Non-Convex Weighted Lp Nuclear Norm based ADMM Framework for Image Restoration
This work addresses image restoration for applications such as photography and medical imaging, representing an incremental improvement over existing nuclear norm methods.
The authors tackled the problem of image restoration by proposing a non-convex weighted Lp nuclear norm minimization method to better enforce structural sparsity and self-similarity, achieving superior performance over state-of-the-art methods in tasks like deblurring, inpainting, and compressive sensing recovery.
Since the matrix formed by nonlocal similar patches in a natural image is of low rank, the nuclear norm minimization (NNM) has been widely used in various image processing studies. Nonetheless, nuclear norm based convex surrogate of the rank function usually over-shrinks the rank components and makes different components equally, and thus may produce a result far from the optimum. To alleviate the above-mentioned limitations of the nuclear norm, in this paper we propose a new method for image restoration via the non-convex weighted Lp nuclear norm minimization (NCW-NNM), which is able to more accurately enforce the image structural sparsity and self-similarity simultaneously. To make the proposed model tractable and robust, the alternative direction multiplier method (ADMM) is adopted to solve the associated non-convex minimization problem. Experimental results on various types of image restoration problems, including image deblurring, image inpainting and image compressive sensing (CS) recovery, demonstrate that the proposed method outperforms many current state-of-the-art methods in both the objective and the perceptual qualities.