# Convolutional Analysis Operator Learning: Acceleration and Convergence

arXiv: https://arxiv.org/abs/1802.05584 · HTML: https://mlsanity.com/paper/1802.05584/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Feb 2018.

## Built on by (most cited first, 10 of 10)

- [Content-aware Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2207.09313/) (2022)
- [DPER: Diffusion Prior Driven Neural Representation for Limited Angle and Sparse View CT Reconstruction](https://mlsanity.com/paper/2404.17890/) (2024)
- [Self-Supervised Scalable Deep Compressed Sensing](https://mlsanity.com/paper/2308.13777/) (2023)
- [Provably Convergent Learned Inexact Descent Algorithm for Low-Dose CT Reconstruction](https://mlsanity.com/paper/2104.12939/) (2021)
- [Convolutional Analysis Operator Learning by End-To-End Training of Iterative Neural Networks](https://mlsanity.com/paper/2203.02166/) (2022)
- [Multi-Channel Convolutional Analysis Operator Learning for Dual-Energy CT Reconstruction](https://mlsanity.com/paper/2203.05968/) (2022)
- [Accelerated MRI With Deep Linear Convolutional Transform Learning](https://mlsanity.com/paper/2204.07923/) (2022)
- [LAMA: Stable Dual-Domain Deep Reconstruction For Sparse-View CT](https://mlsanity.com/paper/2410.21111/) (2024)
- [A Learned Proximal Alternating Minimization Algorithm and Its Induced Network for a Class of Two-block Nonconvex and Nonsmooth Optimization](https://mlsanity.com/paper/2411.06333/) (2024)
- [LAMA-Net: A Convergent Network Architecture for Dual-Domain Reconstruction](https://mlsanity.com/paper/2507.22316/) (2025)

## Abstract (arXiv)

Convolutional operator learning is gaining attention in many signal processing and computer vision applications. Learning kernels has mostly relied on so-called patch-domain approaches that extract and store many overlapping patches across training signals. Due to memory demands, patch-domain methods have limitations when learning kernels from large datasets -- particularly with multi-layered structures, e.g., convolutional neural networks -- or when applying the learned kernels to high-dimensional signal recovery problems. The so-called convolution approach does not store many overlapping patches, and thus overcomes the memory problems particularly with careful algorithmic designs; it has been studied within the "synthesis" signal model, e.g., convolutional dictionary learning. This paper proposes a new convolutional analysis operator learning (CAOL) framework that learns an analysis sparsifying regularizer with the convolution perspective, and develops a new convergent Block Proximal Extrapolated Gradient method using a Majorizer (BPEG-M) to solve the corresponding block multi-nonconvex problems. To learn diverse filters within the CAOL framework, this paper introduces an orthogonality constraint that enforces a tight-frame filter condition, and a regularizer that promotes diversity between filters. Numerical experiments show that, with sharp majorizers, BPEG-M significantly accelerates the CAOL convergence rate compared to the state-of-the-art block proximal gradient (BPG) method. Numerical experiments for sparse-view computational tomography show that a convolutional sparsifying regularizer learned via CAOL significantly improves reconstruction quality compared to a conventional edge-preserving regularizer. Using more and wider kernels in a learned regularizer better preserves edges in reconstructed images.