Minimax Concave Penalty Regression for Superresolution Image Reconstruction

Fast and robust superresolution image reconstruction techniques can be beneficial in improving the safety and reliability of various consumer electronics applications. The least absolute shrinkage and selection operator (LASSO) penalty is widely used in sparse coding-based superresolution image reconstruction (SCSR) tasks. However, the performance of the previously developed models is constrained by bias generated by the LASSO penalty. Meanwhile, no efficient and fast computing algorithms are available for unbiased $l_{0}$ regression, and this situation restricts the practical application of $l_{0}$ -based SCSR methods. To address bias and efficiency problems, we propose a model called minimax concave penalty-based superresolution (MCPSR). First, we introduce a minimax concave penalty (MCP) into the SCSR task to eliminate bias. Second, we design a convergent, efficient algorithm for solving the MCPSR model and present a strict convergence analysis. Numerical experiments show that this model and the designed supporting algorithm can produce reconstructed images with richer textures at a fast computing speed. Moreover, MCPSR even shows robustness in the superresolution reconstruction of noisy images compared with other SCSR methods and has two flexible parameters to control the smoothness of the final reconstruction results.

I. Introduction

Superresolution image reconstruction is beneficial in certain consumer electronics applications to improve the image/video quality captured by end devices, thus benefiting high-end consumer markets. This technique has already been successfully applied, as evidenced by its implementation in [1], [2]. For instance, a fast computing superresolution image reconstruction model can be the basis of superresolution video reconstruction [3], [4], improving the safety and reliability of artificial intelligence, and superresolution images are also beneficial for medical and chemical analyses because the details of medicines and other chemical products can reveal whether they are harmful [5], [6].