LMS and FRLS 2-D Lattice Filters

Abstract

Abstract In this paper we examine the two-dimensional extensions of some popular adaptive lattice filters. Adaptation is based on either the normalized least mean squares NLMS or the fast recursive least squares algorithms. These algorithms can update the filter coefficients in growing-order form with a moderate computational complexity. Derivation of the 2-D adaptive lattice TDAL-NLMS algorithm is straightforward, ones the 2-D lattice structure has been appropriately defined. The causality is first specified by associating the past 2-D data with the region of support. Then by appropriately defining the partial order of 2-D data, order recursion relations are obtained. In case of the FRLS algorithm we also make use of the 1-D multichannel analogy to derive the order recursion relations and the shift invariance property. The corresponding 2-D prediction problem is solved using the geometrical approaches of the vector space and the orthogonal projection. To compare the performances of these algorithms we consider first an adaptive estimation problem, then the implementation of the 2-D joint process lattice TDJPL filters for adaptive restoration of noisy images. Performance evaluation of LMS and FRLS based noise cancelling filters was done using artificially degraded image data at different signal to noise SNR ratio. The results show that higher improvement with the FRLS lattice filters can be expected .