A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution

We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the 1 -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 waveletregularized deconvolution more widely accessible, even for applications with a strong limitation on computational complexity. We present promising results in 3...

• Type: Journal
• Year: 2008
• Where: TIP
• Authors: Cédric Vonesch, Michael Unser
• Keywords: Fast Variational Deconvolution, Quadratic Data Term, TIP 2008, Wavelet-domain Soft-thresholding Operation