Least $l_{p}$-norm Design of Centro-symmetric 2-D FIR Filters Using a Bi-matrix-based IRLS Algorithm

This paper investigates the least
$l_{p}$
-norm design of two-dimensional (2-D) FIR filters. We first formulate this design as an optimization problem which includes two matrix variables. Then, a bi-matrix-based iterative reweighted least squares (IRLS) algorithm is proposed to solve the problem. The algorithm converts the original problem into a series of weighted least squares (WLS) subproblems and then solves each of them using an efficient bi-matrix-based WLS algorithm. By retaining the natural coefficient matrix form and using appropriate initial points in the bi-matrix-based WLS algorithm, considerable design time is saved. The proposed method exhibits the lower complexity and higher numerical stability compared with existing methods. A design example is provided to illustrate the high computational efficiency and design precision of the proposed method.