用少量测量重建稀疏信号，突破传统采样极限。
Compressed Sensing: Mathematical Foundations, Implementation, and Advanced Optimization Techniques
- 基于稀疏性假设，通过优化求解实现信号压缩重建。
- 在真实信号上验证了低采样率下的高精度重构能力。
- 适合信号处理、医学成像等需高效采样的场景。
压缩感知是一种信号处理技术，可从少量测量中重构信号。其核心思想是：许多现实信号本质上稀疏，可在另一空间中用极少成分高效表示。本文探讨压缩感知的数学原理、逻辑基础及潜在缺陷，并将其应用于真实信号。通过优化算法，在远低于奈奎斯特采样率的条件下实现了高质量信号重构，验证了该方法在降低数据采集成本方面的有效性。
原文摘要 · Abstract (English)
Compressed sensing is a signal processing technique that allows for the reconstruction of a signal from a small set of measurements. The key idea behind compressed sensing is that many real-world signals are inherently sparse, meaning that they can be efficiently represented in a different space with only a few components compared to their original space representation. In this paper we will explore the mathematical formulation behind compressed sensing, its logic and pathologies, and apply compressed sensing to real world signals.
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