Wavelet-based image denoising using nonstationary stochastic geometrical image priors

Abstract

In this paper a novel stochastic image model in the transform domain is presented and its superior performance in image denoising applications is demonstrated. The proposed model exploits local subband image statistics and is based on geometrical priors. Contrarily to complex models based on local correlations, or to mixture models, the proposed model performs a partition of the image into non-overlapping regions with distinctive statistics. A close form analytical solution of the image denoising problem for AWGN is derived and its performance bounds are analyzed. Despite being very simple, the proposed stochastic image model provides a number of advantages in comparison to the existing approaches: (a) simplicity of stochastic image modeling; (b) completeness of the model, taking into account multiresolution, non-stationary image behavior, geometrical priors and providing an excellent fit to the global image statistics; (c) very low complexity of the algorithm; (d) tractabiity of the model and of the obtained results due to the closed-form solution and to the existence of analytical performance bounds; (e) extensibility to different transform domains, such as orthogonal, biorthogonal and overcomplete data representations. The results of benchmarking with the state-of-the-art image denoising methods demonstrate the superior performance of the proposed approach.