Image Super-Resolution Based on Sparsity Prior via Smoothed $l_0$ Norm

TL;DR

This paper introduces a novel super-resolution method that uses a smoothed $l_0$ norm approach to find sparse representations, leading to improved high-resolution image reconstruction from low-resolution inputs.

Contribution

It proposes a new algorithm employing the smoothed $l_0$ norm for sparse representation, enhancing super-resolution quality over traditional methods.

Findings

Higher PSNR and SSIM scores in reconstructed images

Effective sparse representation with the SL0 algorithm

Improved image quality in most tested cases

Abstract

In this paper we aim to tackle the problem of reconstructing a high-resolution image from a single low-resolution input image, known as single image super-resolution. In the literature, sparse representation has been used to address this problem, where it is assumed that both low-resolution and high-resolution images share the same sparse representation over a pair of coupled jointly trained dictionaries. This assumption enables us to use the compressed sensing theory to find the jointly sparse representation via the low-resolution image and then use it to recover the high-resolution image. However, sparse representation of a signal over a known dictionary is an ill-posed, combinatorial optimization problem. Here we propose an algorithm that adopts the smoothed $l_0$-norm (SL0) approach to find the jointly sparse representation. Improved quality of the reconstructed image is obtained for most images in terms of both peak signal-to-noise-ratio (PSNR) and structural similarity (SSIM) measures.