Learning Structured Compressed Sensing with Automatic Resource Allocation

2024-10-24

arXiv.org

AI Summary

To address the challenges of excessive parameter count in compression matrix design, heuristic pre-specification of sampling resources, and high hardware/storage overhead in multidimensional data acquisition, this paper proposes SCOSARA—a structured compressive sensing framework. Methodologically, SCOSARA introduces the first unsupervised learning strategy based on Fisher information maximization, jointly optimizing dimension-specific compression matrices and cross-dimensional sampling resource allocation without requiring labeled data, thereby adaptively determining the number of samples per axis. The approach integrates structured compressive sensing, information geometry, and multidimensional sparse modeling. Evaluated on ultrasound localization, SCOSARA significantly reduces the Cramér–Rao bound compared to state-of-the-art methods, while simultaneously decreasing trainable parameters, computational complexity, and memory footprint—achieving a favorable trade-off between reconstruction accuracy and system efficiency.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Search and Optimization: Sampling/Simulation-based Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Multidimensional data acquisition often requires extensive time and poses significant challenges for hardware and software regarding data storage and processing. Rather than designing a single compression matrix as in conventional compressed sensing, structured compressed sensing yields dimension-specific compression matrices, reducing the number of optimizable parameters. Recent advances in machine learning (ML) have enabled task-based supervised learning of subsampling matrices, albeit at the expense of complex downstream models. Additionally, the sampling resource allocation across dimensions is often determined in advance through heuristics. To address these challenges, we introduce Structured COmpressed Sensing with Automatic Resource Allocation (SCOSARA) with an information theory-based unsupervised learning strategy. SCOSARA adaptively distributes samples across sampling dimensions while maximizing Fisher information content. Using ultrasound localization as a case study, we compare SCOSARA to state-of-the-art ML-based and greedy search algorithms. Simulation results demonstrate that SCOSARA can produce high-quality subsampling matrices that achieve lower Cram'er-Rao Bound values than the baselines. In addition, SCOSARA outperforms other ML-based algorithms in terms of the number of trainable parameters, computational complexity, and memory requirements while automatically choosing the number of samples per axis.

Problem

• Optimizes resource allocation in multidimensional data acquisition.
• Reduces complexity in learning subsampling matrices using unsupervised learning.
• Improves data compression quality and efficiency in structured compressed sensing.

Innovation

• Structured compressed sensing with adaptive sampling
• Unsupervised learning maximizes Fisher information
• Reduces parameters, complexity, and memory usage