# Performance Analysis of Compressed Sensing Given Insufficient Random Measurements

• Rateb, Ahmad M. (Telecommunications Research Group, Faculty of Electrical Engineering, Universiti Teknologi Malaysia) ;
• Syed-Yusof, Sharifah Kamilah (Telecommunications Research Group, Faculty of Electrical Engineering, Universiti Teknologi Malaysia)
• Received : 2012.05.22
• Accepted : 2012.10.26
• Published : 2013.04.01

#### Abstract

Most of the literature on compressed sensing has not paid enough attention to scenarios in which the number of acquired measurements is insufficient to satisfy minimal exact reconstruction requirements. In practice, encountering such scenarios is highly likely, either intentionally or unintentionally, that is, due to high sensing cost or to the lack of knowledge of signal properties. We analyze signal reconstruction performance in this setting. The main result is an expression of the reconstruction error as a function of the number of acquired measurements.

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