Multi-Wiener SURE-LET Deconvolution

Feng Xue, Florian Luisier and Thierry Blu

Outline

We extend the SURE-LET approach initially developed for image denoising, to image deconvolution. The deconvolution process is linearly parametrized by using multiple Wiener filters as elementary functions, followed by undecimated Haar-wavelet (subband-dependent) thresholding. Three key contributions make this approach novel, feasible, and even computationally efficient:

• The quality criterion to optimize is a statistical estimate of the Mean-Squared Error (MSE) of the full deconvolution process, which depends only on observed data (Stein's Unbiased Risk Estimate—SURE);
• The deconvolution process is parametrized as a linear combination of known elementary functions (Linear Expansion of Thresholds—LET);
• The use of several "Wiener" filterings with different (but fixed) regularization parameters.

Thanks to the quadratic nature of SURE and to the linear representation of the restoration algorithm, the algorithm merely amounts to solving a linear system of equations, whose solution, i.e. the linear coefficients, constitutes the best combination of the Wiener-Haar-threshold bases.
A very interesting aspect of this approach is that the loss of degrees of freedom resulting from having fixed (non-linear) regularization parameters is totally compensated by the degrees of freedom brought by the (many) linear parameters.

References

[1] Xue, F., Luisier, F. & Blu, T.,"SURE-LET image deconvolution using multiple Wiener filters", Proceedings of the 2012 IEEE International Conference on Image Processing (ICIP'12), Orlando, USA, pp. 3037-3040, September 30--October 3, 2012.

[2] Xue, F., Luisier, F. & Blu, T.,"Multi-Wiener SURE-LET Deconvolution", IEEE Transactions on Image Processing, Vol. 22 (5), pp. 1954-1968, 2013.

Matlab Software

The Matlab code available here is a demo of the algorithm described in the above papers. This package implements the multi-Wiener SURE-LET deconvolution. Download the zip archive. To understand how to use these files, please read the file README.txt or the online help in the routines.

Demo snapshot

Conditions of use — You are free to use this software for research purposes, but you should not redistribute it without our consent. In addition, we expect you to include an adequate citation and acknowledgment whenever you present or publish results that are based on it.