[Paper Review] On some common compressive sensing recovery algorithms and applications - Review paper

Andjela Draganić, Irena Orović+1 more|arXiv (Cornell University)|Apr 21, 2017

Sparse and Compressive Sensing Techniques65 references21 citations

TL;DR

This review paper provides a comprehensive analysis of compressive sensing (CS) recovery algorithms and their applications in signal processing. It explains how CS enables accurate signal reconstruction from sub-Nyquist sampling rates using sparsity-based optimization techniques, with key contributions including a systematic comparison of major recovery algorithms and their real-world performance across diverse signal types such as audio, images, and biomedical signals.

ABSTRACT

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensive growth of signal processing possibilities. Hence, some of the existing practical applications assuming different types of signals in real-world scenarios are described and analyzed as well.

Motivation & Objective

• To provide a structured overview of the theoretical foundations and practical implementations of compressive sensing in signal acquisition.
• To analyze and compare the performance of commonly used compressive sensing recovery algorithms across different signal types.
• To examine real-world applications of CS in fields such as biomedical imaging, audio processing, and wireless communications.
• To identify strengths, limitations, and computational trade-offs of existing recovery algorithms.
• To guide researchers and practitioners in selecting appropriate CS methods based on signal characteristics and application constraints.

Proposed method

• The paper reviews the mathematical framework of compressive sensing, emphasizing signal sparsity and incoherent sampling matrices.
• It evaluates major recovery algorithms including Basis Pursuit, Orthogonal Matching Pursuit (OMP), CoSaMP, and SPGL1, detailing their algorithmic structure and convergence behavior.
• The authors analyze reconstruction performance using metrics such as mean squared error (MSE) and signal-to-noise ratio (SNR), comparing results across synthetic and real data.
• The paper discusses the role of optimization techniques such as L1-minimization and greedy pursuit strategies in enabling stable signal recovery from undersampled measurements.
• It presents case studies on applications in ECG, MRI, and radar, illustrating how CS reduces sampling requirements while preserving signal fidelity.
• The review includes a comparative discussion of computational complexity, convergence speed, and robustness to noise across different algorithms.

Experimental results

Research questions

• RQ1 How do different compressive sensing recovery algorithms compare in terms of reconstruction accuracy and computational efficiency?
• RQ2 What are the key factors influencing the performance of CS algorithms in real-world signal reconstruction tasks?
• RQ3 In which practical signal processing applications does compressive sensing offer measurable advantages over traditional sampling methods?
• RQ4 How does signal sparsity and measurement matrix design affect the success of CS-based reconstruction?
• RQ5 What are the limitations of current CS algorithms when applied to non-sparse or noisy signals?

Key findings

• Basis Pursuit and L1-minimization-based methods generally achieve higher reconstruction accuracy but at the cost of higher computational complexity.
• Greedy algorithms like OMP and CoSaMP offer faster convergence and are more suitable for real-time applications, especially with sparse signals.
• CoSaMP and SPGL1 demonstrate robust performance across a wide range of signal-to-noise ratios and sampling rates, outperforming standard OMP in noisy environments.
• In biomedical applications such as ECG and MRI, compressive sensing reduces data acquisition time by up to 70% while maintaining diagnostic-quality reconstruction.
• The choice of sensing matrix significantly impacts reconstruction success, with Gaussian and Bernoulli matrices showing strong performance across diverse signal types.
• The paper confirms that CS is most effective when signals exhibit inherent sparsity in a known transform domain, such as Fourier or wavelet representations.