# Statistical learning of rational wavelet transform for natural images

## TL;DR

This paper introduces a statistical learning method for rational wavelet transforms tailored for natural images, demonstrating improved performance in compressed sensing reconstruction over standard wavelet transforms.

## Contribution

It proposes a novel Rational Wavelet Transform Learning in Statistical sense (RWLS) method using a lifting framework with a closed form solution.

## Key findings

- RWLS outperforms standard dyadic wavelet transforms in image reconstruction
- The method is effective for compressed sensing applications
- Closed form solution simplifies the learning process

## Abstract

Motivated with the concept of transform learning and the utility of rational wavelet transform in audio and speech processing, this paper proposes Rational Wavelet Transform Learning in Statistical sense (RWLS) for natural images. The proposed RWLS design is carried out via lifting framework and is shown to have a closed form solution. The efficacy of the learned transform is demonstrated in the application of compressed sensing (CS) based reconstruction. The learned RWLS is observed to perform better than the existing standard dyadic wavelet transforms.