Method for reconstruction of magnetic resonance images

1. A method for constructing an image, the method comprising:

acquiring image data in a sensing domain;

transforming the acquired image data into a sparse domain;

approximating sparse coefficients based on the transformed acquired image data;

performing a Bayes Least Squares estimation on the sparse coefficients based on a Gaussian Scale Mixtures Model to generate weights;

approximating the updated sparse coefficients by using the updated weights and acquired image data;

constructing an image based on the updated sparse coefficients; and

displaying the constructed image.

2. The method of claim 1 , wherein the approximating of the sparse coefficients and updated sparse coefficients is performed using compressed sensing.

3. The method of claim 2 , wherein the compressed sensing comprises performing one of Reweighted L 1 minimization (RL 1 ), Iteratively Reweighted Least Squares (IRLS), and Iterative Hard Thresholding (IHT) on the transformed acquired image data.

4. The method of claim 1 , wherein the performing of the Bayes Least Squares estimation comprises modeling a neighborhood of wavelet coefficients of the sparse coefficients as a sum of a zero-mean Gaussian random vector and a noise vector with a variance.

5. The method of claim 4 , wherein the transforming comprises performing a wavelet transform on the acquired image data to generate a plurality of sub-bands.

6. The method of claim 5 , wherein the variance is based on a standard deviation of wavelet coefficients of a selected one of the sub-bands having a diagonal orientation and the highest frequency.

7. The method of claim 6 , wherein the sub-bands include LL, HH, LH, and HL sub-bands, and wherein the selected one sub-band is the HH sub-band.

8. The method of claim 4 , wherein the zero-mean Gaussian vector is multiplied by a scalar variable.

9. The method of claim 8 , wherein the noise vector is additive white Gaussian noise, and the Gaussian random vector, the scalar variable, and the noise vector are independent of each other.

10. The method of claim 4 , further comprising:

decreasing the variance to generate an updated variance;

performing a Bayes Least Squares estimation on the updated sparse coefficients based on the updated variance to generate an updated weight;

approximating the second updated sparse coefficients by using the updated weights and acquired image data;

constructing an updated image based on the second updated sparse coefficients; and

displaying the updated constructed image.

11. The method of claim 1 , wherein the acquiring comprises performing one of a magnetic resonance imaging or a computed tomography scan over an area of the body.

12. The method of claim 1 , wherein the constructing comprises performing an inverse wavelet transform on the updated sparse coefficients.

13. A non-transitory computer readable storage medium embodying instructions executable by a processor to perform method steps for constructing an image, the method steps comprising instructions for:

acquiring image data in a sensing domain;

transforming the acquired image data into a sparse domain;

approximating sparse coefficients based on the transformed acquired image data;

performing a Bayes Least Squares estimation on the sparse coefficients based on a Gaussian Scale Mixtures Model to generate weights;

approximating the updated sparse coefficients by using the updated weights and acquired image data;

constructing an image based on the updated sparse coefficients; and

displaying the constructed image.

14. A method for constructing an image, the method comprising:

acquiring image data in a sensing domain;

transforming the acquired image data into a sparse domain;

setting a variance based on a standard deviation of wavelet coefficients of a sub-band of the transformed acquired image data having a diagonal orientation and the highest frequency;

performing a Bayes Least Squares estimation on sparse coefficients of the wavelet coefficients based on a Gaussian Scale Mixtures Model with the variance to generate weights;

approximating the updated sparse coefficients by using the updated weights and acquired image data;

constructing an image based on the updated sparse coefficients; and

displaying the constructed image.

15. The method of claim 14 , wherein the approximating of the sparse coefficients and updated sparse coefficients is performed using compressed sensing.

16. The method of claim 15 , wherein the compressed sensing comprises performing one of Reweighted L 1 minimization (RL 1 ), Iteratively Reweighted Least Squares (IRLS), and Iterative Hard Thresholding (IHT) on the transformed acquired image data.

17. The method of claim 14 , wherein the performing of the Bayes Least Squares estimation comprises modeling a neighborhood of wavelet coefficients of the sparse coefficients as a sum of a zero-mean Gaussian random vector and a noise vector with the variance.

18. The method of claim 17 , further comprising:

decreasing the variance to generate an updated variance;

performing a Bayes Least Squares estimation on the updated sparse coefficients based on the updated variance to generate an updated weight;

approximating second updated sparse coefficients by using the updated weights and acquired image data;

constructing an updated image based on the second updated sparse coefficients; and

displaying the updated constructed image.

19. The method of claim 18 , wherein the zero-mean Gaussian vector is multiplied by a scalar variable.

20. The method of claim 19 , wherein the noise vector is additive white Gaussian noise, and the Gaussian random vector, the scalar variable, and the noise vector are independent of each other.