BM3D Frames and Variational Image Deblurring

TL;DR

This paper introduces analysis and synthesis frames based on BM3D algorithms to develop new iterative image deblurring methods, demonstrating superior results and convergence proofs.

Contribution

It formalizes BM3D image modeling through analysis and synthesis frames and proposes novel deblurring algorithms, including a decoupled approach based on Nash equilibrium.

Findings

Decoupled Nash equilibrium algorithm outperforms existing methods.

Proved convergence of the proposed algorithms.

Simulation shows superior visual and numerical results.

Abstract

A family of the Block Matching 3-D (BM3D) algorithms for various imaging problems has been recently proposed within the framework of nonlocal patch-wise image modeling [1], [2]. In this paper we construct analysis and synthesis frames, formalizing the BM3D image modeling and use these frames to develop novel iterative deblurring algorithms. We consider two different formulations of the deblurring problem: one given by minimization of the single objective function and another based on the Nash equilibrium balance of two objective functions. The latter results in an algorithm where the denoising and deblurring operations are decoupled. The convergence of the developed algorithms is proved. Simulation experiments show that the decoupled algorithm derived from the Nash equilibrium formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field, confirming a valuable potential of BM3D-frames as an advanced image modeling tool.