Title:FTVd is beyond Fast Total Variation regularized Deconvolution

Abstract:In this paper, we revisit the "FTVd" algorithm for Fast Total Variation Regularized Deconvolution, which has been widely used in the past few years. Both its original version implemented in the MATLAB software FTVd 3.0 and its related variant implemented in the latter version FTVd 4.0 are considered \cite{Wang08FTVdsoftware}. In FTVd 3.0, the operator splitting, quadratic penalty and the continuation scheme are the key concepts of the algorithm and our novel point here is that the intermediate results during the continuation procedure are in fact the solutions of a combination of Tikhonov and total variation regularizations for image deconvolution, and therefore some of them often have a better image quality than its final solution, which is corresponding to the pure total variation regularized model. In FTVd 4.0, the quadratic penalty are augmented with a lagrangian term in order to implicitly performing the continuation scheme for better computational efficiency and stability. Correspondingly, some intermediate results during the iterations still empirically achieve better recovery quality than the final solution, in terms of reduced staircase effect.