Feature extraction from acoustic backscattered signals using wavelet dictionaries
Discrimination problems differ in nature from reconstruction tasks. While in reconstruction, it is the mean squared error that is often used to measure the quality of the scheme, classification requires a different measure which often is not related to the former. The discrimination power of a certain basis or a set of basis function is not necessarily connected to the quality of reconstruction associated with this set. Furthermore, the degree of relevance of the orthonormality constraint to the quality of the discrimination is questionable. For example, linear discriminant analysis [1] searches for linear projections which maximize the between-class variance divided by the sum of within-class variance. Such projections do not necessarily coincide with the principal components of the data which are the directions that optimize MSE reconstruction. A successful approach to discrimination is based on an appropriate preprocessing to create an efficient signal representation, which then leads to an efficient dimensionality reduction. The next step is again some combination of feature extraction and classification. In this paper we briefly review several methods for finding data representation via optimal decomposition of wavelet basis functions and discuss their reconstruction properties. We then discuss some signal decomposition methods for the purpose of discrimination. This is followed by a brief discussion on a combination of feature extraction and classification scheme and with discrimination results on two acoustic data-sets.