Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Mathematical methods in image reconstruction
Mathematical methods in image reconstruction
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
A Variational Approach to Reconstructing Images Corrupted by Poisson Noise
Journal of Mathematical Imaging and Vision
Parallel Medical Image Reconstruction: From Graphics Processors to Grids
PaCT '09 Proceedings of the 10th International Conference on Parallel Computing Technologies
Primal and Dual Bregman Methods with Application to Optical Nanoscopy
International Journal of Computer Vision
Deconvolving Poissonian images by a novel hybrid variational model
Journal of Visual Communication and Image Representation
Parallel medical image reconstruction: from graphics processing units (GPU) to Grids
The Journal of Supercomputing
A Novel Sparsity Reconstruction Method from Poisson Data for 3D Bioluminescence Tomography
Journal of Scientific Computing
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Measurements in nanoscopic imaging suffer from blurring effects concerning different point spread functions (PSF). Some apparatus even have PSFs that are locally dependent on phase shifts. Additionally, raw data are affected by Poisson noise resulting from laser sampling and "photon counts" in fluorescence microscopy. In these applications standard reconstruction methods (EM, filtered backprojection) deliver unsatisfactory and noisy results. Starting from a statistical modeling in terms of a MAP likelihood estimation we combine the iterative EM algorithm with TV regularization techniques to make an efficient use of a-priori information. Typically, TV-based methods deliver reconstructed cartoon-images suffering from contrast reduction. We propose an extension to EM-TV, based on Bregman iterations and inverse scale space methods, in order to obtain improved imaging results by simultaneous contrast enhancement. We illustrate our techniques by synthetic and experimental biological data.