Compressive Sensing: A Survey on Theory, Algorithms and Applications

Abstract

Compressive Sensing (CS) is an advanced signal acquisition paradigm that enables the reconstruction of sparse or compressible signals from far fewer samples than required by classical Nyquist–Shannon sampling theory. This paper provides a comprehensive overview of the fundamental principles, algorithmic developments, and practical applications of CS. It begins by examining the core concept of sparsity, which forms the theoretical foundation for efficient signal representation in suitable transform domains. The paper then discusses the role of sensing matrices and their influence on measurement stability, robustness, and feasibility in real-world systems. Various reconstruction algorithms including optimization-based, greedy, and iterative thresholding techniques are analysed with respect to their computational complexity and reconstruction performance. Additionally, the paper highlights factors affecting CS performance, such as sparsity level, noise tolerance, and algorithmic scalability. Beyond theoretical insights, this work explores major application areas where CS has demonstrated significant impact, including medical imaging, wireless communications, radar systems, remote sensing, and low-power Internet-of-Things (IoT) devices. Recent advancements integrating deep learning with CS frameworks are also reviewed, underscoring the growing shift toward data-driven reconstruction methods. Overall, this paper aims to provide a unified understanding of CS, emphasizing its relevance, challenges, and emerging research directions in modern signal processing.