Method for tomographic reconstruction with non-linear diagonal estimators

• US 20040028264A1
• Filed: 06/24/2003
• Published: 02/12/2004
• Est. Priority Date: 04/28/2000
• Status: Active Grant

• Current Assignee: Trustees Of Columbia University In The City Of New York (Columbia University)
• Original Assignee: Trustees Of Columbia University In The City Of New York (Columbia University)
• Inventors: Kalifa, Jerome
• Granted Patent: US 7,139,420 B2
• Time in Patent Office: Days
• US Class Current: 382/131
• CPC Class Codes: G06T 11/008 Specific post-processing after tomographic reconstruction, e.g. voxelisation, metal artifact correction
• CPC Class Codes: Y10S 378/901 Computer tomography program or processor

Abstract

Techniques for tomographic reconstruction using non-linear diagonal estimators are disclosed. In a preferred embodiment, tomographic data from a tomographic device is decomposed in a wavelet vector family. Regularization of the tomographic data is accomplished by performing a thresholding operation on coefficients of the decomposed data. The regularized data is reconstructed into image data that may he displayed. In another preferred embodiment, a wavelet packet vector family is used to decompose the tomographic data. The wavelet packet is selected from a dictionary of wavelet packets using the best basis algorithm.

Claims

1. A method for reconstructing image data corresponding to a desired two-dimensional image from initial tomographic data associated with a plurality of initial tomographic projections of said desired image, comprising:

backprojecting said initial tomographic data to form backprojected image data;

selecting a vector family to decompose said backprojected image data from the group consisting of 1-D orthogonal wavelet packet basis, 2-D orthogonal wavelet packet basis, 1-D biorthogonal wavelet packet basis, 2-D biorthogonal wavelet packet basis, 1 -D wavelet packet frame, 2-D wavelet packet frame, 1-D complex wavelet frame, 2-D complex wavelet frame, 1-D complex wavelet packet frame, and 2-D complex wavelet packet frame;

decomposing said backprojected image data to generate decomposed coefficients associated with said selected vector family;

diagonally operating on said decomposed coefficients to generate modified decomposed coefficients; and

recomposing said image data corresponding to said desired two- dimensional image from said modified decomposed coefficients.

5. The method of claim 1, 2, 3 or 4 wherein said diagonally operating comprises thresholding the data operated on.

6. The method of claim 1, 2, 3 or 4 wherein said selecting a vector family step further comprises:

deriving a model of noise present in said data to be decomposed;

repeatedly selecting a wavelet packet decomposition from a predetermined plurality of wavelet packet decompositions;

calculating an estimation of final estimation error based on at least said selected wavelet packet decomposition and said noise model; and

choosing a wavelet packet decomposition that minimizes the estimation of final estimation error calculated in said repeatedly selecting step.

7. The method of claim 6 wherein said calculating an estimation of final estimation error is also based on prior information about said desired two-dimensional image.

2. A method for reconstructing image data corresponding to a desired two-dimensional image from initial tomographic data associated with a plurality of initial tomographic projections of said desired image, comprising:

selecting a vector family to decompose said initial tomographic data from the group consisting of 1-D orthogonal wavelet packet basis, 2-D orthogonal wavelet packet basis, 1-D biorthogonal wavelet packet basis, 2-D biorthogonal wavelet packet basis, 1-D wavelet packet frame, 2-D wavelet packet frame, 1-D complex wavelet frame, 2-D complex wavelet frame, 1-D complex wavelet packet frame, and 2-D complex wavelet packet frame;

decomposing said initial tomographic data into decomposed coefficients associated with said selected vector family;

diagonally operating on said decomposed coefficients to generate modified decomposed coefficients; and

recomposing said modified decomposed coefficients to generate regularized data associated with a plurality of regularized tomographic projections; and

backprojecting said regularized data to form said image data corresponding to said desired two-dimensional image.

3. A method for reconstructing image data corresponding to a desired two-dimensional image from initial tomographic data associated with a plurality of 10 initial tomographic projections of said desired image, comprising:

selecting a vector family to decompose said initial tomographic data from the group consisting of 1-D orthogonal wavelet packet basis, 2-D orthogonal wavelet packet basis, 1-D biorthogonal wavelet packet basis, 2-D biorthogonal wavelet packet basis, 1-D wavelet packet frame, 2-D wavelet packet frame, 1 -D complex wavelet packet frame, and 2-D complex wavelet packet frame;

decomposing said initial tomographic data into decomposed coefficients associated with said selected vector family;

diagonally operating on said decomposed coefficients to generate modified decomposed coefficients;

selectively amplifying said modified decomposed coefficients to generate selectively amplified coefficients;

recomposing said selectively amplified coefficients to generate regularized data associated with a plurality of regularized tomographic projections; and

radially interpolating said regularized data to form said image data corresponding to said desired two-dimensional image.

4. A method for reconstructing image data corresponding to a desired two-dimensional image from initial tomographic data associated with a plurality of initial tomographic projections of said desired image, comprising:

selecting a vector family to decompose said initial tomographic data from the group consisting of 1-D orthogonal wavelet packet basis, 2-D orthogonal wavelet packet basis, 1-D biorthogonal wavelet packet basis, 2-D biorthogonal wavelet packet basis, 1-D wavelet packet frame, 2-D wavelet packet frame, 1-D complex wavelet packet frame, and 2-D complex wavelet packet frame;

decomposing said initial tomographic data into decomposed coefficients associated with said selected vector family;

selectively amplifying said decomposed coefficients to generate selectively amplified coefficients;

diagonally operating on said selectively amplified coefficients to generate modified decomposed coefficients;

recomposing said modified decomposed coefficients to generate regularized data associated with a plurality of regularized tomographic projections; and

radially interpolating said regularized data to form said image data corresponding to said desired two-dimensional image.

8. A method for reconstructing image data corresponding to a plurality of two-dimensional slices of a desired three-dimensional image from initial tomographic data associated with a plurality of tomographic projections of said plurality of two-dimensional slices, comprising:

selecting a vector family to decompose said initial tomographic data selected from the group consisting of wavelet vector family and wavelet packet vector family;

decomposing said initial tomographic data to generate decomposed coefficients associated with said selected vector family;

diagonally operating on said decomposed coefficients to generate modified decomposed coefficients; and

recomposing said modified decomposed coefficients to generate regularized data associated with a plurality of regularized tomographic projections of said plurality of two-dimensional slices of said desired image;

and

backprojecting said regularized data to form said image data corresponding to said plurality of two-dimensional slices of said desired three-dimensional image.

10. The method of claim 8 further comprising performing slice-by-slice two-dimensional regularization on said initial tomographic data to form regularized data corresponding to a series of regularized two-dimensional slices before said decomposing step wherein said decomposing step is performed on the entirety of said regularized data.

13. The method of claim 8 or 9 wherein said diagonally operating comprises thresholding the data operated on.

14. The method of claim 8 or 9 wherein said selecting a vector family step further comprises:

deriving a model of noise present in said data to be decomposed;

repeatedly selecting a wavelet packet decomposition from a predetermined plurality of wavelet packet decompositions;

calculating an estimation of final estimation error based on at least said selected wavelet packet decomposition and said noise model; and

choosing a wavelet packet decomposition that minimizes the estimation of final estimation error calculated in said repeatedly selecting step.

15. The method of claim 14, wherein said calculating an estimation of final estimation error is also based on prior information about said plurality of two dimensional slices of said desired three-dimensional image.

9. A method for reconstructing image data corresponding to a plurality of two-dimensional slices of a desired three-dimensional image from initial tomographic data associated with a plurality of tomographic projections of said plurality of two-dimensional slices, comprising:

backprojecting said initial tomographic data to form backprojected image data associated with said plurality of two-dimensional slices;

selecting a wavelet vector family to decompose said backprojected image data;

decomposing said backprojected image data to generate decomposed coefficients associated with said selected vector family;

diagonally operating on said decomposed coefficients to generate modified decomposed coefficients; and

recomposing said modified decomposed coefficients to form said image data corresponding to said plurality of two-dimensional slices of said desired three-dimensional image.

11. The method of claim 9 further comprising performing slice-by-slice two-dimensional regularization on said initial tomographic data to form regularized data corresponding to a series of regularized two-dimensional slices before said backprojecting step wherein said backprojecting step is performed slice-by-slice on the entirety of said regularized data

12. The method of claim 9 further comprising performing slice-by-slice two-dimensional regularization on said backprojected image data to form regularized data corresponding to a series of regularized two-dimensional slices before said decomposing step wherein said decomposing step is performed on the entirety of said regularized data