# Image Super-Resolution Based on Sparsity Prior via Smoothed l0 Norm

arXiv: https://arxiv.org/abs/1603.06680 · HTML: https://mlsanity.com/paper/1603.06680/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2016.

## Built on by (most cited first, 1 of 1)

- [Robust Internal Representations for Domain Generalization](https://mlsanity.com/paper/2309.15522/) (2023)

## Abstract (arXiv)

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 l0-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.