# Adaptive Block Sparse Regularization under Arbitrary Linear Transform

arXiv: https://arxiv.org/abs/2401.15292 · HTML: https://mlsanity.com/paper/2401.15292/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 27 references that are in the map.
- First posted on arXiv 27 Jan 2024.

## Builds on (most cited first, 4 of 4)

- [Framelet Representation of Tensor Nuclear Norm for Third-Order Tensor Completion](https://mlsanity.com/paper/1909.06982/) (2019)
- [Learning Regularization Parameters of Inverse Problems via Deep Neural Networks](https://mlsanity.com/paper/2104.06594/) (2021)
- [Missing Slice Recovery for Tensors Using a Low-rank Model in Embedded Space](https://mlsanity.com/paper/1804.01736/) (2018)
- [Pattern-Coupled Sparse Bayesian Learning for Recovery of Block-Sparse Signals](https://mlsanity.com/paper/1311.2150/) (2013)

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

- [Nonconvex Latent Optimally Partitioned Block-Sparse Recovery via Log-Sum and Minimax Concave Penalties](https://mlsanity.com/paper/2603.01304/) (2026)

## Abstract (arXiv)

We propose a convex and fast signal reconstruction method for block sparsity under arbitrary linear transform with unknown block structure. The proposed method is a generalization of the similar existing method and can reconstruct signals with block sparsity under non-invertible transforms, unlike the existing method. Our work broadens the scope of block sparse regularization, enabling more versatile and powerful applications across various signal processing domains. We derive an iterative algorithm for solving proposed method and provide conditions for its convergence to the optimal solution. Numerical experiments demonstrate the effectiveness of the proposed method.