Dr. Cédric Vonesch Profile

Dr. Cédric Vonesch

Postdoctoral Research Associate

Publications (2)

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Proceedings Article | 20 September 2007 Paper

A fast iterative thresholding algorithm for wavelet-regularized deconvolution

Cédric Vonesch, Michael Unser

Proceedings Volume 6701, 67010D (2007) https://doi.org/10.1117/12.733532

KEYWORDS: Wavelets, Deconvolution, Confocal microscopy, Microscopy, Algorithm development, Denoising, Luminescence, Magnetic resonance imaging, Biomedical optics, Surgery

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We present an iterative deconvolution algorithm that minimizes a functional with a non-quadratic wavelet-domain regularization term. Our approach is to introduce subband-dependent parameters into the bound optimization framework of Daubechies et al.; it is sufficiently general to cover arbitrary choices of wavelet bases (non-orthonormal or redundant). The resulting procedure alternates between the following two steps: 1. a wavelet-domain Landweber iteration with subband-dependent step-sizes; 2. a denoising operation with subband-dependent thresholding functions. The subband-dependent parameters allow for a substantial convergence acceleration compared to the existing optimization method. Numerical experiments demonstrate a potential speed increase of more than one order of magnitude. This makes our "fast thresholded Landweber algorithm" a viable alternative for the deconvolution of large data sets. In particular, we present one of the first applications of wavelet-regularized deconvolution to 3D fluorescence microscopy.

Proceedings Article | 17 September 2005 Paper

Generalized biorthogonal Daubechies wavelets

Cedric Vonesch, Thierry Blu, Michael Unser

Proceedings Volume 5914, 59141X (2005) https://doi.org/10.1117/12.616536

KEYWORDS: Wavelets, Optical filters, Image processing, Image filtering, Wavelet transforms, Biological research, Chemical elements, Biomedical optics, Electronic filtering, Modulation

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We propose a generalization of the Cohen-Daubechies-Feauveau (CDF) and 9/7 biorthogonal wavelet families. This is done within the framework of non-stationary multiresolution analysis, which involves a sequence of embedded approximation spaces generated by scaling functions that are not necessarily dilates of one another. We consider a dual pair of such multiresolutions, where the scaling functions at a given scale are mutually biorthogonal with respect to translation. Also, they must have the shortest-possible support while reproducing a given set of exponential polynomials. This constitutes a generalization of the standard polynomial reproduction property. The corresponding refinement filters are derived from the ones that were studied by Dyn et al. in the framework of non-stationary subdivision schemes. By using different factorizations of these filters, we obtain a general family of compactly supported dual wavelet bases of L₂. In particular, if the exponential parameters are all zero, one retrieves the standard CDF B-spline wavelets and the 9/7 wavelets. Our generalized description yields equivalent constructions for E-spline wavelets. A fast filterbank implementation of the corresponding wavelet transform follows naturally; it is similar to Mallat's algorithm, except that the filters are now scale-dependent. This new scheme offers high flexibility and is tunable to the spectral characteristics of a wide class of signals. In particular, it is possible to obtain symmetric basis functions that are well-suited for image processing.

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