MultiScale WAvelet Representation and its application to signal classification

The theoretical development of a novel technique for the representation of one and two-dimensional discrete signals, called the MultiScale WAvelet Representation (MSWAR), is described. In essence, this technique is the generalization of Mallat's MultiResolution WAvelet Representation (MRWAR). It is shown that the MS WAR, in addition to possessing aU of the properties of MRWAR, also possesses the property of shift-invariance. Having this property facilitates the utilization of MSWAR in such tasks as signal classification. The computational efficiency of MSWAR is proved to compare favorably to an alternative approach for generating shift-invariant wavelet coefficients. In fact, it is shown that the number of operations required by MSWAR is fewer by a factor of N/2^{j for 1-D, and (N/2j)2 for 2-D discrete signals; (N) and (j) denote the support of the input signal and the index of the scale reduction, respectively. Other pertinent attributes of MSWAR are stated and proved to exist theoretically. The development of a technique for the classification of 1-D and 2-D discrete signals is also described. The effectiveness of MSWAR is evaluated through its utilization in this classification technique. The necessary measures of similarity and the corresponding decision rules are derived theoretically and experimentally. The design and development of the proposed classifier is accomplished assuming that the observed signal may be subjected to five types of deformities. These deformities are categorized as a shift, a DC offset, linear transformation, additive Gaussian noise, and a local defect. The latter four are all combined with a shift. Furthermore, conditions under which a correct classification can be expected for each type of deformity are discussed. Preliminary results obtained by applying the proposed technique to the classification of 2-D objects embedded in constant intensity as well as textured backgrounds are included. These results demonstrate the effectiveness of MSWAR as a representation tool. Two other signal representation methodologies, fractal and spatial-frequency analysis, are also studied. In this work, several representation techniques from each method ology are implemented and evaluated. Furthermore, theoretical modifications are introduced to enhance the utilization of these techniques as feature extractors in a classification system.}