US7124044B2
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Method for reconstructing complex wave attributes from limited view measurements
Assignee: Individual
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Filing: 2004-03-01
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Granted: 2006-10-17
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Expires: 2024-03-01
Abstract
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.
Inventors
- 👤 Alan Witten
Bibliographic Details
Application Number
—
Jurisdiction
US
Data Source
google_patents
Last Synchronized
2026-11-07 07:20
CPC Classifications
G; G01; G01V; G01V1/00; G01V1/28; G01N; G01N29/00; G01N29/04; G01N29/06; G01N29/0654; G01N29/0672; G01N29/07; G01N29/11; G01N29/44; G01N29/46; G06; G06F; G06F17/00; G06F17/10; G06F17/14; G06F17/141; G06F17/17
Claims Analysis
Total Claims: 22
Claim 1
Independent Claim
117 words
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 Õ; 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; reconstructing said complex wave attributes by inverting said analytically extended Fourier transform of Õ; and, presenting said reconstructed complex wave attributes as an image.
Claim 2
Independent Claim
117 words
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 Õ; 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; reconstructing said complex wave attributes by inverting said analytically extended Fourier transform of Õ; and, presenting said reconstructed complex wave attributes as an image.
Claim 3
Dependent Claim
15 words
The method of claim 1 wherein said complex wave attributes are wave speed and attenuation.
Claim 4
Dependent Claim
15 words
The method of claim 1 wherein said complex wave attributes are dielectric and electric conductivity.
Claim 5
Dependent Claim
17 words
The method of claim 1 wherein said complex wave attributes are acoustic wave speed density and compressibility.
Claim 6
Dependent Claim
11 words
The method of claim 1 wherein said object function is one-dimensional.
Claim 7
Dependent Claim
11 words
The method of claim 1 wherein said object function is two-dimensional.
Claim 8
Dependent Claim
11 words
The method of claim 1 wherein said object function is three-dimensional.
Claim 9
Dependent Claim
13 words
The method of claim 1 wherein said measurement surface r comprises a ring.
Claim 10
Dependent Claim
13 words
The method of claim 1 wherein said measurement surface r comprises a sphere.
Claim 11
Dependent Claim
13 words
The method of claim 1 wherein said measurement surface r comprises a cylinder.
Claim 12
Dependent Claim
16 words
The method of claim 1 wherein said measurement surface r comprises a plurality of parallel lines.
Claim 13
Dependent Claim
16 words
The method of claim 1 wherein said measurement surface r comprises a plurality of perpendicular lines.
Claim 14
Dependent Claim
17 words
The method of claim 1 wherein said measurement surface r comprises a line and a curved surface.
Claim 15
Dependent Claim
14 words
The method of claim 1 wherein said limited view measurements are time domain measurements.
Claim 16
Dependent Claim
14 words
The method of claim 1 wherein said limited view measurements are frequency domain measurements.
Claim 17
Independent Claim
168 words
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: 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; reconstructing said complex wave attributes by shifting said shifted complex wave attributes back to said midpoint; and, presenting said reconstructed complex wave attributes as an image.
Claim 18
Independent Claim
168 words
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: 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; reconstructing said complex wave attributes by shifting said shifted complex wave attributes back to said midpoint; and, presenting said reconstructed complex wave attributes as an image.
Claim 19
Dependent Claim
43 words
The method of claim 16 wherein said step of determining a midpoint comprises the steps of: determining the complex contrast of said object; determining the magnitude of said complex contrast; and, choosing said midpoint to be the center location of said complex contrast.
Claim 20
Dependent Claim
42 words
The method of claim 16 wherein said step of determining a midpoint comprises the steps of: determining the complex contrast of said object; determining the magnitude of said complex contrast; and, choosing said midpoint to be the mid-depth of said complex contrast.
Claim 21
Dependent Claim
34 words
The method of claim 16 wherein said midpoint is a spatial component and said step of determining a midpoint comprises choosing said midpoint to be the depth achieved at the maximum measured travel time.
Claim 22
Dependent Claim
30 words
The method of claim 16 wherein said midpoint is a temporal component and said step of determining a midpoint comprises choosing said midpoint to be the maximum measured travel time.
References Cited (Backward Citations)
No citation records indexed.
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