A new formulation for the Karhunen-Loeve expansion

The expansion of a random signal into series of functions, with uncorrelated random variables for decomposition coefficients, appears in many aspects of signal processing. These possibilities are offered by the Karhunen-Loeve expansion, This expansion is rarely used in practice, because we are not able to estimate it quickly and efficiently. After recalling the Karhunen-Loeve expansion for a one-dimensional random signal, we describe a new method to approximate the solutions of the Fredholm integral equation. Then, we propose a new formulation of the Karhunen-Loeve expansion. Next, we extend this new formulation to the case of a two-dimensional random signal. An application to image interpolation is proposed where we compare our results with the results obtained using the classical formulation. (C) 1999 Elsevier Science B.V. All rights reserved.