ASSESSMENT OF THE DIAGNOSTIC SIGNIFICANCE OF SPARSE REPRESENTATION COEFFICIENTS OF SPHYGMOGRAM SIGNALS IN PSYCHOPHYSIOLOGICAL TELEMONITORING SYSTEMS

Abstract

The paper addresses the quantitative assessment of the diagnostic significance of individual coefficients of the sparse representation of a sphygmogram, a signal carrying information on the psychophysiological state in post-traumatic stress disorder. Experimental data were obtained on a measuring channel with quartz piezoresonance applanation sensors; the sample comprises thirteen records of about 14.8 minutes total duration in two sampling formats. Spectral analysis based on the 99 % power containment bandwidth showed that the actual signal bandwidth lies between 3.5 and 11.6 Hz at a sampling rate of 500 Hz, which corresponds to a digitization redundancy of 21.6 to 70.6 times. This redundancy is removed by a sparse representation based on the discrete cosine transform with a compression ratio of about 31, lowering the link load from about 6 to 0.19 kbit/s per channel. A measure termed the diagnostic weight of a coefficient is introduced and defined as the normalized weighted sum of the sensitivities of the positions of the fiducial points of the pulse contour to a perturbation of that coefficient; the sensitivities are evaluated by central differences with sub-sample localization of the systolic peak, the dicrotic notch and the interbeat interval. A computational experiment showed that the energy and diagnostic weight profiles are oppositely directed: about 94 % of the total diagnostic weight is carried by coefficients with indices of eight and above, the sensitivity of the dicrotic notch peaking near the twentyeighth coefficient, whereas the first eight coefficients, which contain the predominant part of the frame energy, provide less than 6 % of the diagnostic weight. On this basis a diagnostic integrity criterion and its measurable form, the deviation of the SDNN index, are formulated.