Robust two-step image restoration with adaptive regularization parameter

Abstract

Restoration of noisy blurred images is a typical ill-posed inverse problem, which requires suitable regularization techniques to guarantee high-quality solutions. Total variation (TV), among the most popular regularizers, has attracted considerable attention during the past two decades. In particular, TV regularizer is known for its capacity of reducing undesirable noise while preserving image edges. Due to the non-smooth and non-differentiable natures of TV regularizer, TV-regularized variational image restoration models are inherently difficult to solve directly through commonly-used numerical methods. Motivated by the success of proximal forward-backward splitting algorithm, we tend to decompose the original image restoration problem into two steps, i.e., direct deconvolution and TV-regularized image denoising. The simple image denoising problem could be easily dealt with using the alternating direction method of multipliers (ADMM). To further improve the image quality, an automatic method was introduced to adaptively calculate the spatially invariant regularization parameters during image denoising (not the whole process of restoring noisy blurred images). Comprehensive experiments have been conduced on different imaging degradation conditions to verify the effectiveness of our proposed method. Both quantitative results and extensive qualitative comparisons illustrate that the proposed method outperforms several widely-used image restoration methods.