# FRIST - Flipping and Rotation Invariant Sparsifying Transform Learning and Applications

arXiv: https://arxiv.org/abs/1511.06359 · HTML: https://mlsanity.com/paper/1511.06359/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Nov 2015.

## Built on by (most cited first, 7 of 7)

- [Imaging with Equivariant Deep Learning](https://mlsanity.com/paper/2209.01725/) (2022)
- [Model-based Reconstruction with Learning: From Unsupervised to Supervised and Beyond](https://mlsanity.com/paper/2103.14528/) (2021)
- [Pivotal Auto-Encoder via Self-Normalizing ReLU](https://mlsanity.com/paper/2406.16052/) (2024)
- [Reconciliation of Statistical and Spatial Sparsity For Robust Image and Image-Set Classification](https://mlsanity.com/paper/2106.00256/) (2021)
- [Accelerated MRI With Deep Linear Convolutional Transform Learning](https://mlsanity.com/paper/2204.07923/) (2022)
- [Multi-Linear Kernel Regression and Imputation in Data Manifolds](https://mlsanity.com/paper/2304.03041/) (2023)
- [PE-CSNet: An equivariant network architecture with learnable patch-based sparse representation](https://mlsanity.com/paper/2608.14708/) (2026)

## Abstract (arXiv)

Features based on sparse representation, especially using the synthesis dictionary model, have been heavily exploited in signal processing and computer vision. However, synthesis dictionary learning typically involves NP-hard sparse coding and expensive learning steps. Recently, sparsifying transform learning received interest for its cheap computation and its optimal updates in the alternating algorithms. In this work, we develop a methodology for learning Flipping and Rotation Invariant Sparsifying Transforms, dubbed FRIST, to better represent natural images that contain textures with various geometrical directions. The proposed alternating FRIST learning algorithm involves efficient optimal updates. We provide a convergence guarantee, and demonstrate the empirical convergence behavior of the proposed FRIST learning approach. Preliminary experiments show the promising performance of FRIST learning for sparse image representation, segmentation, denoising, robust inpainting, and compressed sensing-based magnetic resonance image reconstruction.