A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Image Sharpening by Flows Based on Triple Well Potentials
Journal of Mathematical Imaging and Vision
Image Deblurring in the Presence of Impulsive Noise
International Journal of Computer Vision
Total Variation Models for Variable Lighting Face Recognition
IEEE Transactions on Pattern Analysis and Machine Intelligence
Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization
Journal of Mathematical Imaging and Vision
A comparison of three total variation based texture extraction models
Journal of Visual Communication and Image Representation
Fast Global Minimization of the Active Contour/Snake Model
Journal of Mathematical Imaging and Vision
Non-smooth SOR for L1-Fitting: Convergence Study and Discussion of Related Issues
Journal of Scientific Computing
One-iteration dejittering of digital video images
Journal of Visual Communication and Image Representation
An Improved LOT Model for Image Restoration
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Multiplicative Noise Cleaning via a Variational Method Involving Curvelet Coefficients
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Nonlocal Variational Image Deblurring Models in the Presence of Gaussian or Impulse Noise
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Theoretical Foundations for Discrete Forward-and-Backward Diffusion Filtering
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
Properties of Higher Order Nonlinear Diffusion Filtering
Journal of Mathematical Imaging and Vision
Color Image Restoration Using Nonlocal Mumford-Shah Regularizers
EMMCVPR '09 Proceedings of the 7th International Conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Efficient minimization method for a generalized total variation functional
IEEE Transactions on Image Processing
Adaptive total variation denoising based on difference curvature
Image and Vision Computing
Fast Two-Phase Image Deblurring Under Impulse Noise
Journal of Mathematical Imaging and Vision
Multiplicative Noise Removal Using L1 Fidelity on Frame Coefficients
Journal of Mathematical Imaging and Vision
Counter-examples for Bayesian MAP restoration
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Evaluating a general class of filters for image denoising
SCIA'07 Proceedings of the 15th Scandinavian conference on Image analysis
New total variation regularized L1 model for image restoration
Digital Signal Processing
An Augmented Lagrangian Method for TVg+L1-norm Minimization
Journal of Mathematical Imaging and Vision
Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction
IEEE Transactions on Image Processing
SIAM Journal on Imaging Sciences
A Multi-Scale Vectorial Lτ-TV Framework for Color Image Restoration
International Journal of Computer Vision
A fast solver for truncated-convex priors: quantized-convex split moves
EMMCVPR'11 Proceedings of the 8th international conference on Energy minimization methods in computer vision and pattern recognition
SIAM Journal on Imaging Sciences
Integro-Differential Equations Based on $(BV, L^1)$ Image Decomposition
SIAM Journal on Imaging Sciences
Variational deblurring of images with uncertain and spatially variant blurs
PR'05 Proceedings of the 27th DAGM conference on Pattern Recognition
Exact optimization of discrete constrained total variation minimization problems
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
Geometry of total variation regularized Lp-model
Journal of Computational and Applied Mathematics
Augmented Lagrangian Method for Generalized TV-Stokes Model
Journal of Scientific Computing
Constrained total variation minimization and application in computerized tomography
EMMCVPR'05 Proceedings of the 5th international conference on Energy Minimization Methods in Computer Vision and Pattern Recognition
Image deblurring in the presence of salt-and-pepper noise
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Color image deblurring with impulsive noise
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
VLSM'05 Proceedings of the Third international conference on Variational, Geometric, and Level Set Methods in Computer Vision
A new coarse-to-fine framework for 3d brain MR image registration
CVBIA'05 Proceedings of the First international conference on Computer Vision for Biomedical Image Applications
Fast algorithms for l1 norm/mixed l1 and l2 norms for image restoration
ICCSA'05 Proceedings of the 2005 international conference on Computational Science and Its Applications - Volume Part IV
A fast and exact algorithm for total variation minimization
IbPRIA'05 Proceedings of the Second Iberian conference on Pattern Recognition and Image Analysis - Volume Part I
An adaptive norm algorithm for image restoration
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Journal of Visual Communication and Image Representation
A fixed-point augmented Lagrangian method for total variation minimization problems
Journal of Visual Communication and Image Representation
Total variation regularization algorithms for images corrupted with different noise models: a review
Journal of Electrical and Computer Engineering
A Combined First and Second Order Variational Approach for Image Reconstruction
Journal of Mathematical Imaging and Vision
Hi-index | 0.02 |
We present a theoretical study of the recovery of an unknown vector $x\in{\mathbb R}^p$ (such as a signal or an image) from noisy data $y\in{\mathbb R}^q$ by minimizing with respect to $x$ a regularized cost-function ${\cal F}(x,y)=\Psi(x,y)+\alpha\Phi(x)$, where $\Psi$ is a data-fidelity term, $\Phi$ is a smooth regularization term, and $\alpha0$ is a parameter. Typically, $\Psi(x,y)=\|Ax-y \|^2$, where A is a linear operator. The data-fidelity terms $\Psi$ involved in regularized cost-functions are generally smooth functions; only a few papers make an exception to this and they consider restricted situations. Nonsmooth data-fidelity terms are avoided in image processing. In spite of this, we consider both smooth and nonsmooth data-fidelity terms. Our goal is to capture essential features exhibited by the local minimizers of regularized cost-functions in relation to the smoothness of the data-fidelity term.In order to fix the context of our study, we consider $\Psi(x,y)=\sum_i\psi(a_i^Tx-y_i)$, where $a_i^T$ are the rows of $A$ and $\psi$ is ${\cal C}^m$ on ${\mathbb R}\setminus \{0\}$. We show that if $\psi\1(0^-)y give rise to local minimizers $\hat x$ of ${\cal F}(.,y)$ which fit exactly a certain number of the data entries: there is a possibly large set $\hat h$ of indexes such that $a_i^T\hat x=y_i$ for every $i\in\hat h$. In contrast, if $\psi$ is smooth on ${\mathbb R}$, for almost every y, the local minimizers of ${\cal F}(.,y)$ do not fit any entry of y. Thus, the possibility that a local minimizer fits some data entries is due to the nonsmoothness of the data-fidelity term. This is a strong mathematical property which is useful in practice. By way of application, we construct a cost-function allowing aberrant data (outliers) to be detected and to be selectively smoothed. Our numerical experiments advocate the use of nonsmooth data-fidelity terms in regularized cost-functions for special purposes in image and signal processing.