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Stéphane Mallat and Guoshen Yu

Summary:

We introduce a class of inverse problem estimators computed by mixing adaptively a family of linear estimators corresponding to different priors. Sparse mixing weights are calculated over blocks of coefficients in a frame providing a sparse signal representation. They minimize an l1 norm taking into account the signal regularity in each block. Adaptive directional image interpolations are computed over a wavelet frame with an O(N logN) algorithm.

Keywords:

Super-resolution, interpolation, image zooming, mixing estimators, sparse representation, structured sparsity, Tikhonov regularization.

References:

• S.Mallat and G.Yu, Super-Resolution with Sparse Mixing Estimators, submitted to IEEE Trans. on Image Processing, 2009.

Software:  

Download Matlab code.  Unzip the package and see readme for details.

Examples:

Images used in the numerical experiments:

Methods under comparison:

• SME (the proposed Sparse Mixing Estimation) [1]

• Bicubic interpolation

• NEDI (New edge directed interpolation) [2]

• DFDF (Directional filtering and data fusion) [3]

• Curvelet [4]

• Contourlet [5]

• SAI (Soft-decision Adaptive Interpolation) [6]

PSNR comparison (in dB)

The PSNRs are computed over the whole images shown above.

Zoomed illustration I

The PSNRs are computed over the zoomed areas.

Zoomed illustration II

The PSNRs are computed over the zoomed areas.

[1] S.Mallat and G.Yu, Super-Resolution with Sparse Mixing Estimators, submitted to IEEE Trans. on Image Processing, 2009.

[2] X. Li and M. T. Orchard. New edge-directed interpolation. Image Processing, IEEE Transactions on, 10(10):1521–1527, 2001.

[3] L. Zhang and X. Wu. An edge-guided image interpolation algorithm via directional filtering and data fusion. IEEE Transactions on Image Processing, 15(8):2226, 2006.

[4] M.J. Fadili, J.L. Starck, and F. Murtagh. Inpainting and Zooming Using Sparse Representations. The Computer Journal, 2007.

[5] N. Mueller, Y. Lu, and M.N. Do. Image interpolation using multiscale geometric representations. In Computational Imaging V. Edited by Bouman, Charles A.; Miller, Eric L.; Pollak, Ilya. Proceedings of the SPIE, volume 6498, page 64980A, 2007.

[6] X. Zhang and X. Wu. Image interpolation by adaptive 2-d autoregressive modeling and soft-decision estimation. IEEE Transactions on Image Processing, 17(6):887–896, 2008.