An adaptive procedure for signal representation is proposed. The representation is built up through functions (atoms) selected from a redundant family (dictionary). At each iteration the algorithm gives rise to an approximation of a given signal, which is guaranteed a) to be the orthogonal projection of a signal onto the subspace generated by the selected atoms, and b) to minimise the norm of the corresponding residual error. The approach is termed Optimised Orthogonal Matching Pursuit because it improves upon the earlier proposed Matching Pursuit and Orthogonal Matching Pursuit approaches.

An effective method for compression of ECG signals, which falls within the transform lossy compression category, is proposed. The transformation is realized by a fast wavelet transform. The effectiveness of the approach, in relation to the simplicity and speed of its implementation, is a consequence of the efficient storage of the outputs of the algorithm which is realized in compressed Hierarchical Data Format. The compression performance is tested on the MIT-BIH Arrhythmia database producing compression results which largely improve upon recently reported benchmarks on the same database. For a distortion corresponding to a percentage root-mean-square difference (PRD) of 0.53, in mean value, the achieved average compression ratio is 23.17 with quality score of 43.93. For a mean value of PRD up to 1.71 the compression ratio increases up to 62.5. The compression of a 30 min record is realized in an average time of 0.14 s. The insignificant delay for the compression process, together with the high compression ratio achieved at low level distortion and the negligible time for the signal recovery, uphold the suitability of the technique for supporting distant clinical health care.

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A recursive approach for shrinking coefficients of an atomic decomposition is proposed. The corresponding algorithm evolves so as to provide at each iteration a) the orthogonal projection of a signal onto a reduced subspace and b) the index of the coefficient to be disregarded in order to construct a coarser approximation minimizing the norm of the residual error.

A method for data subset selection, which is based on the q=1 / 2 maximum information measure formalism, is proposed. The method evolves iteratively by selecting, at each iteration, the measure yielding a q=1 / 2 distribution capable of making predictions minimizing the Euclidean distance to the available data.