OpenNovelty.org

Hierarchical Multi-Stage Recovery Framework for Kronecker Compressed Sensing

ICLR 2026 Conference SubmissionAnonymous Authors
OpenReview Score: 6.0Download Report PDF
Compressed sensing;Kronecker product;Restricted isometry property;Hierarchical sparsity;Tensor operation
Abstract:

In this paper, we study the Kronecker compressed sensing problem, which focuses on recovering sparse vectors using linear measurements obtained using the Kronecker product of two or more matrices. We first introduce the hierarchical view of the Kronecker compressed sensing, showing that the Kronecker product measurement matrix probes the sparse vector from different levels, following a block-wise and hierarchical structure. Leveraging this insight, we develop a versatile multi-stage sparse recovery algorithmic framework and tailor it to three different sparsity models: standard, hierarchical, and Kronecker-supported. We further analyze the restricted isometry property of Kronecker product matrices under different sparsity models, and provide theoretical recovery guarantees for our multi-stage algorithm. Simulations demonstrate that our method achieves comparable recovery performance to other state-of-the-art techniques while substantially reducing run time owing to the hierarchical, multi-stage recovery process.

Disclaimer
This report is AI-GENERATED using Large Language Models and WisPaper (A scholar search engine). It analyzes academic papers' tasks and contributions against retrieved prior work. While this system identifies POTENTIAL overlaps and novel directions, ITS COVERAGE IS NOT EXHAUSTIVE AND JUDGMENTS ARE APPROXIMATE. These results are intended to assist human reviewers and SHOULD NOT be relied upon as a definitive verdict on novelty.
NOTE that some papers exist in multiple, slightly different versions (e.g., with different titles or URLs). The system may retrieve several versions of the same underlying work. The current automated pipeline does not reliably align or distinguish these cases, so human reviewers will need to disambiguate them manually.
If you have any questions, please contact: mingzhang23@m.fudan.edu.cn

Overview

Taxonomy

Core-task Taxonomy Papers
50
3
Claimed Contributions
24
Contribution Candidate Papers Compared
7
Refutable Paper

Research Landscape Overview

Core task: sparse signal recovery using Kronecker product measurement matrices. This field exploits the structured factorization of measurement operators to reduce computational complexity and storage requirements in compressed sensing. The taxonomy reveals several main branches: Theoretical Foundations and Properties establish guarantees such as restricted isometry properties for Kronecker structures (e.g., Kronecker RIP[4]), while Measurement Matrix Design and Construction focuses on crafting efficient sensing operators (e.g., Kronecker Compressive Sensing[21], Sparse Kronecker Recovery[3]). Algorithm Development and Optimization encompasses diverse recovery strategies, including multi-stage and hierarchical methods, Bayesian approaches like Bayesian Kronecker IRS[6] and BP-VB-EP Kronecker[13], and adaptive schemes such as Adaptive Weighted Kronecker[14]. Application Domains span wireless communications (mmWave systems, IRS-assisted MIMO), medical imaging (MRI, CT, ECG), and cryptographic tasks, while Specialized Recovery Problems address tensor-based and covariance estimation challenges. Recent work has concentrated on hierarchical and multi-stage recovery algorithms that decompose the reconstruction process into sequential steps, exploiting the natural factorization of Kronecker matrices. Hierarchical Multi-Stage Recovery[0] sits within this active branch alongside Hierarchical Sparse Recovery[12] and Sequential Progressive Sensing[17], emphasizing staged refinement to balance accuracy and efficiency. Nearby efforts such as Hybrid mmWave G-KCS[8] and Successive Decision mmWave[44] apply similar multi-stage philosophies to wireless channel estimation, while Kronecker IRS-MIMO[15] integrates intelligent reflecting surfaces with Kronecker-structured sensing. A key trade-off across these methods is the granularity of stage decomposition versus computational overhead: finer stages can improve convergence but may introduce additional tuning complexity. Open questions include optimal stage selection criteria and the interplay between hierarchical recovery and emerging deep-learning-based unfolding techniques like Physics-guided Deep Unfolding[32].

Claimed Contributions

Hierarchical view of Kronecker compressed sensing

The authors introduce a novel hierarchical perspective showing that each factor matrix in the Kronecker product measurement matrix probes the sparse vector at different hierarchical levels following a block-wise structure. This unified view enables handling different sparsity models within a single framework.

9 retrieved papers
Can Refute
Multi-stage sparse recovery algorithmic framework

The authors develop a versatile multi-stage recovery algorithm (MSR) that exploits the Kronecker structure through tensor operations. The method accommodates standard, hierarchical, and Kronecker-supported sparsity patterns within a unified framework while substantially reducing computational complexity compared to existing methods.

9 retrieved papers
Can Refute
Unified restricted isometry property analysis and recovery guarantees

The authors provide a unified RIP analysis for Kronecker product matrices under different sparsity models, introducing the generalized (s,N)-RIP condition. They prove that sparsity at each hierarchical level determines recovery success and establish RIP-based recovery guarantees for their multi-stage algorithm, improving existing bounds for standard sparsity.

6 retrieved papers
Can Refute

Core Task Comparisons

Comparisons with papers in the same taxonomy category

Contribution Analysis

Detailed comparisons for each claimed contribution

Contribution

Hierarchical view of Kronecker compressed sensing

The authors introduce a novel hierarchical perspective showing that each factor matrix in the Kronecker product measurement matrix probes the sparse vector at different hierarchical levels following a block-wise structure. This unified view enables handling different sparsity models within a single framework.

Contribution

Multi-stage sparse recovery algorithmic framework

The authors develop a versatile multi-stage recovery algorithm (MSR) that exploits the Kronecker structure through tensor operations. The method accommodates standard, hierarchical, and Kronecker-supported sparsity patterns within a unified framework while substantially reducing computational complexity compared to existing methods.

Contribution

Unified restricted isometry property analysis and recovery guarantees

The authors provide a unified RIP analysis for Kronecker product matrices under different sparsity models, introducing the generalized (s,N)-RIP condition. They prove that sparsity at each hierarchical level determines recovery success and establish RIP-based recovery guarantees for their multi-stage algorithm, improving existing bounds for standard sparsity.

Table of Contents