# Hybrid Function Sparse Representation towards Image Super Resolution

## TL;DR

This paper introduces a hybrid function-based dictionary for image super resolution that is scalable, does not require training, and improves results especially on detailed images, outperforming non-learning methods.

## Contribution

The authors propose a novel hybrid function sparse representation method using a directly generated, scalable dictionary for super resolution, eliminating the need for training.

## Key findings

- Outperforms non-learning state-of-the-art methods on Set14 dataset.
- Effective on images with rich details and contexts.
- Utilizes multi-scale refinement to enhance super resolution results.

## Abstract

Sparse representation with training-based dictionary has been shown successful on super resolution(SR) but still have some limitations. Based on the idea of making the magnification of function curve without losing its fidelity, we proposed a function based dictionary on sparse representation for super resolution, called hybrid function sparse representation (HFSR). The dictionary we designed is directly generated by preset hybrid functions without additional training, which can be scaled to any size as is required due to its scalable property. We mixed approximated Heaviside function (AHF), sine function and DCT function as the dictionary. Multi-scale refinement is then proposed to utilize the scalable property of the dictionary to improve the results. In addition, a reconstruct strategy is adopted to deal with the overlaps. The experiments on Set14 SR dataset show that our method has an excellent performance particularly with regards to images containing rich details and contexts compared with non-learning based state-of-the art methods.