Learning Filter Bank Sparsifying Transforms

TL;DR

This paper introduces a novel filter bank-based framework for learning sparsifying transforms, which improves image denoising performance by leveraging global convolutional models over traditional patch-based methods.

Contribution

It proposes using undecimated perfect reconstruction filter banks as sparsifying transforms, allowing independent filter length and channel number, enhancing flexibility and performance.

Findings

Filter bank transforms outperform patch-based methods in image denoising.

The proposed method offers greater flexibility in filter design.

Numerical results demonstrate superior denoising performance.

Abstract

Data is said to follow the transform (or analysis) sparsity model if it becomes sparse when acted on by a linear operator called a sparsifying transform. Several algorithms have been designed to learn such a transform directly from data, and data-adaptive sparsifying transforms have demonstrated excellent performance in signal restoration tasks. Sparsifying transforms are typically learned using small sub-regions of data called patches, but these algorithms often ignore redundant information shared between neighboring patches. We show that many existing transform and analysis sparse representations can be viewed as filter banks, thus linking the local properties of patch-based model to the global properties of a convolutional model. We propose a new transform learning framework where the sparsifying transform is an undecimated perfect reconstruction filter bank. Unlike previous transform learning algorithms, the filter length can be chosen independently of the number of filter bank channels. Numerical results indicate filter bank sparsifying transforms outperform existing patch-based transform learning for image denoising while benefiting from additional flexibility in the design process.