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• W2110140246 abstract "Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $mtimes n$ measurement matrix $A$ is required to act as a near isometry on the set of all $k$-sparse signals (Restricted Isometry Property or RIP). Although it is known that certain probabilistic processes generate $m times n$ matrices that satisfy RIP with high probability, there is no practical algorithm for verifying whether a given sensing matrix $A$ has this property, crucial for the feasibility of the standard recovery algorithms. In contrast this paper provides simple criteria that guarantee that a deterministic sensing matrix satisfying these criteria acts as a near isometry on an overwhelming majority of $k$-sparse signals; in particular, most such signals have a unique representation in the measurement domain. Probability still plays a critical role, but it enters the signal model rather than the construction of the sensing matrix. We require the columns of the sensing matrix to form a group under pointwise multiplication. The construction allows recovery methods for which the expected performance is sub-linear in $n$, and only quadratic in $m$; the focus on expected performance is more typical of mainstream signal processing than the worst-case analysis that prevails in standard Compressed Sensing. Our framework encompasses many families of deterministic sensing matrices, including those formed from discrete chirps, Delsarte-Goethals codes, and extended BCH codes." @default.
• W2110140246 created "2016-06-24" @default.
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• W2110140246 date "2010-04-01" @default.
• W2110140246 modified "2023-10-02" @default.
• W2110140246 title "Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property" @default.
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• W2110140246 doi "https://doi.org/10.1109/jstsp.2010.2043161" @default.
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