An iterative formulation for the least squares approximation of 2-D signals

Construction of an approximate representation of a signal from a weighted sum of prototype waveforms has application to many areas of signal processing including data compression, modeling and analysis. In this paper, we focus on the problem of approximating a two-dimensional (2-D) signal in the least squares sense by a weighted sum of non-orthogonal 2-D prototype waveforms, each of which may be represented by a rank one matrix. We develop an iterative technique for determining the optimal weights, as well as formulating a closed form solution analogous to the normal equations. Convergence of the iterative technique is examined and applications are discussed