A new non-convex low rank minimization model to decompose an image into cartoon and texture components

Abstract

Decomposition of an image into cartoon and texture components is frequently used in many image processing applications. Here, the cartoon component has been characterized by the frequently used total variation norm. However, it becomes very challenging to obtain the texture component due to the varying nature of the texture. In general, the texture component has oscillatory behavior locally or globally. Owing to this oscillatory behavior, the texture component has been characterized via low-rank regularization which is widely used to extract texture component from the image. In the works reported till now, convex nuclear norm has been frequently used as a surrogate of the matrix rank, which is suboptimal because of shrinking each singular value equally, while the non-convex surrogate of the rank treats each singular value adaptively. In this paper, we are introducing a new tightest non-convex surrogate of the rank that assigns different weights to each singular value. The new non-convex image decomposition minimization model provides us cartoon and texture components by minimizing the total variation norm and non-convex function simultaneously. This model can also work best for many image restoration problems such as image deblurring and inpainting. The conventional alternating direction method of multiplier (ADMM) has been exploited as the solver of the non-convex minimization model. The proposed model works well on both globally patterned and natural images. In the experimental section, we demonstrate the outperformance of the proposed model over the state-of-the-art methods.