Matrix analysis
Visual reconstruction
Scale-Space and Edge Detection Using Anisotropic Diffusion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Constrained Restoration and the Recovery of Discontinuities
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
Markov random field modeling in computer vision
Markov random field modeling in computer vision
Iterative methods for total variation denoising
SIAM Journal on Scientific Computing - Special issue on iterative methods in numerical linear algebra; selected papers from the Colorado conference
Journal of Mathematical Imaging and Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
IEEE Transactions on Image Processing
ML parameter estimation for Markov random fields with applications to Bayesian tomography
IEEE Transactions on Image Processing
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This is a theoretical study on the minimizers of cost-functions composed of an l2 data-fidelity term and a possibly nonsmooth or nonconvex regularization term acting on the differences or the discrete gradients of the image or the signal to restore. More precisely, we derive general nonasymptotic analytical bounds characterizing the local and the global minimizers of these cost-functions. We provide several bounds relevant to the observation model. For edge-preserving regularization, we exhibit a tight bound on the l∞ norm of the residual (the error) that is independent of the data, even if its l2 norm is being minimized. Then we focus on the smoothing incurred by the (local) minimizers in terms of the differences or the discrete gradient of the restored image (or signal).