A fast multilevel algorithm for wavelet-regularized image restoration
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
A SURE approach for digital signal/image deconvolution problems
IEEE Transactions on Signal Processing
A subband adaptive iterative shrinkage/thresholding algorithm
IEEE Transactions on Signal Processing
Block Based Deconvolution Algorithm Using Spline Wavelet Packets
Journal of Mathematical Imaging and Vision
Image deconvolution using incomplete Fourier measurements
International Journal of Imaging Systems and Technology
Coupling Image Restoration and Segmentation: A Generalized Linear Model/Bregman Perspective
International Journal of Computer Vision
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We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the -norm of the wavelet coefficients of the solution. Previously available methods have essentially consisted in alternating between a Landweber iteration and a wavelet-domain soft-thresholding operation. While having the advantage of simplicity, they are known to converge slowly. By expressing the cost functional in a Shannon wavelet basis, we are able to decompose the problem into a series of subband-dependent minimizations. In particular, this allows for larger (subband-dependent) step sizes and threshold levels than the previous method. This improves the convergence properties of the algorithm significantly. We demonstrate a speed-up of one order of magnitude in practical situations. This makes wavelet-regularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3-D deconvolution microscopy, where the size of typical data sets does not permit more than a few tens of iterations.