Decoupled inverse and denoising for image deblurring: Variational BM3D-frame technique

Recently within the framework of nonlocal patch-wise estimation a family of the Block Matching 3-D (BM3D) algorithms has been developed for various imaging problems [1], [2]. In [3] we demonstrated that BM3D modeling allows frame interpretation and constructed the corresponding analysis and synthesis frames which we call BM3D-frames. In this paper we use the BM3D-frames to develop an image deblurring algorithm based on the alternating optimization of two objective functions corresponding to decoupled denoising and deblurring operations. Compared to the standard approach based on minimization of a single objective function, decoupling allows to achieve both better reconstruction performance and essential simplification of the algorithm. Simulated experiments demonstrate numerical and visual superiority of the proposed algorithm over the current state-of-the-art methods confirming the advantage of the BM3D-frames as an image modeling tool.