Recovery of Missing Samples Using Sparse Approximation via a Convex Similarity Measure
This work addresses image inpainting for signal processing applications, presenting an incremental improvement by simplifying SSIM to a convex metric.
The paper tackles the missing sample recovery problem in image signals, proposing an iterative sparse recovery algorithm with a new convex similarity metric (CSIM) based on constrained l1-norm minimization and solved via ADMM, showing efficiency in simulations for 1D patch vectors and 2D image inpainting.
In this paper, we study the missing sample recovery problem using methods based on sparse approximation. In this regard, we investigate the algorithms used for solving the inverse problem associated with the restoration of missed samples of image signal. This problem is also known as inpainting in the context of image processing and for this purpose, we suggest an iterative sparse recovery algorithm based on constrained $l_1$-norm minimization with a new fidelity metric. The proposed metric called Convex SIMilarity (CSIM) index, is a simplified version of the Structural SIMilarity (SSIM) index, which is convex and error-sensitive. The optimization problem incorporating this criterion, is then solved via Alternating Direction Method of Multipliers (ADMM). Simulation results show the efficiency of the proposed method for missing sample recovery of 1D patch vectors and inpainting of 2D image signals.