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Convolutions, integral transforms and integral equations by means of the theory of reproducing kernels

Castro L. P., Saitoh S., Tuan N. M.

Opuscula Mathematica

2012

Vol. 32, no. 4

633-646

This paper introduces a general concept of convolutions by means of the theory of reproducing kernels which turns out to be useful for several concrete examples and applications. Consequent properties are exposed (including, in particular, associated norm inequalities).

Reducing the spatial signal correlation for the compression of multilead electrocardiographic recordings

Augustyniak P.

Journal of Medical Informatics & Technologies

2001

Vol. 2, Part. 2

MT107--MT115

This paper is devoted to the transform-based method for decorrelation of simultaneously recorded ECG channels. The conventional 12-lead ECG recordings, due to the non-optimal lead positioning, contain highly redundant data. Eliminating this redundancy yields new possibilities for lossless coding of the ECG, meeting the most severe expectations about the quality of stored signal. The statistical properties featured by uncorrelated signals in the transform domain are more appropriate for the data distribution-based coding techniques. In our work four linear transforms are studied and numerically verified with use of the real ECG data. Additionally, the combination of spatial and temporal decorreation is proposed and discussed as the practical and lossless method for a real implementation. The compression efficiency significantly exceeds the values obtained with use of general-purpose lossless algorithms.