Adaptive LMS discrete 2-D orthogonal transforms

Two-dimensional discrete orthogonal transforms (2-D DOT) are widely used in many communications and signal processing applications. This paper presents and analyses the general relation between such transforms and the 2-D LMS adaptive algorithm. It is shown that, by proper choice of the adaptation constant, the 2-D LMS provides an exact estimate to the forward as well as backward transform coefficients employing any set of 2-D DOT. The 2-D LMS DOT is modular and allows concurrent computation for the transform coefficients and therefore has the potential for fast parallel computations and VLSI implementation. An efficient 2-D threshold LMS DOT algorithm that is robust against impulsive noise is also presented. The efficiency of the 2-D LMS DOT against roundoff errors is demonstrated. Simulation experiments are conducted to justify the analysis and algorithms introduced.