Sensitivity Analysis in RIPless Compressed Sensing
North Carolina State University Raleigh United States
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The compressive sensing framework finds a wide range of applications in signal processing and analysis. Within this framework, various methods have been proposed to find a sparse solution x from a linear measurement model y Ax. In practice, the linear model is often an approximation. One basic issue is the robustness of the solution in the presence of uncertainties. In this paper, we are interested in compressive sensing solutions under a general form of measurement y A B x v in which B and v describe modeling and measurement inaccuracies, respectively. We analyze the sensitivity of solutions to infinitesimal modeling error B or measurement inaccuracy v. Exact solutionsare obtained. Specifically, the existence of sensitivity is established and the equation governing the sensitivity is obtained. Worst-case sensitivity bounds are derived. The bounds indicate that sensitivity is linear to measurement in accuracy due to the linearity of the measurement model, and roughly proportional to the solution for modeling error. An approach to sensitivity reduction is subsequently proposed.
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