Aim: The objective of this work is to determine the optimal basis function to perform wavelet analysis for tissue characterization of radio frequency intravascular ultrasound (IVUS) backscattered data. This is the most important step in wavelet analysis as it ensures accurate decomposition of the original signal into the various frequency bands. The criterion to choose the mother wavelet that is best suited to the data depends on the intended application. Wavelet families possessing properties like orthogonality, regularity, stability and admissibility have previously been shown to have application in tissue characterization.
Algorithm: Depending on the usable data bandwidth known from previous studies we decomposed data using a 4-level decomposition scheme. We then calculated Shannon’s entropy for every level and employed “minimum Shannon entropy criterion” to determine the best mother wavelet for signal decomposition. According to this criterion, accurate decomposition is indicated when the total entropy of the daughter (decomposed) levels is lower than the entropy of the parent level.
Analysis and Results: We acquired 40 MHz IVUS data ex-vivo from 10 left anterior descending (LAD) coronary arteries. Data was acquired such that each frame comprised of 256 scanlines. Next, we randomly selected 3 scanlines for each LAD and applied the above-mentioned Shannon entropy criterion for these 30 scanlines. We analyzed 23 mother wavelets from different families. Daubechies 3rd order wavelet accurately decomposes 29/30 scanlines at all levels. Daubechies 6th order wavelet appears optimal for 21/30 scanlines.
Future direction: To obtain more precise signal decomposition, the optimal mother wavelet should be selected at every decomposition level. The best mother wavelet is indicated by the lowest Shannon entropy for that particular level.