Towards generic theory of data compression

In this paper, we consider an extension and rigorous justification of Karhunen-Loeve transform (KLT) which is an optimal technique for data compression. We propose and study the generic KLT which is treated as the best weighted linear estimator of a given rank under the condition that the associated covariance matrix is singular. As a result, the generic KLT is constructed in terms of the pseudo-inverse matrices that imply a development of the special technique. In particular, we give a solution of the new low-rank matrix approximation problem that provides a basis for the generic KLT. Theoretical aspects of the generic KLT are carefully studied.