BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

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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