Dynamic image denoising using a sparse representation

1. An apparatus, comprising:

an interface configured to obtain a plurality of images, each of the plurality of images being reconstructed by performing computed tomography (CT) on data acquired via a CT scan at a respective time interval of a plurality of time intervals; and

processing circuitry configured to

transform the plurality of images into an aggregate image and at least one transform-domain image, each of the at least one transform-domain image comprising at least one difference image between an image of the plurality of images and the aggregate image,

denoise the at least one transform-domain image by

training on pixel arrays of the at least one transform-domain image to generate basis functions of a dictionary, each pixel array including respective pixel values of the at least one transform-domain image, the pixel values of a respective pixel array corresponding to a same pixel location on each image of the at least one transform-domain image, the basis functions of the dictionary being generated to approximate the pixel arrays subject to a sparsity condition, and

approximating each transform-domain image by using one of a matching pursuit method and an orthogonal matching pursuit method to approximate the pixel arrays of the at least one transform-domain image using the dictionary, and

transform the aggregate image and the denoised at least one transform-domain image to generate a plurality of denoised images, each of the plurality of denoised images being a respective image of the plurality of images that has been denoised.

2. The apparatus according to claim 1 , wherein the processing circuitry is further configured to transform the plurality of images by

averaging the plurality of images to generate the aggregate image, and

determining each of the at least one transform-domain image using a difference between a respective image of the plurality of images and the aggregate image.

3. The apparatus according to claim 1 , wherein the processing circuitry is further configured to transform the plurality of images by

averaging the plurality of images to generate the aggregate image, and

determining each of the at least one transform-domain image using a difference between a respective pair of the plurality of images.

4. The apparatus according to claim 1 , wherein the processing circuitry is further configured to transform the plurality of images by

calculating a covariance matrix of the plurality of images;

performing an eigenvalue decomposition of the covariance matrix;

selecting, as basis functions for the transforming of the plurality of images, eigenvectors corresponding to a plurality of largest eigenvalues of the eigenvalue decomposition of the covariance matrix; and

transforming the plurality of images into the aggregate image and the at least one transform-domain image by projecting the plurality of images onto the basis functions.

5. The apparatus according to claim 1 , wherein the processing circuitry is further configured to transform the plurality of images by

performing a principal component analysis on the plurality of images to generate principal components;

selecting a plurality of largest principal components as basis functions for the transforming of the plurality of images; and

transforming the plurality of images into the aggregate image and the at least one transform-domain image by projecting the plurality of images onto the basis functions.

6. The apparatus according to claim 5 , wherein the principal component analysis is performed subject to a sparsity constraint constraining at least one of an L1 norm of the principal components and an L0 norm of the principal components.

7. The apparatus according to claim 5 , wherein the processing circuitry is further configured to transform the aggregate image and the denoised at least one transform-domain image to generate the plurality of denoised images by

combining the aggregate image and the denoised at least one transform-domain image using a linear superposition weighted by respective coefficients of the basis functions to generate a corresponding denoised image of the plurality of denoised images.

8. The apparatus according to claim 1 , wherein the processing circuitry is further configured to transform the aggregate image and the denoised at least one transform-domain image by

performing an inverse of the transformation on the aggregate image and the denoised at least one transform-domain image, the inverse transformation yielding an identity operator when the inverse transformation is applied to the transformation that transforms the plurality of images into the aggregate image and the at least one transform-domain image.

9. The apparatus according to claim 1 , wherein the processing circuitry is further configured to denoise the at least one transform-domain image by

generating at least one sparse approximation of the at least one transform-domain image, the at least one sparse approximation being the denoised at least one transform-domain image.

10. The apparatus according to claim 1 , wherein the processing circuitry is further configured to denoise the at least one transform-domain image by

filtering the at least one transform-domain image using at least one of a low-pass filtering method, an anisotropic diffusion filtering method, a total-variation minimization filtering method, a median filtering method, a nonlinear filtering method, and a non-local means-filtering method.

11. The apparatus according to claim 1 , wherein the processing circuitry is further configured to register the plurality of images using at least one of rotations of the plurality of images and translations of the plurality of images.

12. The apparatus according to claim 1 , further comprising:

an X-ray source radiating X-rays; and

a plurality of detector elements each configured to detect a plurality of energy components of the X-rays that are radiated from the X-ray source and generate projection data,

wherein the processing circuitry is further configured to reconstruct the plurality of images from using the projection data by performing computed tomography (CT).

13. A method, comprising:

obtaining a plurality of images, each of the plurality of images being reconstructed by performing computed tomography (CT) on data acquired via a CT scan at a respective time interval of a plurality of time intervals;

transforming the plurality of images into an aggregate image and at least one transform-domain image, each of the at least one transform-domain image comprising at least one difference image between an image of the plurality of images and the aggregate image,

denoising the at least one transform-domain image by

training on pixel arrays of the at least one transform-domain image to generate basis functions of a dictionary, each pixel array including respective pixel values of the at least one transform-domain image, the pixel values of a respective pixel array corresponding to a same pixel location on each image of the at least one transform-domain image, the basis functions of the dictionary being generated to approximate the pixel arrays subject to a sparsity condition, and

approximating each transform-domain image by using one of a matching pursuit method and an orthogonal matching pursuit method to approximate the pixel arrays of the at least one transform-domain image using the dictionary; and

transforming the aggregate image and the denoised at least one transform-domain image to generate a plurality of denoised images, each of the plurality of denoised images being a respective image of the plurality of images that has been denoised.

14. The method according to claim 13 , further comprising

registering the plurality of images using at least one of rotations of the plurality of images and translations of the plurality of images.

15. The method according to claim 13 , wherein the transforming of the plurality of images includes

performing a principal component analysis on the plurality of images to generate principal components,

selecting a plurality of largest principal components as basis functions for the transforming of the plurality of images, and

transforming the plurality of images into the aggregate image and the at least one transform-domain image by projecting the plurality of images onto the basis functions.

16. A non-transitory computer readable storage medium including executable instruction, wherein the instructions, when executed by circuitry, cause the circuitry to perform the method according to claim 13 .

17. An apparatus, comprising:

an interface configured to obtain a plurality of images, each of the plurality of images being reconstructed by performing computed tomography (CT) on data acquired via a CT scan at a respective time interval of a plurality of time intervals; and

processing circuitry configured to

transform the plurality of images into an aggregate image and at least one transform-domain image, each of the at least one transform-domain image comprising at least one difference image between an image of the plurality of images and the aggregate image,

denoise the at least one transform-domain image by

partitioning a set of pixel arrays of the at least one transform-domain image into a training set and another set, each pixel array of the set of pixel arrays including respective pixel values of the at least one transform-domain image, the pixel values of a respective pixel array corresponding to a same pixel location on each image of the at least one transform-domain image,

training basis functions of a dictionary and generating sparse approximations to the training set by using a k-means clustering singular value decomposition (K-SVD) method operating on the training set,

fixing the basis functions of the dictionary after the training of the basis functions, and

generating sparse approximations of the respective pixel arrays of the another set using the fixed basis functions of the dictionary, and

transform the aggregate image and the denoised at least one transform-domain image to generate a plurality of denoised images, each of the plurality of denoised images being a respective image of the plurality of images that has been denoised.

18. The apparatus according to claim 17 , wherein the processing circuitry is further configured to denoise the at least one transform-domain image by

generating the sparse approximations of the respective pixel arrays of the another set using the fixed basis functions of the dictionary and using one of a matching pursuit method and an orthogonal matching pursuit method.

19. The apparatus according to claim 17 , wherein the processing circuitry is further configured to denoise the at least one transform-domain image by

downsampling the pixel arrays of the training set before the training of the basis functions of the dictionary, and

upsampling the trained basis functions of the dictionary before the generating of the sparse approximations of the respective pixel arrays of the another set.