A Fast Iterative Thresholding Algorithm for Wavelet-Regularized Deconvolution
C. Vonesch, M. Unser
Proceedings of the SPIE Optics and Photonics 2007 Conference on Mathematical Methods: Wavelet XII, San Diego CA, USA, August 26-29, 2007, vol. 6701, pp. 67010D-1/67010D-5.
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:
- a wavelet-domain Landweber iteration with subband-dependent step-sizes;
- 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.
@INPROCEEDINGS(http://bigwww.epfl.ch/publications/vonesch0703.html,
AUTHOR="Vonesch, C. and Unser, M.",
TITLE="A Fast Iterative Thresholding Algorithm for Wavelet-Regularized
Deconvolution",
BOOKTITLE="Proceedings of the {SPIE} Conference on Mathematical Imaging:
{W}avelet {XII}",
YEAR="2007",
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address="San Diego CA, USA",
month="August 26-29,",
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