Two-dimensional transform domain adaptive filters based on one-dimensional orthogonal transforms

Recently it has been shown that two-dimensional (2-D) orthogonal transforms can be incorporated into 2-D FIR adaptive filters to improve the conditioning of the input auto correlation matrix eigenvalue spread, thereby improving the convergence rates for 2-D adaptive filters operating in colored noise. This paper considers two approaches to incorporating the transform. The first involves mapping the 2-D input data into a long 1-D vector, and then performing the orthogonalization with a 1-D sliding window orthogonal transform (the FFT is considered in this paper). The second approach performs the transform directly with a 2-D transform algorithm. Experiments demonstrate that similar reductions in eigenvalue spread result with both 1-D and 2-D transformations, both of which can greatly speed convergence in 2-D adaptive filters that have inherently slow convergence rates due to the large number of coefficients required in two dimensions.