Improved Image Compressive Sensing Recovery with Low-Rank Prior and Deep Image Prior

Compressive sensing (CS) aims to recover images with rich and accurate information from a small amount of sampled data. Due to its ill-posedness, the model-based CS method has been widely used ever. In recent years, with the development of the arisen learning-based method, enormous progress has been made in combining learning-based strategy with traditional methods. However, at a low sampling ratio, most such methods tend to over-suppress image information, making the recovered results less satisfactory. In order to push the limits of image CS recovery, we propose a novel non-convex low-rank(NCLR) prior by utilizing weighted Schatten p-norm as a surrogate function of the rank function in low-rank approximation. We then provide a new NCLR-based CS model for image CS recovery by plugging the deep prior as a modular part. In addition, we present an efficient iterated algorithm to solve the proposed model by using the alternating direction method of multiplier (ADMM). Further, the convergence of the proposed method is also illustrated. Extensive experimental results demonstrate that our method achieves good performance in both quantity evaluation and visual perception compared to the existing image CS recovery methods, especially at a low sampling ratio.