$ l _{ p } $ -Multiresolution Analysis: How to Reduce Ringing and Sparsify the Error

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.


Published in:
IEEE Transactions on Image Processing, 11, 6, 656–669
Year:
2002
Publisher:
IEEE
Keywords:
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 Record created 2005-11-30, last modified 2018-10-07

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