Outline
We extend the SURELET
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 Haarwavelet (subbanddependent)
thresholding. Three key contributions make this approach novel, feasible, and
even computationally efficient:

The quality criterion to optimize is a
statistical estimate of the MeanSquared 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 WienerHaarthreshold bases.
A very interesting aspect of this approach is that the loss of degrees of freedom resulting from having fixed (nonlinear) regularization parameters is totally compensated by the degrees of freedom brought by the (many) linear parameters.
References
[1] Xue, F., Luisier, F. & Blu, T.,"SURELET image deconvolution using multiple Wiener filters", Proceedings of the 2012 IEEE International Conference on Image Processing (ICIP'12), Orlando, USA, pp. 30373040, September 30October 3, 2012.

[2] Xue, F., Luisier, F. & Blu, T.,"MultiWiener SURELET Deconvolution", IEEE Transactions on Image Processing, Vol. 22 (5), pp. 19541968, 2013.

Matlab Software
The Matlab code available here is a demo of the algorithm described in the above papers. This package
implements the multiWiener SURELET 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.