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Theoretical framework demonstrates the construction of compactly supported orthonormal wavelets with arbitrary regularity, establishing a linear relationship between smoothness and support width.
We construct orthonormal bases of compactly supported wavelets, with arbitrarily high regularity. The order of regularity increases linearly with the support width. We start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction. The construction then follows from a synthesis of these different approaches.
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Ingrid Daubechies (1988) studied this question.
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