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Learning Structured Compressed Sensing with Automatic Resource Allocation

Han Wang, Eduardo Pérez, Iris A. M. Huijben, Hans van Gorp, Ruud van Sloun, Florian Römer

TL;DR

SCOSARA tackles the challenge of high-dimensional data acquisition by introducing a Fisher-information–driven framework for structured compressed sensing with automatic resource allocation. By replacing task-based learning with unsupervised maximization of the trace of the Fisher Information Matrix and employing a differentiable Gumbel-softmax pipeline, SCOSARA automatically distributes samples across multiple axes while delivering axis-specific, one-hot subsampling matrices. In a multichannel ultrasound localization case, SCOSARA yields lower CRB values and better reconstruction quality than ML-based and greedy baselines, all while reducing trainable parameters and computational/memory demands. This approach enables efficient, hardware-friendly sub-sampling with minimal manual tuning and shows promise for broader multidimensional sensing tasks requiring dimension-wise adaptive sampling.

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 Cramér-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.

Learning Structured Compressed Sensing with Automatic Resource Allocation

TL;DR

SCOSARA tackles the challenge of high-dimensional data acquisition by introducing a Fisher-information–driven framework for structured compressed sensing with automatic resource allocation. By replacing task-based learning with unsupervised maximization of the trace of the Fisher Information Matrix and employing a differentiable Gumbel-softmax pipeline, SCOSARA automatically distributes samples across multiple axes while delivering axis-specific, one-hot subsampling matrices. In a multichannel ultrasound localization case, SCOSARA yields lower CRB values and better reconstruction quality than ML-based and greedy baselines, all while reducing trainable parameters and computational/memory demands. This approach enables efficient, hardware-friendly sub-sampling with minimal manual tuning and shows promise for broader multidimensional sensing tasks requiring dimension-wise adaptive sampling.

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 Cramér-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.

Paper Structure

This paper contains 6 sections, 10 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Structured subsampling
  3. Automatic Resource Allocation
  4. Optimization Target
  5. Evaluation
  6. Conclusion

Figures (3)

  • Figure 1: Flowchart of automatic resource allocation in SCOSARA. There are two parallel ways to obtain the subsampling matrices and the regularizer: the top path perturbs the logits with Gumbel noise to approximate the process of sampling from a categorical distribution, while the lower path directly uses the logits to produce the regularizer.
  • Figure 2: CRB as a function of the compression factor (higher factor denotes more selected samples).
  • Figure 3: Reconstructed images comparison in the multi-scatterer cases when $M_{\sum}=120$. The ground truth scatterers are represented by red circles.