Recursive Risk Estimation For Non-Linear Image Deconvolution With A Wavelet-Domain Sparsity Constraint

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 nonlinear 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 he 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.