Iteratively reweighted least squares minimization for sparsely corrupted measurements

In this paper we have studied an alternative method of determining a sparse signal from sparsely corrupted measurements using iteratively reweighted least squares (IRLS). It is well known that the theory of compressive sensing (CS) has shown that if a signal having length N has a sparse representation on an orthonormal basis, then it is possible to recover this signal exactly from M≪N measurements. Using l_p minimization with p<;1 instead of l₁ minimization can further decrease the number of measurements. Simulation results are given for different values of p for IRLS and compare it to iteratively reweighted l₁ minimization for sparsely corrupted measurements. Simulations show that fewer measurements are needed for exact reconstruction compared to iteratively reweighted l₁ minimization.