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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
First Claim
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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 dk (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 dk '"'"' (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 dk and dk, 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 dk and dk'"'"' 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 dk and dk'"'"' 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

    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.

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