Weighted low-rank approximation of general complex matrices and its application in the design of 2-D digital filters

In this brief we present a method for the weighted low-rank approximation of general complex matrices along with an algorithmic development for its computation. The method developed can be viewed as an extension of the conventional singular value decomposition to include a nontrivial weighting matrix in the approximation error measure. It is shown that the optimal rank-K weighted approximation can be achieved by computing K generalized Schmidt pairs and an iterative algorithm is presented to compute them. Application of the proposed algorithm to the design of FIR two-dimensional (2-D) digital filters is described to demonstrate the usefulness of the algorithm proposed.