2-d Fir Wiener Efilter Realizations Using Orthogonal Lattice Structures

The authors propose a new realization algorithm for the 2-D FIR Wiener filters. The reduced-order 2-D orthogonal lattice filter structure is used as its principal component as in the 1-D case. A numerical example is included to verify the formulation. Introduction: One-dimensional (1-D) lattice structures have been wiedly used, as a subsystem, to solve FIR Wiener filtering problem. The lattice realization for the 1-D FIR Wiener is shown in Fig. 8.25 in [1]. The resulting implementation exhibits excellent numerical behavior, and has a modular structure. Recently, an efficient solution was given in [2] for the determination of 2-D orthogonal lattice filters for autoregressive modeling of random fields. In this letter, we shall introduce a simple and computationally efficient algorithm to obtain for 2-D Wiener filtering using the orthogonal backward prediction error fields of the 2-D lattice configuration in [2]. Moreover, it will be shown that the set of normalized versions of the transfer functions of the backward prediction error filters are the 2-D analogues of the single-variable Szegö polynomials discussed in [3]. 2-D FIR Wiener Filter: We suppose that we are given arrays   ) , ( 2 1 k k x  x and   0 , 0 , ) , ( 2 1 2 1    k k k k y y and we are required to find on ) 1 ( ) 1 (     m by n filter array,   ) , ( 2 1 k k a  a for which it is true that the convolution a x  is the best least-square approximation to the output array y [3]. It is well-known that the solution satisfies the following normal equations,