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.
authors.affiliation: Biomedical Imaging Group, Lausanne, Switzerland. cedric.vonesch@epfl.ch
authors.forename: C
authors.initials: C
authors.lastname: Vonesch
authors.forename: M
authors.initials: M
authors.lastname: Unser
mesh_terms: D000465:Algorithms; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D008856:Microscopy, Fluorescence / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D012815:Signal Processing, Computer-Assisted; D013997:Time Factors