Sensitivity Analysis of Compressive Sensing Solutions - Dai, Liyi (Frontiers in Robotics and AI, 2015)
The compressive sensing framework □nds a wide range of applications in signal processing, data analysis and fusion. Within this framework, various methods have been proposed to □nd 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 in□nitesimal modeling error B or measurement inaccuracy v. Exact solutions are obtained. Speci□cally, 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 inaccuracy 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.