Inverse wavelet transforms for the diagnosis of multiple sclerosis

Multiple sclerosis can be diagnosed using Auditory Evoked Potentials (AEP). Experienced doctors are able to diagnose the sickness with a success rate of 70-82% based on the shape of the principal components of the AEP signal. Wavelets are useful in the analysis of AEP's because, like principal components, they are localized both in time and frequency. We transform the AEP's using different wavelet bases. For each base we select a few coefficients (8 to 20) which discriminate best between sick and healthy subjects. The coefficients are selected using several statistic measures: Student T-test, Kolmogorov-Smirnov, Shannon Entropy. For each wavelet basis, and each selection, the inverse wavelet transform of these coefficients represents a characteristic feature, a "hidden component". For a particular wavelet basis and a selection of the coefficients, we characterize the typical profile of a healthy person, and compare it with the signal of the patient. We can visually detect how far a patient deviates from the standard healthy profile. We quantify the level of abnormality by using the L-1, L-2, L-infinity distances between the two curves. For each component we determine the optimal threshold of the distance to the standard, as the value that insures the maximum number of correct diagnoses.