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lp-multiresolution analysis:: How to reduce ringing and sparsify the error
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DOI：10.1109/TIP.2002.1014997.png)
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Abstract
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We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the l(p)-sense (not restricted to the usual p = 2), where p can take non-integer values. The underlying image model is specified using shift-invariant basis functions, such as B-splines. The solution is well-defined and determined by an iterative optimization algorithm based on digital filtering. Its convergence is accelerated by the use of first and second order derivatives. For p close to 1, we show that the ringing is reduced and that the histogram of the detail image is sparse as compared with the standard case, where p = 2.
Keywords:
Banach spaces
multiresolution
non-Euclidean norms
splines
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