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 $ \ell ^{ 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.


Published in:
IEEE Transactions on Image Processing, 17, 4, 539–549
Year:
2008
Publisher:
IEEE
Keywords:
Other identifiers:
Laboratories:




 Record created 2008-12-10, last modified 2018-03-17

n/a:
Download fulltextPDF
External links:
Download fulltextURL
Download fulltextURL
Rate this document:

Rate this document:
1
2
3
 
(Not yet reviewed)