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Fast Wavelet-based Deconvolution of Fluorescence Micrographs

C. Vonesch, M. Unser

Proceedings of the 2007 Annual Meeting of the Swiss Society of Biomedical Engineering (SSBE'07), Neuchâtel NE, Swiss Confederation, September 13-14, 2007, pp. 6-7.


Modern biology depends crucially on two research modalities [1]: fluorescent markers and high-resolution microscopy. The need to track biological compounds down to molecular scales poses considerable challenges to the instrumentation. In this context, deconvolution microscopy is becoming a key-element in the experimental process.

Wavelet-based deconvolution methods are a recent and promising development [2]. However, they have not been considered as a serious alternative to existing deconvolution methods so far, mainly due to their computational cost. Our contribution shows the feasibility of wavelet-regularized deconvolution at a cost comparable to a few tens of iterations of a standard algorithm. This can be considered the present tolerance limit, given the size of usual biomicroscopy data sets.

Wavelets have proven to be a very successful tool for the estimation of signals that are corrupted by noise. Denoising methods based on a thresholding of the wavelet coefficients were first introduced and justified in a statistical framework [3]. They were later reinterpreted in a variational framework [4], which can be extended to more general inverse problems such as deconvolution.

References

  1. C. Vonesch, F. Aguet, J.-L. Vonesch, M. Unser, "The Colored Revolution of Bioimaging," IEEE Signal Processing Magazine, vol. 23, no. 3, pp. 20-31, May 2006.

  2. M.A.T. Figueiredo, R.D. Nowak, "An EM Algorithm for Wavelet-based Image Restoration," IEEE Transactions on Image Processing, vol. 12, no. 8, pp. 906-916, August 2003.

  3. D.L. Donoho, I.M. Johnstone, "Ideal Spatial Adaptation by Wavelet Shrinkage," Biometrika, vol. 81, no. 3, pp. 425-455, August 1994.

  4. A. Chambolle, R.A. DeVore, N.-y. Lee, B.J. Lucier, "Nonlinear Wavelet Image Processing: Variational Problems, Compression, and Noise Removal through Wavelet Shrinkage," IEEE Transactions on Image Processing, vol. 7, no. 3, pp. 319-335, March 1998.

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© 2007 SSBE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from SSBE. This material is presented to ensure timely dissemination of scholarly and technical work. Copyright and all rights therein are retained by authors or by other copyright holders. All persons copying this information are expected to adhere to the terms and constraints invoked by each author's copyright. In most cases, these works may not be reposted without the explicit permission of the copyright holder.
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