An adaptive lapped biorthogonal transform and its application in orientation adaptive image coding
Signal Processing - Image and Video Coding beyond Standards
Constructing fixed rank optimal estimators with method of best recurrent approximations
Journal of Multivariate Analysis
Relative Karhunen-Loeve Transform Method for Pattern Recognition
ICPR '98 Proceedings of the 14th International Conference on Pattern Recognition-Volume 2 - Volume 2
Kernel projection classifiers with suppressing features of other classes
Neural Computation
Optimal multilinear estimation of a random vector under constraints of causality and limited memory
Computational Statistics & Data Analysis
Towards theory of generic Principal Component Analysis
Journal of Multivariate Analysis
Stochastic MV-PURE estimator: robust reduced-rank estimator for stochastic linear model
IEEE Transactions on Signal Processing
Pattern recognition by kernel Wiener filter
SPPRA '08 Proceedings of the Fifth IASTED International Conference on Signal Processing, Pattern Recognition and Applications
Recursive implementation of the distributed Karhunen-Loève transform
IEEE Transactions on Signal Processing
Kernel Wiener filter and its application to pattern recognition
IEEE Transactions on Neural Networks
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part II
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The Karhunen-Loeve transform (KLT) provides the best approximation for a stochastic signal under the condition that its rank is fixed. It has been successfully used for data compression in communication. However, since the KLT does not consider noise, its ability to suppress noise is very poor. For the optimum linear data compression in the presence of noise, we propose the concept of a relative Karhunen-Loeve transform (RKLT). It minimizes the sum of the mean squared error between the original signal and its approximation and the mean squared error caused by a noise under the condition that its rank is fixed. We also provide another type of RKLT. It minimizes the same sum under the condition that its rank is not greater than a fixed integer. Since the former type of RKLT does not always exist, we provide a necessary and sufficient condition under which it does exist. We also provide their general forms. The advantage of RKLTs is illustrated through computer simulations