Neural model for Karhunen-Loeve transform with application to adaptive image compression

摘要

A neural model approach to perform adaptive calculation of the principal components (eigenvectors) of the covariance matrix of an input sequence is proposed. The algorithm is based on the successive application of the modified Hebbian learning rule proposed by Oja (see J. Math. Biol., vol.15, p.267-73, 1982) on every new covariance matrix that results after calculating the previous eigenvectors. The approach is shown to converge to the next dominant component that is linearly independent of all previously determined eigenvectors. The optimal learning rate is calculated by minimising an error function of the learning rate along the gradient descent direction. The approach is applied to encode grey-level images adaptively, by calculating a limited number of the Karhunen-Loeve transform coefficients that meet a specified performance criterion. The effect of changing the size of the input sequence (number of image subimages), the maximum number of coding coefficients on the bit-rate values, the compression ratio, the signal-to-noise ratio, and the generalisation capability of the model to encode new images are investigated.