SBM3D: Sparse Regularization Model Induced by BM3D for Weighted Diffraction Imaging

How to explore many priors of the underlying image for diffraction imaging, i.e., recovering the image from recorded diffraction patterns, is an important issue. To address this issue, we present a sparse regularization model called sparse regularization model induced by block-matching and 3-D filtering (SBM3D). The proposed SBM3D exploits the sparsity of the residual image (difference image between the underlying image and its filtered version). The filtered image can be obtained by filtering the estimated image. The proposed regularization model is suitable for any inverse imaging problem. Specially, we incorporate the proposed SBM3D into the diffraction imaging field. Inspired by the effectiveness of the reweighted approach in compressed sensing, we formulate the weighted and regularized diffraction imaging problem. The smooth technique and the accelerated gradient descent approach with an adaptive step size are utilized to solve this challenging problem. Experimental simulations for coded diffraction imaging demonstrate that the proposed diffraction imaging algorithm outperforms the previous algorithms in terms of the reconstruction quality.