# Two-layer Residual Sparsifying Transform Learning for Image Reconstruction

## TL;DR

This paper introduces a two-layer residual sparsifying transform model for improved image reconstruction, demonstrating enhanced performance in low-dose CT imaging through efficient optimization algorithms.

## Contribution

It proposes a novel two-layer transform learning framework that better captures residual sparsity, advancing image reconstruction methods with efficient algorithms.

## Key findings

- Two-layer model outperforms previous schemes in CT reconstruction.
- Efficient block coordinate descent algorithms enable practical implementation.
- Preliminary results show improved image quality from limited measurements.

## Abstract

Signal models based on sparsity, low-rank and other properties have been exploited for image reconstruction from limited and corrupted data in medical imaging and other computational imaging applications. In particular, sparsifying transform models have shown promise in various applications, and offer numerous advantages such as efficiencies in sparse coding and learning. This work investigates pre-learning a two-layer extension of the transform model for image reconstruction, wherein the transform domain or filtering residuals of the image are further sparsified in the second layer. The proposed block coordinate descent optimization algorithms involve highly efficient updates. Preliminary numerical experiments demonstrate the usefulness of a two-layer model over the previous related schemes for CT image reconstruction from low-dose measurements.