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
Convex Optimization
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Multiplicative Updates for Nonnegative Quadratic Programming
Neural Computation
Reconstructing specimens using DIC microscope images
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Understanding the optics to aid microscopy image segmentation
MICCAI'10 Proceedings of the 13th international conference on Medical image computing and computer-assisted intervention: Part I
Restoring DIC microscopy images from multiple shear directions
IPMI'11 Proceedings of the 22nd international conference on Information processing in medical imaging
Analysis of performance of palmprint matching with enforced sparsity
Digital Signal Processing
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Image segmentation in microscopy, especially in interference-based optical microscopy modalities, is notoriously challenging due to inherent optical artifacts. We propose a general algebraic framework for preconditioning microscopy images. It transforms an image that is unsuitable for direct analysis into an image that can be effortlessly segmented using global thresholding. We formulate preconditioning as the minimization of nonnegative-constrained convex objective functions with smoothness and sparseness-promoting regularization. We propose efficient numerical algorithms for optimizing the objective functions. The algorithms were extensively validated on simulated differential interference (DIC) microscopy images and challenging real DIC images of cell populations. With preconditioning, we achieved unprecedented segmentation accuracy of 97.9% for CNS stem cells, and 93.4% for human red blood cells in challenging images.