . . . , mn and t is a natural number) of each of mn pieces of picture elements in accordance with the following equations based on the X-ray density values d_k (3) and d_k (4) measured in step (b) and length of the X-ray beams passing through each of the picture elements, ##EQU55## L is a band matrix of dimension m(n+1)×

mn, T indicates the transpose of a matrix and α

is a length of an X-ray beam passing through each picture element from directions of θ

₃, θ

₄ ;

(d) reconstructing the computed tomographic image of said tested tissue of a body, where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂, . . . , μ

_mn calculated in step (c) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

10. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₁, θ

₂) toward tested tissue of a body for producing first and second X-ray projectional distributions D₁, D₂ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (1) (k(1) is a natural number, k(1)=1, 2, . . . , m) of X-ray density on said first X-ray projectional distribution D₁ at m (m is a natural number) positions spaced apart from each other from one end of said first projectional X-ray distribution D₁ toward the other end thereof, and at the same time measuring the values d_k (2) (k(2) is a natural number, k(2)=1, 2, . . . , m) of X-ray density on said second projectional X-ray distribution D₂ at m positions spaced apart from each other from one end of said second projectional X-ray distribution D₂ toward the other end thereof, where said m positions spaced apart from each other on the first and second X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density are selected according to the following three criteria;

(i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₁, D₂, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a columnc, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2, . . . ,n from the left and that said m pieces of picture elements in each row are numbered respectively 1,2, . . . ,m;

m+1, m+2, . . . , 2m;

. . . ;

(n-1)m+1, (n-1)m+2, . . .mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₁, D₂ in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (θ

₁, θ

₂) are divided into the first group of X-ray beams in a direction of θ

₁ and the second group of X-ray beams in a direction of θ

₂, where the first group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left lower corner of each picture element in said first part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of a plane, and the second group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left upper corner of each picture element in said second part of a plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of a plane, and said m positions spaced apart from each other on said two X-ray projectional distributions D₁, D₂ for measurement of the values d_k (1) and d_k (2) of X-ray density correspond to the positions on said two X-ray projectional distribution D₁, D₂ which have X-ray density information to be obtained by passing first m X-ray beams through said pseudo-tomographic plane based on the above-mentioned criteria, θ

₁ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₁ = tan^-1m/ 2, and θ

₂ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₂ = -tan^-1m/ 2;

(c) calculating the X-ray absorption coefficients μ

₁˜

μ

_2m of m picture elements in the first part of a plane and m picture elements in the second part of a plane comprising the picture elements in the first and second columns of the pseudo-tomographic plane, in accordance with the following equations based on the values d_k (1), d_k (2) of X-ray density measured in step (b) and the length of the X-ray beams passing through each picture element in the first and second parts of a plane, ##EQU56## L is a square matrix of dimension 2m×

2m, T indicates a matrix transpose and α

is a length of an X-ray beam passing through each picture element from directions of θ

₁, θ

₂ ;

(d) memorizing the X-ray absorption coefficients μ

₁ ˜

μ

_m which are the first m of the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c);

(e) measuring each of the values d_k (1) and d_k (2) (k(1), k(2)=m/2+1, m/2+2,...,3m/2) of X-ray density on the first and second X-ray projectional distributions D₁ and D₂ respectively at the positions numbering m spaced apart from each other from the ##EQU57## position from one end of said first and second X-ray projectional distributions D₁, D₂ toward the other end thereof, where said positions numbering m spaced apart from each other on each of said first X-ray projectional distribution D₁ and said second X-ray projectional distribution D₂ for measurement of the values d_k (1), d_k (2) (k(1), k(2)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said first X-ray projectional distribution D₁ for measurement of the values d_k (1) (k(1)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said first X-ray projectional distribution D₁ which have X-ray density information obtained as a result of the m X-ray beams passing through the left lower corner of each of the respective picture elements numbered (m+1) to 3m/2 and (2m+1) to 5m/2 passing through said first part of a plane based on the three assumptions in step (b), and said positions numbering m spaced apart from each other on said second X-ray projectional distribution D₂ for measurement of the values d_k (2) (k(2)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said second X-ray projectional distribution D₂ for measurement of the values d_k (2) (k(2)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said second X-ray projectional distribution D₂ which have X-ray density information obtained as a result of the m X-ray beams passing through the left upper corner of each of the respective picture elements numbered ##EQU58## to 2m and ##EQU59## ˜

3m passing through said second part of a plane based on the three criteria in step (b);

(f) calculating the X-ray absorption coefficients μ

_m+1 ˜

μ

_3m/2 and μ

_2m+1 ˜

μ

5m/2 based on the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c), the values d_k (1) (k(1)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3m/2 and (2m+1)˜

5m/2 from the θ

₁ direction, and at the same time, calculating the X-ray absorption coefficients μ

_3m/2 +1˜

μ

_2m and μ

_5m/2 ˜

μ

_3m based on the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c), the values d_k (2) (k(2)=m/2+1, m/2+2, . . . ,3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered ##EQU60## to 2m and ##EQU61## to 3m from the θ

₂ direction, where the method of calculating the X-ray absorption coefficients μ

_m+1 ˜

μ

_3m is the same as in ste (c) and the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c) are selectively used;

(g) memorizing the X-ray absorption coefficients μ

_m+1 ˜

μ

_2m, comprising the first m of the X-ray absorption coefficients μ

_m+1 ˜

μ

_3m calculated in step (f);

11. (h) calculating the X-ray absorption coefficient μ

_2m+1 ˜

μ

_4m, μ

_3m+1 ˜

μ

_5m, . . . ,μ

.sub.(n-1)m+1 ˜

μ

.sub.(n+1)m repeating substantially the same steps as steps (e), (f) and (g) and memorizing the first m of the X-ray absorption coefficients μ

_2m+1 ˜

μ

_3m, μ

_3m+1 ˜

μ

_4m, . . . , μ

.sub.(n-1)m+1 ˜

μ

_mn;

(i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients μ

₁ ˜

μ

_m, μ

_m+1 ˜

μ

_2m, . . . , μ

.sub.(n-1)m+1 ˜

μ

_mn memorized in steps (d), (g) and (h), where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂, . . . , μ

_mn memorized in steps (d), (g) and (h) are positioned at the locations of said picture elements numbered 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed computed tomographic plane of the tested tissue of body.

12. A reconstruction method of a computed tomographic image from a few X-ray projections comprising:

(a) projecting X-rays from two symmetrical desired directions (θ

₃, θ

₄) toward tested tissue of a body for producing first and second X-ray projectional distributions D₃, D₄ of X-rays which have passed through the tested tissue;

(b) measuring the values d_k (3) (k(3) is a natural number, k(3)=1, 2, . . . , m) of X-ray density on said first X-ray projectional distribution D₃ Heach other from one end of said second X-ray projectional distribution D₄ toward the other end thereof, where said m positions spaced apart from each other on the first and second X-ray projectional distributions D₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density are selected according to the following three criteria, (i) that the tomographic plane of the tested tissue of a body to be reconstructed is expressed by a pseudo-tomographic plane which is constituted collectively by mn pieces of square picture elements, with m pieces of picture elements in a row and n in a column (both m and n are natural numbers), which are formed by dividing said tomographic plane of the tested tissue of a body into small sections and each of which has a single piece of X-ray density information, and that said pseudo-tomographic plane is placed between an X-ray source and said two X-ray projectional distributions D₃, D₄, (ii) that said pseudo-tomographic plane is divided into a first part of a plane and a second part of a plane which are constituted collectively by said picture elements with m/2 pieces in a row and n pieces in a column, respectively, (iii) that n rows, each of which is constituted by m pieces of picture elements are numbered in order 1, 2,..., n from the left and that said m pieces of picture elements in each row are numbered respectively 1, 2, . . . , m;

m+1, m+2, . . . , 2m;

. . .;

(n-1)m+1, (n-1)m+2, . . .mn from the side of said X-ray source toward the side of said two X-ray projectional distributions D₃, D₄ in order and that at least m(n+1) X-ray beams passing through said pseudo-tomographic plane from two directions (θ

₃, θ

₄) are divided into the first group of X-ray beams in a direction of θ

₃ and the second group of X-ray beams in a direction of θ

₄, wherein the first group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left lower corner of each picture element in said first part of the plane and at least m/2 X-ray beams passing through the picture elements in the n-th column in the first part of the plane, and the second group of X-ray beams is constituted by mn/2 X-ray beams passing through respectively the left upper corner of each picture element in said second part of the plane at at least m/2 X-ray beams passing through the picture elements in the n-th column in the second part of the plane, said m positions spaced apart from each other on said two X-ray projectional distributions D₃, D₄ for measurement of the values d_k (3) and d_k (4) of X-ray density correspond to the positions on said two X-ray projectional distributions D₃, D₄ which have X-ray density information to be obtained by passing the first m X-ray beams through said pseudo-tomographic plane based on the above-mentioned criteria, θ

₃ indicates the angle at which each X-ray beam of the first group crosses with the base of each picture element in the first part of a plane, and θ

₃ = tan^-1 m, and θ

₄ indicates the angle at which each X-ray beam of the second group crosses with the base of each picture element in the second part of a plane, and θ

₄ = tan^-1 m;

(c) calculating the X-ray absorption coefficients μ

1˜

μ

_2m of m picture elements in the first part of a plane and m picture elements in the second part of a plane comprising the picture elements in the first and second columns of the pseudo-tomographic plane, in accordance with the following equations based on the values d_k (3), d_k (4) of X-ray density measured in step (b) and the length of the X-ray beams passing through each picture element in the first and second parts of a plane, ##EQU62## L is a square matrix of dimension 2m×

2m, T indicates a matrix transpose and α

is a length of the X-ray beam passing through each picture element from directions of θ

₃, θ

₄ ;

(d) memorizing the X-ray absorption coefficients μ

₁ ˜

μ

_m comprising the first m of the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c);

(e) measuring each of the values d_k (3) and d_k (4) (k(3), k(4)=m/2+1, m/2+2,..., 3m/2) of X-ray density on the first and second X-ray projectional distributions D₃ and D₄ respectively at the positions numbering m spaced apart from each other from the ##EQU63## position from one end of said first and second X-ray projectional distributions D₃, D₄ toward the other end thereof, where said positions numbering m spaced apart from each other on each of said first X-ray projectional distribution D₃ and said second X-ray projectional distribution D₄ for measurement of the values d_k (3), d_k (4) (k(3), d(4)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said first X-ray projectional distribution D₃ for measurement of the values d_k (3) (k(3)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said first X-ray projectional distribution D₃ which have X-ray density information obtained as a result of the m X-ray beams passing through the left lower corner of each of the respective picture elements numbered (m+1) to 3m/2 and (2m+1) to 5m/2 passing through said first part of a plane based on the three assumptions in step (b), and said positions numbering m spaced apart from each other on said second X-ray projectional distribution D₄ for measurement of the values d_k (4) (k(4)=m/2+1, m/2+2, . . . ,3m/2) of X-ray density are selected such that said positions numbering m spaced apart from each other on said second X-ray projectional distribution D₄ for measurement of the values d_k (4) (k(4)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density correspond to the positions on said second X-ray projectional distribution D₄ which have X-ray density information obtained as a result of the m X-ray beams passing through the left upper corner of each of the respective picture elements numbered ##EQU64## to 2m and ##EQU65## ˜

3m passing through said second part of a plane based on the three assumptions in step (b);

(f) calculating the X-ray absorption coefficients μ

_m+ 1˜

μ

.sub. 3m/2 and μ

.sub. 2m+1˜

μ

.sub. 5m/2 based on the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c), the values d_k (3) (k(3)=m/2+1, m/2+2, . . . , 3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered (m+1) to 3m/2 and (2m+1)˜

5m/2 from the θ

₃ direction, and at the same time, calculating the X-ray absorption coefficients μ

_3m/2 +1˜

μ

_2m and μ

_5m/2 ˜

μ

_3m based on the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c), the values d_k (4) (k(4)=m/2+1, m/2+2,...., 3m/2) of X-ray density measured in step (e), and the length of X-ray beams passing through the picture elements numbered ##EQU66## to 2m and ##EQU67## to 3m from the θ

₄ direction, where the method of calculating the X-ray absorption coefficients μ

_m+1 ˜

μ

_3m is the same as in step (c) and the X-ray absorption coefficients μ

₁ ˜

μ

_2m calculated in step (c) are selectively used;

(g) memorizing the X-ray absorption coefficients μ

_m+1˜

μ

_2m comprising the first m of the X-ray absorption coefficients μ

_m+1˜

μ

_3m calculated in step (f);

(h) calculating the X-ray absorption coefficient μ

_2m+1 ˜

μ

_4m, μ

_3m+1 ˜

μ

_5m,....., μ

.sub.(n-1)m+1 ˜

μ

.sub.(n+1)m repeating substantially the same steps (e), (f) and (g) and memorizing the first m of the X-ray absorption coefficients μ

_2m+1 ˜

μ

_3m, μ

_3m+1 ˜

μ

_4m, . . . , μ

.sub.(n-1)m+1 ˜

μ

_mn ;

(i) reconstructing the computed tomographic image of said tested tissue of a body based on the X-ray absorption coefficients μ

₁ ˜

μ

_m, μ

_m+1 ˜

μ

_2m, . . . , μ

.sub.(n-1)m+1 ˜

μ

_mn memorized in steps (f), (g) and (h), where the picture elements having respective X-ray absorption coefficients μ

₁, μ

₂. . . , μ

_mn memorized in steps (f), (g) and (h) are positioned at the locations of said picture elements number 1, 2, . . . , mn of the pseudo-tomographic plane and wherein the complete collection of picture elements located in the m×

n array constitute the reconstructed compouted tomographic plane of the tested tissue of a body.