Proceedings PaperNew wavelet class for fine structure identification
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This paper looks at a novel technique for designing wavelets. Based only on orthonormality, the technique exploits the degrees of freedom in discrete wavelets when the Strang accuracy conditions are abandoned. For an N order matrix, orthonormality guarantees perfect reconstruction when compression is not used, and N/2 equations remain for specifying the new wavelets. Classically the moment conditions provide polynomial accuracy to degree N/2 - 1. By not using the Strang accuracy conditions, reconstruction degrades more quickly for smooth images, but more slowly for irregular images. One dimensional signals are considered, as well as black and white images using a gray scale range of 256 on 128 X 128 pixels. For this discussion, 2 dimensional images are treated by 1 dimensional slicing. The transform process is that of Mallat forward and backward transformations with compression affected in the usual way by coefficient chopping. The novel feature is the departure from Strang's accuracy conditions.