#147: Multiscale Tikhonov-total variation image restoration using spatially varying edge coherence exponent


Abstract

Edge preserving regularization using partial differential equation (PDE) based schemes are now widely used in image restoration. We propose an adaptive multiscale variable exponent-based anisotropic variational PDE scheme that avoids current limitations such as over smoothing and blockiness artifacts while still retaining and enhancing edge structures across scale. The innovative model automatically balances between Tikhonov and total variation (TV) regularization effects using scene content information by adopting a spatially varying edge coherence exponent term constructed from the eigenvalues of the smoothed structure tensor. The multiscale exponent model considered here leads to a novel denoising method which preserves edges and provides selective denoising without generating artifacts for both additive and multiplicative noise models. Mathematical analysis of the proposed method in variable exponent space demonstrates its robustness, and that the approach theoretically satisfies the maximum-minimum principle which guarantees that artificial edge regions are not created. Extensive experimental results on synthetic, natural and biomedical images indicate that the proposed Multiscale Tikhonov-Total Variation (MTTV) and Dynamical MTTV (D-MTTV) schemes perform better than sixteen other denoising algorithms in terms of several metrics including signal-to-noise ratio improvement and structure preservation. Promising extensions to handle multiplicative noise models and multichannel imagery are also provided.