2 FAST APPROXIMATE WAVELET ALGORITHMS FOR IMAGE-PROCESSING, CLASSIFICATION, AND RECOGNITION

We use large libraries of template waveforms with remarkable orthogonality properties to recast the relatively complex principal orthogonal decomposition (POD) into an optimization problem with a fast solution algorithm. Then it becomes practical to use POD to solve two related problems: recognizing or classifying images, and inverting a complicated map from a low-dimensional configuration space to a high-dimensional measurement space. In the case where the number N of pixels or measurements is more than 1000 or so, the classical O(N3) POD algorithm becomes very costly, but it can be replaced with an approximate best-basis method that has complexity O(N2 logN). A variation of POD can also be used to compute an approximate Jacobian for the complicated map.