An Approximation of FOCUSS Mean Squared Error

Abstract

FOCal Underdetermined System Solver (FOCUSS) is an estimation method for finding a n unknown vector that potentially has a sparse structure. The application of this estimation technique can be found in several areas, e.g., sparse signal recovery in image reconstruction, wireless communications, etc. The convergence analysis performance and order of convergence of this technique are the focuses of this study. In this work, we investigate its estimation error performance on the second order, in terms of error variance or mean squared error. Since the computation in this algorithm is nonlinear, an exact form of the error performance seems infeasible. Therefore, we derive a closed-form expression that approximates the mean squared error of the FOCUSS. Numerical simulation was conducted to illustrate the closeness of our prediction to the real estimation error.