Tchebichef and Adaptive Steerable-Based Total Variation Model for Image Denoising

Structural information, in particular, the edges present in an image, is the most important part to be noticed by human eyes. Therefore, it is important to denoise this information effectively for better visualization. Recently, research work has been carried out to characterize the structural information into plain and edge patches and denoise them separately. However, the information about the geometrical orientation of the edges is not considered, leading to sub-optimal denoising results. This has motivated us to introduce in this paper an adaptive steerable total variation regularizer (ASTV) based on geometric moments. The proposed ASTV regularizer is capable of denoising the edges based on their geometrical orientation, thus boosting the denoising performance. Further, earlier works exploited the sparsity of the natural images in DCT and wavelet domains which help in improving the denoising performance. Based on this observation, we introduce the sparsity of an image in orthogonal moment domain, in particular, the Tchebichef moment. Then, we propose a new sparse regularizer, which is a combination of the Tchebichef moment and ASTV-based regularizers. The overall denoising framework is optimized using split Bregman-based multivariable minimization technique. Experimental results demonstrate the competitiveness of the proposed method compared with the existing ones in terms of both the objective and subjective image qualities.