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
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
IEEE Transactions on Pattern Analysis and Machine Intelligence
Exploiting fast hardware floating point in high precision computation
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
TV Based Image Restoration with Local Constraints
Journal of Scientific Computing
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Tube Methods for BV Regularization
Journal of Mathematical Imaging and Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Second-order Cone Programming Methods for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Introduction to the cell multiprocessor
IBM Journal of Research and Development - POWER5 and packaging
3-D image reconstruction from exponential X-ray projections using Neumann series
ICASSP '01 Proceedings of the Acoustics, Speech, and Signal Processing, 2001. on IEEE International Conference - Volume 03
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We present an iterative framework for robustly solving large inverse problems arising in imaging using only single-precision (or other reduced-precision) arithmetic, which allows the use of high-density processors (e.g. Cell BE and Graphics Processing Units). Robustness here means linear-convergence even for large problems (billions of variables), with high levels of noise (signal-to-noise levels less than unity). This framework handles problems formulated as quadratic and general non-linear minimization problems. Sparse and dense problems can be treated, as long as there are efficient parallelizable matrix-vector products for the transformations involved. Outer iterations correspond to approximate solutions of a quadratic minimization problem, using a single Newton step. Inner iterations correspond to the estimation of the step via truncated Neumann series or minimax polynomial approximations built from operator splittings. Given the convergence analysis, this approach can also be used in embedded environments with fixed computation budgets, or certification requirements, like real-time medical imaging. We describe a benchmark problem from MRI, and a series of penalty functions suited to this framework. An important family of such penalties is motivated by both bilateral filtering and total variation, and we show how they can be optimized using linear programming. We also discuss penalties designed to segment images, and use different types of a priori knowledge, and show numerically that the different penalties are effective when used in combination.