Image decomposition and completion using relative total variation and schatten quasi-norm regularization

Abstract

Both image decomposition and data completion are not only ubiquitous but also challenging tasks in the study of computer vision. In this paper, different from existing approaches, we propose a novel regularization model for image decomposition and data completion, which integrates relative total variation (RTV) with Schatten-1/2 or Schatten-2/3 norm, respectively. RTV is shown to be able to extract the fundamental structure effectively from the complicated texture patterns and largely to avoid the drawback of oil painting artifacts. Schatten quasi-norm is used to capture texture patterns in a completely-separated manner. The proposed model is in essence divided into “RTV+ double nuclear norm” and “RTV+ Frobenius/nuclear hybrid norm”, which can be solved by splitting variables and then by using the alternating direction method of multiplier (ADMM). Convergence of the algorithm is discussed in detail. The proposed approach is applied to several benchmark low-level vision problems: gray-scale image decomposition and reconstruction, text removal, color natural scene image completion, and visual data completion, demonstrating the distinguishable effectiveness of the new model, comparing to the latest developments in literature.