The existence and uniqueness conditions are a prerequisite to ensure the reliable reconstruction of sparse signals from reduced sets of measurements within the compressive sensing (CS) paradigm. However, despite their underpinning role in practical applications, the existing uniqueness relations are either computationally prohibitive to implement [the restricted isometry property (RIP)] or involve mathematical tools that are beyond the standard background of engineering graduates (the coherence index). This may introduce conceptual and computational obstacles in the development of engineering intuition, design of suboptimal practical solutions, and understanding of theoretical and practical limitations of the CS framework.

中文翻译：

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揭秘压缩感知中的相干指数 [讲座笔记]


存在性和唯一性条件是确保压缩感知（CS）范例中从减少的测量集可靠地重建稀疏信号的先决条件。然而，尽管它们在实际应用中发挥着基础作用，但现有的唯一性关系要么在计算上无法实现[受限等距属性（RIP）]，要么涉及超出工程毕业生标准背景的数学工具（相干指数）。这可能会在工程直觉的发展、次优实际解决方案的设计以及对 CS 框架的理论和实践局限性的理解方面引入概念和计算障碍。