# M-RWTL: Learning Signal-Matched Rational Wavelet Transform in Lifting Framework

arXiv: https://arxiv.org/abs/1710.10394 · HTML: https://mlsanity.com/paper/1710.10394/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2017.

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

- [Efficient Oriented Object Detection with Enhanced Small Object Recognition in Aerial Images](https://mlsanity.com/paper/2412.12562/) (2024)

## Abstract (arXiv)

Transform learning is being extensively applied in several applications because of its ability to adapt to a class of signals of interest. Often, a transform is learned using a large amount of training data, while only limited data may be available in many applications. Motivated with this, we propose wavelet transform learning in the lifting framework for a given signal. Significant contributions of this work are: 1) the existing theory of lifting framework of the dyadic wavelet is extended to more generic rational wavelet design, where dyadic is a special case and 2) the proposed work allows to learn rational wavelet transform from a given signal and does not require large training data. Since it is a signal-matched design, the proposed methodology is called Signal-Matched Rational Wavelet Transform Learning in the Lifting Framework (M-RWTL). The proposed M-RWTL method inherits all the advantages of lifting, i.e., the learned rational wavelet transform is always invertible, method is modular, and the corresponding M-RWTL system can also incorporate nonlinear filters, if required. This may enhance the use of RWT in applications which is so far restricted. M-RWTL is observed to perform better compared to standard wavelet transforms in the applications of compressed sensing based signal reconstruction.