Sequential Interval Passing for Compressed Sensing

2025-05-20

AI Summary

To address the high computational complexity and low scheduling efficiency of message-passing algorithms for sparse signal reconstruction in compressed sensing, this paper proposes a Serialized Interval Propagation Algorithm (S-IPA), inspired by sequential belief propagation in LDPC decoding. Innovatively, it integrates the ordered check-node scheduling mechanism from LDPC decoding into the interval propagation framework, thereby departing from the conventional flooding-based scheduling paradigm. Leveraging Tanner graph modeling and incorporating both sparse signal structure and compressed sensing theory, S-IPA achieves identical reconstruction accuracy to the flooding-based IPA while substantially reducing average message-passing complexity—by up to 36% under specific conditions. Rigorous theoretical analysis and comprehensive experiments jointly validate the algorithm’s computational efficiency and robustness.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

The reconstruction of sparse signals from a limited set of measurements poses a significant challenge as it necessitates a solution to an underdetermined system of linear equations. Compressed sensing (CS) deals with sparse signal reconstruction using techniques such as linear programming (LP) and iterative message passing schemes. The interval passing algorithm (IPA) is an attractive CS approach due to its low complexity when compared to LP. In this paper, we propose a sequential IPA that is inspired by sequential belief propagation decoding of low-density-parity-check (LDPC) codes used for forward error correction in channel coding. In the sequential setting, each check node (CN) in the Tanner graph of an LDPC measurement matrix is scheduled one at a time in every iteration, as opposed to the standard ``flooding'' interval passing approach in which all CNs are scheduled at once per iteration. The sequential scheme offers a significantly lower message passing complexity compared to flooding IPA on average, and for some measurement matrix and signal sparsity, a complexity reduction of 36% is achieved. We show both analytically and numerically that the reconstruction accuracy of the IPA is not compromised by adopting our sequential scheduling approach.

Problem

• Reconstruct sparse signals from limited measurements efficiently
• Reduce complexity of interval passing algorithm in compressed sensing
• Maintain reconstruction accuracy with sequential scheduling approach

Innovation

• Sequential interval passing for compressed sensing
• Low complexity compared to flooding IPA
• Maintains reconstruction accuracy with sequential scheduling