Iteratively Reweighted Least Squares by Diagonal Regularization

Abstract

We consider a sparse signal reconstruction problem. The signal can be captured into a vector whose elements can be zeros. Standing for iteratively reweighted least squares, IRLS is a technique designed for extracting the signal vector from the available observation data. A new algorithm based on the IRLS is proposed by using diagonal regularization for sparse image reconstruction. A closed-form solution of the IRLS minimization is derived and then we have developed a variational IRLS algorithm based on the available solution. Since the matrix inverse in the iterative computation can be subject to ill condition, we apply a diagonal regularization to such a problem. Numerical simulation is conducted to illustrate the performance of the new IRLS with the comparison to the former IRLS algorithm. Numerical results indicate that the new IRLS method provides lower signal recovery error than the conventional IRLS approach at the expense of more complexity in terms of more computational time.