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
Signal and image restoration using shock filters and anisotropic diffusion
SIAM Journal on Numerical Analysis
Convex analysis and variational problems
Convex analysis and variational problems
High-Order Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
A Variational Approach to Remove Outliers and Impulse Noise
Journal of Mathematical Imaging and Vision
Iterative Image Restoration Combining Total Variation Minimization and a Second-Order Functional
International Journal of Computer Vision
Image decomposition combining staircase reduction and texture extraction
Journal of Visual Communication and Image Representation
Error estimation for Bregman iterations and inverse scale space methods in image restoration
Computing - Special Issue on Industrial Geometry
Split Bregman Algorithm, Douglas-Rachford Splitting and Frame Shrinkage
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
Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Cahn-Hilliard Inpainting and a Generalization for Grayvalue Images
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
Global Solutions of Variational Models with Convex Regularization
SIAM Journal on Imaging Sciences
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
Foundations and Trends® in Machine Learning
Image enhancement and denoising by complex diffusion processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Image Processing
Image quality assessment: from error visibility to structural similarity
IEEE Transactions on Image Processing
Hessian-Based Norm Regularization for Image Restoration With Biomedical Applications
IEEE Transactions on Image Processing
Higher-Order TV Methods--Enhancement via Bregman Iteration
Journal of Scientific Computing
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In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images--a known disadvantage of the ROF model--while being simple and efficiently numerically solvable.