Name
Title | ||
|---|---|---|
A fast thresholded landweber algorithm for wavelet-regularized multidimensional deconvolution. |
Abstract | ||
|---|---|---|
We present a fast variational deconvolution algorithm that minimizes a quadratic data term subject to a regularization on the l(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 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. |
Year | DOI | Venue |
|---|---|---|
2008 | 10.1109/TIP.2008.917103 | IEEE Transactions on Image Processing |
Keywords | Field | DocType |
3-d deconvolution microscopy,wavelet coefficient,fast thresholded landweber algorithm,wavelet-regularized deconvolution,shannon wavelet basis,available method,landweber iteration,typical data set,wavelet-regularized multidimensional deconvolution,fast variational deconvolution algorithm,quadratic data term subject,subband-dependent minimization,convergence,optical imaging,nonlinear,sparsity,wavelets,fluorescence,thresholding,algorithms,deconvolution,iterative,cost function,optical microscopy,fluorescence microscopy,minimisation,multidimensional systems,computational complexity,fast | Shannon wavelet,Blind deconvolution,Landweber iteration,Deconvolution,Artificial intelligence,Wavelet,Mathematical optimization,Pattern recognition,Iterative method,Algorithm,Mathematics,Multidimensional systems,Computational complexity theory | Journal |
Volume | Issue | ISSN |
17 | 4 | 1057-7149 |
Citations | PageRank | References |
41 | 1.89 | 10 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| C. Vonesch | 1 | 224 | 17.13 |
| Unser, M. | 2 | 3438 | 442.40 |