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Fast Wavelet Decomposition of Linear Operators through Product-Convolution Expansions

Paul Escande 1, 2 Pierre Weiss 3, 2
IMT - Institut de Mathématiques de Toulouse UMR5219, ITAV - Institut des Technologies Avancées en sciences du Vivant
Abstract : Wavelet decompositions of integral operators have proven their efficiency in reducing computing times for many problems, ranging from the simulation of waves or fluids to the resolution of inverse problems in imaging. Unfortunately, computing the decomposition is itself a hard problem which is oftentimes out of reach for large scale problems. The objective of this work is to design fast decomposition algorithms based on another representation called product-convolution expansion. This decomposition can be evaluated efficiently assuming that a few impulse responses of the operator are available, but it is usually less efficient than the wavelet decomposition when incorporated in iterative methods. The proposed decomposition algorithms, run in quasi-linear time and we provide some numerical experiments to assess its performance for an imaging problem involving space varying blurs.
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Contributor : Paul Escande <>
Submitted on : Monday, July 27, 2020 - 11:54:53 AM
Last modification on : Saturday, August 1, 2020 - 11:08:13 AM


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  • HAL Id : hal-02612434, version 2
  • ARXIV : 2005.09870


Paul Escande, Pierre Weiss. Fast Wavelet Decomposition of Linear Operators through Product-Convolution Expansions. 2020. ⟨hal-02612434v2⟩



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