The JPEG still picture compression standard
Communications of the ACM - Special issue on digital multimedia systems
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
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
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
Convergence of an Iterative Method for Total Variation Denoising
SIAM Journal on Numerical Analysis
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Global Total Variation Minimization
SIAM Journal on Numerical Analysis
Principles of computerized tomographic imaging
Principles of computerized tomographic imaging
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Signal Processing - Image and Video Coding beyond Standards
Reconstruction of Wavelet Coefficients Using Total Variation Minimization
SIAM Journal on Scientific Computing
Combining total variation and wavelet packet approaches for image deblurring
VLSM '01 Proceedings of the IEEE Workshop on Variational and Level Set Methods (VLSM'01)
Image Denoising and Decomposition with Total Variation Minimization and Oscillatory Functions
Journal of Mathematical Imaging and Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Dual Norms and Image Decomposition Models
International Journal of Computer Vision
Image Decomposition into a Bounded Variation Component and an Oscillating Component
Journal of Mathematical Imaging and Vision
Adapted Total Variation for Artifact Free Decompression of JPEG Images
Journal of Mathematical Imaging and Vision
Exact optimization of discrete constrained total variation minimization problems
IWCIA'04 Proceedings of the 10th international conference on Combinatorial Image Analysis
A property of the minimum vectors of a regularizing functionaldefined by means of the absolute norm
IEEE Transactions on Signal Processing
Nonuniform fast Fourier transforms using min-max interpolation
IEEE Transactions on Signal Processing
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
Convex set theoretic image recovery by extrapolated iterations of parallel subgradient projections
IEEE Transactions on Image Processing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
Wavelet methods for inverting the Radon transform with noisy data
IEEE Transactions on Image Processing
An adaptive level set method for nondifferentiable constrained image recovery
IEEE Transactions on Image Processing
Minimizing the total variation under a general convex constraint for image restoration
IEEE Transactions on Image Processing
Hi-index | 0.00 |
We present a simple framework for solving different ill-posed inverse problems in image processing by means of constrained total variation minimizations. We argue that drawbacks commonly attributed to total variation algorithms (slowness and incomplete fit to the image model) can be easily bypassed by performing only a few number of iterations in our optimization process. We illustrate this approach in the context of computerized tomography, that comes down to inverse a Radon transform obtained by illuminating an object by straight and parallel beams of x-rays. This problem is ill-posed because only a finite number of line integrals can be measured, resulting in an incomplete coverage of the frequency plane and requiring, for a direct Fourier reconstruction, frequencies interpolation from a polar to a Cartesian grid. We introduce a new method of interpolation based on a total variation minimization constrained by the knowledge of frequency coefficients in the polar grid, subject to a Lipschitz regularity assumption. The experiments show that our algorithm is able to avoid Gibbs and noise oscillations associated to the direct Fourier method, and that it outperforms classical reconstruction methods such as filtered backprojection and Rudin-Osher-Fatemi total variation restoration, in terms of both PSNR and visual quality.