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# lp-Multiresolution Analysis: How to Reduce Ringing and Sparsify the Error

## A. Muñoz Barrutia, T. Blu, M. Unser

### IEEE Transactions on Image Processing, vol. 11, no. 6, pp. 656-669, June 2002.

We propose to design the reduction operator of an image pyramid so as to minimize the approximation error in the lp-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.

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AUTHOR="Mu{\~{n}}oz Barrutia, A. and Blu, T. and Unser, M.",
TITLE="{$\ell_{p}$}-{M}ultiresolution Analysis: {H}ow to Reduce
Ringing and Sparsify the Error",
JOURNAL="{IEEE} Transactions on Image Processing",
YEAR="2002",
volume="11",
number="6",
pages="656--669",
month="June",
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