Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Deconvolution in optical microscopy
Deconvolution of images and spectra (2nd ed.)
Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics
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The deconvolution of images obtained by means of optical-sectioning widefield fluorescence microscopy, is a relevant problem in biological applications. Several methods have been proposed in the last few years, with different degrees of success, to improve the quality of the images, but the data complexity and the computational cost remain a limiting factor in this problem. We present in this paper an approach to perform the deconvolution of three-dimensional data obtained by fluorescence microscopy (widefield) based on the Projection onto Convex Sets theory. Initially, a brief review of the Projection onto Convex Sets theory is presented. In the restoration algorithm, we combine some constraint sets to restore the out-of-focus blur, to reduce the Poisson noise due to the acquisition process, to retrieve the missing frequencies due to the transfer function of the optical system, and to prevent the regularization errors. Some examples using a phantom and real cell images are presented. The method demonstrates good performance in terms of both visual results and cost-benefit analysis.