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Recursive Risk Estimation for Non-Linear Image Deconvolution with a Wavelet-Domain Sparsity Constraint

C. Vonesch, S. Ramani, M. Unser

Proceedings of the 2008 IEEE International Conference on Image Processing (ICIP'08), San Diego CA, USA, October 12-15, 2008, pp. 665-668.



We propose a recursive data-driven risk-estimation method for non-linear iterative deconvolution. Our two main contributions are 1) a solution-domain risk-estimation approach that is applicable to non-linear restoration algorithms for ill-conditioned inverse problems; and 2) a risk estimate for a state-of-the-art iterative procedure, the thresholded Landweber iteration, which enforces a wavelet-domain sparsity constraint. Our method can be used to estimate the SNR improvement at every step of the algorithm; e.g., for stopping the iteration after the highest value is reached. It can also be applied to estimate the optimal threshold level for a given number of iterations.


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