BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

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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