Single image super resolution and denoising using multiple wavelet domain sparsity

1. A computer-implemented method of enhancing one or more images, the method comprising:

receiving, by a computer, one or more observed images;

identifying, by the computer, a plurality of wavelet bases;

estimating, by the computer, a noise variance value;

estimating, by the computer, a blurring kernel based on one or more system calibration parameters;

determining a low-pass blurring filter operator based on the blurring kernel;

determining a downsampling operator;

selecting, by the computer, a tuning parameter based on the noise variance value;

creating, by the computer, a cost function which generates one or more denoised super-resolution images based on the observed images and the plurality of wavelet bases, the cost function comprising:

a sparsity inducing norm applied to the plurality of wavelet bases,

the tuning parameter applied to the sparsity inducing norm, and

a constraint requiring the one or more denoised super-resolution images to be equal to a result of applying the low-pass blurring filter operator and the downsampling operator to the one or more denoised super-resolution images; and

generating, by the computer, the one or more denoised super-resolution images by minimizing the cost function.

2. The method of claim 1 , wherein the plurality of wavelet bases comprise a plurality of Daubechies wavelet bases.

3. The method of claim 2 , wherein the plurality of wavelet bases further comprise a plurality of cycle-spinned versions of the plurality of Daubechies wavelet bases.

4. The method of claim 2 , wherein the plurality of wavelet bases further comprise a plurality of complex dual wavelet transform versions of the plurality of Daubechies wavelet bases.

5. The method of claim 1 , wherein the cost function is minimized using an alternating direction method of multipliers (ADMM) algorithm.

6. A computer-implemented method of enhancing one or more images, the method comprising:

receiving one or more observed images;

identifying a plurality of wavelet bases;

creating a cost function which generates one or more denoised images based on the observed images and the plurality of wavelet bases, wherein the cost function applies a sparsity-inducing norm to the plurality of wavelet bases; and

generating the one or more denoised images by minimizing the cost function, wherein minimization of the cost function is constrained by applying a low-pass blurring filter operator and a downsampling operator to the one or more denoised images.

7. The method of claim 6 , further comprising:

estimating a noise variance value;

selecting a tuning parameter based on the noise variance value,

wherein the cost function applies the tuning parameter to the sparsity-inducing norm applied to the plurality of wavelet bases.

8. The method of claim 6 , further comprising:

estimating a blurring kernel based on one or more system calibration parameters;

determining the low-pass blurring filter operator based on the blurring kernel; and

determining the downsampling operator.

9. The method of claim 6 , wherein the plurality of wavelet bases comprise a plurality of Daubechies wavelet bases.

10. The method of claim 9 , wherein the plurality of wavelet bases further comprise a plurality of cycle-spinned versions of the plurality of Daubechies wavelet bases.

11. The method of claim 9 , wherein the plurality of wavelet bases further comprise a plurality of complex dual wavelet transform versions of the plurality of Daubechies wavelet bases.

12. The method of claim 6 , wherein the cost function is minimized using an alternating direction method of multipliers (ADMM) algorithm.

13. The method of claim 6 , wherein identifying the plurality of wavelet bases comprises:

receiving a user selection of the plurality of wavelet bases.

14. A method of enhancing observed images, the method comprising:

receiving one or more observed images;

estimating a blurring kernel based on one or more system calibration parameters;

determining a low-pass blurring filter operator based on the blurring kernel;

determining a downsampling operator;

creating a cost function which generates one or more super-resolution images based on the one or more observed images by applying a sparsity-inducing norm to a plurality of wavelet bases; and

generating the one or more super-resolution images by minimizing the cost function, wherein minimization of the cost function is constrained by requiring the one or more super-resolution images to be equal to a result of applying the low-pass blurring filter operator and the downsampling operator to the one or more super-resolution images.

15. The method of claim 14 , wherein minimization of the cost function is performed using an iterative reweighted L−1 norm minimization.

16. The method of claim 14 , wherein the plurality of wavelet bases comprise a plurality of Daubechies wavelet bases.

17. The method of claim 16 , wherein the plurality of wavelet bases further comprise a plurality of cycle-spinned versions of the plurality of Daubechies wavelet bases.

18. The method of claim 16 , wherein the plurality of wavelet bases further comprise a plurality of complex dual wavelet transform versions of the plurality of Daubechies wavelet bases.

19. The method of claim 14 , wherein the cost function includes one or more denoising terms applied to the observed images.

20. The method of claim 19 , further comprising:

estimating a noise variance value; and

selecting a tuning parameter based on the noise variance value,

wherein the cost function applies the tuning parameter to the sparsity-inducing norm applied to the plurality of wavelet bases.