A Fast Iterative Thresholding Algorithm for Wavelet-Regularized Deconvolution

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.

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Proceedings of the SPIE Conference on Mathematical Imaging: Wavelet XII, 1, San Diego CA, USA, 67010D-1–67010D-5

 Record created 2015-09-18, last modified 2018-03-17

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