Method for reconstructing complex wave attributes from limited view measurements
First Claim
1. A method for reconstructing complex wave attributes described by an object function O from limited view measurements u of a measurement surface r with associated wavevector K, said method comprising the steps of:
- processing said limited view measurements u to obtain Fourier transformed measurements ũ
;
determining a Fourier transformed object function Õ
of said object function O;
determining an analytic relationship between said Fourier transformed object function Õ and
said Fourier transformed measurements ũ
;
analytically extending said Fourier transform Õ
by specifying that Õ
(K)=Õ
(−
K), thereby obtaining an analytically extended Fourier transform of Õ
; and
, reconstructing said complex wave attributes by inverting said analytically extended Fourier transform of Õ
.
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Abstract
A method is disclosed for reconstructing complex wave attributes from limited view measurements of a scattering object. The method involves the analytic continuation of the Fourier transform of the object function into the area in which there is an absence of K-space coverage by requiring objects to be an even function. (It is assumed that physical objects are even functions, and it is this assumption that allows analytic continuation.) When the object function is not centered at the origin, the measurements are shifted to the origin prior to determining the analytic continuation and returned to their original location following analytic continuation.
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Citations
20 Claims
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1. A method for reconstructing complex wave attributes described by an object function O from limited view measurements u of a measurement surface r with associated wavevector K, said method comprising the steps of:
-
processing said limited view measurements u to obtain Fourier transformed measurements ũ
;
determining a Fourier transformed object function Õ
of said object function O;
determining an analytic relationship between said Fourier transformed object function Õ and
said Fourier transformed measurements ũ
;
analytically extending said Fourier transform Õ
by specifying that Õ
(K)=Õ
(−
K), thereby obtaining an analytically extended Fourier transform of Õ
; and
,reconstructing said complex wave attributes by inverting said analytically extended Fourier transform of Õ
. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A method for reconstructing complex wave attributes described by an object function O from limited view measurements u of an object with associated wavevector K, said method comprising the steps of:
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processing said measurements u to obtain Fourier transformed measurements ũ
;
determining a midpoint of said object;
creating shifted Fourier transformed measurements ũ
R by shifting said Fourier transformed measurements ũ
so that said midpoint is located at the origin;
determining an analytic relationship between said object function O and said shifted Fourier transformed measurements ũ
R;
determining the Fourier transform Õ
of said object function O from said Fourier transformed measurements ũ
R using said analytic relationship;
analytically extending said Fourier transform Õ
by specifying that Õ
(K)=Õ
(−
K), thereby obtaining an analytically extended Fourier transform of Õ
;
determining shifted complex wave attributes by inverting said analytically extended Fourier transform of Õ
; and
,reconstructing said complex wave attributes by shifting said shifted complex wave attributes back to said midpoint. - View Dependent Claims (17, 18, 19, 20)
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Specification