ADAPTED WAVE-FORM ANALYSIS AS A TOOL FOR MODELING, FEATURE-EXTRACTION, AND DENOISING

We describe the development of adapted waveform analysis (AWA) as a to ol for fast processing of the various identification tasks involved in medical diagnostics and automatic target recognition. Such tasks cons ist of steps: representing the signal as a superposition of component functions, choosing to retain some of the components and discard the o thers, then reconstructing a new, approximate signal from what was kep t. AWA provides tools for each of these steps, accelerating the decomp osition and reconstruction computations, providing new functions for a nalysis and modeling, and extracting new features for recognition and classification. AWA extends Fourier analysis by providing new librarie s of standard waveforms with properties akin to windowed sines and cos ines, and it extends principal component analysis and eigen-function e xpansions by adapting the standard functions to individual operators. The cost of representing a function can be measured by how many compon ents must be superposed to obtain a desired degree of approximation, a nd this cost can be minimized by a fast search through the library of representations. The analysis can be iterated to sift coherent signals from noise. We consider applications to signal and image compression, feature detection, and medical image denoising.