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Experimental results of the manuscript:

 

¡°Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization¡±

 

By Weisheng Dong, Lei Zhang, Guangming Shi, and Xiaolin Wu

 

to appear, IEEE Trans. on Image Processing.

 

Paper: download here

Matlab Code: download here

 

 

Part A: Results on Image Deblurring

 

Notes:

(1)   The deblurring method in [1] is labeled as ¡°Surrogate¡±;

(2)   The deblurring method in [2] is labeled as ¡°FISTA¡±;

(3)   The deblurring method in [5] is labeled as ¡°SWTV¡±;

(4)   The deblurring method in [6] is labeled as ¡°L0Spar¡±;

(5)   The deblurring method in [8] is labeled as ¡°BM3D¡±;

(6)   The proposed method by using only ASDS is labeled as ASDS, by using ASDS plus AR regularization is labeled as ASDS-AR, by using ASDS with both AR and non-local regularization is labeled as ASDS-AR-NL.

(7)   The proposed deblurring method with training image dataset 1 or dataset 2 is labeled as TD1 or TD2.

 

For example, the deblurring result of the method ASDS_AR_NL_TD1 on image Parrot is labeled as ¡°ASDS_AR_NL_TD1_parrot¡±. Other result images are labeled similarly.

 

Experiment 1:  9¡Á9 uniform blur kernel, noise level

 

The deblurring results on Barbara

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The deblurring results on Bike

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The deblurring results on Straw

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The deblurring results on Boats

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The deblurring results on Parrots

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The deblurring results on Baboon

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The deblurring results on Hat

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The deblurring results on Pentagon

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The deblurring results on Cameraman

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The deblurring results on Peppers

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Experiment 2:  9¡Á9 uniform blur kernel, noise level

 

The deblurring results on Barbara

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The deblurring results on Bike

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The deblurring results on Straw

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The deblurring results on Boats

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The deblurring results on Parrots

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The deblurring results on Baboon

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The deblurring results on Hat

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The deblurring results on Pentagon

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The deblurring results on Cameraman

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The deblurring results on Peppers

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Experiment 3: Gaussian blur kernel with standard deviation 3, noise level

 

The deblurring results on Barbara

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The deblurring results on Bike

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The deblurring results on Straw

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The deblurring results on Boats

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The deblurring results on Parrots

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The deblurring results on Baboon

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The deblurring results on Hat

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The deblurring results on Pentagon

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The deblurring results on Cameraman

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The deblurring results on Peppers

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Experiment 4:  Gaussian blur kernel with standard deviation 3, noise level

 

The deblurring results on Barbara

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The deblurring results on Bike

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The deblurring results on Straw

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The deblurring results on Boats

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The deblurring results on Parrots

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The deblurring results on Baboon

Download images

The deblurring results on Hat

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The deblurring results on Pentagon

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The deblurring results on Cameraman

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The deblurring results on Peppers

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Part B: Results on Image Super-resolution

 

Notes:

(1)   The super-resolution method in [1] is labeled as ¡°Surrogate¡±;

(2)   The super-resolution method in [3] is labeled as ¡°Softcuts¡±;

(3)   The super-resolution method in [4] is labeled as ¡°Sparse¡±;

(4)   The super-resolution method in [7] is labeled as ¡°TV¡±;

(5)   The proposed method by using only ASDS is labeled as ASDS, by using ASDS plus AR regularization is labeled as ASDS-AR, by using ASDS with both AR and non-local regularization is labeled as ASDS-AR-NL.

(6)   The proposed deblurring method with training image dataset 1 or dataset 2 is labeled as TD1 or TD2.

 

For example, the reconstructed high resolution image by the method ASDS_AR_NL_TD1 on image Girl is labeled as ¡°ASDS_AR_NL_TD1_girl¡±. Other result images are labeled similarly.

 

In Experiment 1 of super-resolution, the degraded low resolution (LR) images were generated by first applying a truncated 7´7 Gaussian smoothing filter with standard deviation 1.6 to the original image and then down-sampling with a factor of 3.

In Experiment 2, Gaussian white noise with standard deviation 5 was then added to the LR images to simulate the noisy LR images.

 

Experiment 1:  noiseless images

 

The supper-resolution results on Girl

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The supper-resolution results on Parrot

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The supper-resolution results on Butterfly

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The supper-resolution results on Leaves

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The supper-resolution results on Parthenon

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The supper-resolution results on Flower

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The supper-resolution results on Hat

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The supper-resolution results on Racoon

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The supper-resolution results on Bike

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The supper-resolution results on Plant

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Experiment 2:  noisy images

 

The supper-resolution results on Girl

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The supper-resolution results on Parrot

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The supper-resolution results on Butterfly

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The supper-resolution results on Leaves

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The supper-resolution results on Parthenon

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The supper-resolution results on Flower

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The supper-resolution results on Hat

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The supper-resolution results on Racoon

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The supper-resolution results on Bike

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The supper-resolution results on Plant

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Part C: Results on the 1000-Image Dataset

 

To more comprehensively test the robustness of the proposed image restoration method, we performed extensive deblurring and super-resolution experiments on a large dataset that contains 1000 natural images of various contents. To establish this dataset, we randomly downloaded 822 high-quality natural images from the Flickr website (http://www.flickr.com/), and selected 178 high-quality natural images from the Berkeley Segmentation Database (http://www.eecs.berkeley.edu/Research/Projects/CS/vision/grouping/segbench). A 256´256 sub-image that is rich in edge and texture structures was cropped from each of these 1000 images to test our method.

 

Results on Deblurring

 

 

Deblurring_Exp1_GainsDeblurring_Exp2_Gains

(a)                                                                                              (b)

Deblurring_Exp3_GainsDeblurring_Exp4_Gains

(c)                                                                                              (d)

 

Fig. 1. The PSNR gain distributions of deblurring experiments. (a) Uniform blur kernel with sn=1.414; (b) Uniform blur kernel with sn=2; (c) Gaussian blur kernel with sn=1.414; (d) Gaussian blur kernel with sn=2.

 

Results on Superresolution

 

 

Noiseless_GainsNoisy_Gains

(a)                                                                                            (b)

 

Fig. 2. The PSNR gain distributions of super-resolution experiments. (a) Noise level sn=0; (b) Noise level sn=5.

 

 

References

 

       [1].       Daubechies, M. Defriese, and C. DeMol, ¡°An iterative thresholding algorithm for linear inverse problems with a sparsity constraint,¡± Commun. Pure Appl. Math., Vol.57, pp.1413-1457, 2004.

       [2].       A. Beck and M. Teboulle, ¡°Fast gradient-based algorithms for constrained total variation image denoising and deblurring problems,¡± IEEE Trans. On Image Process., vol. 18, no. 11, pp. 2419-2434, Nov. 2009.

       [3].       S. Dai, M. Han, W. Xu, Y. Wu, Y. Gong, and A. K. Katsaggelos, ¡°SoftCuts: a soft edge smoothness prior for color image super-resolution,¡± IEEE Trans. Image Process., vol. 18, no. 5, pp. 969-981, May 2009.

       [4].       J. Yang, J. Wright, Y. Ma, and T. Huang, ¡°Image super-resolution as sparse representation of raw image patches,¡± IEEE Computer Vision and Pattern Recognition, Jun. 2008.

       [5].       G. Chantas, N. P. Galatsanos, R. Molina, A. K. Katsaggelos, ¡°Variational Bayesian image restoration with a product of spatially weighted total variation image priors,¡± IEEE Trans. Image Process., vol. 19, no. 2, pp. 351-362, Feb. 2010.

       [6].       J. Portilla, ¡°Image restoration through L0 analysis-based sparse optimization in tight frames,¡± in Proc. IEEE Int. conf. Image Process., pp. 3909-3912, Nov. 2009.

       [7].       A. Marquina, and S. J. Osher, ¡°Image super-resolution by TV-regularization and Bregman iteration,¡± J. Sci. Comput., vol. 37, pp. 367-382, 2008.

       [8].       K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, Image restoration by sparse 3D transform-domain collaborative filtering,¡±in Society of Photo-Optical Instrumentation Engineers (SPIE) Conference Series, vol. 6812, 2008.