Fast nonconvex nonsmooth minimization methods for image restoration and reconstruction

Authors:
Mila Nikolova;Michael K. Ng;Chi-Pan Tam
Affiliations:
Centre de Mathématiques et de Leurs Applications, CNRS, ENS Cachan, Cachan Cedex, France;Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong;Centre for Mathematical Imaging and Vision and Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
Venue:
IEEE Transactions on Image Processing
Year:
2010

Citing 25
Cited 6

Visual reconstruction

Visual reconstruction
Fundamentals of digital image processing

Fundamentals of digital image processing
Comparison of the Efficiency of Deterministic and Stochastic Algorithms for Visual Reconstruction

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
A GNC algorithm for constrained image reconstruction with continuous-valued line processes

Pattern Recognition Letters
On the unification of line processes, outlier rejection, and robust statistics with applications in early vision

International Journal of Computer Vision
A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions

SIAM Journal on Scientific Computing
Markov Random Field Modeling in Computer Vision

Markov Random Field Modeling in Computer Vision
Minimizers of Cost-Functions Involving Nonsmooth Data-Fidelity Terms. Application to the Processing of Outliers

SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications

Journal of Mathematical Imaging and Vision
A Variational Approach to Remove Outliers and Impulse Noise

Journal of Mathematical Imaging and Vision
Digital Image Processing (3rd Edition)

Digital Image Processing (3rd Edition)
Efficient Minimization Methods of Mixed l2-l1 and l1-l1 Norms for Image Restoration

SIAM Journal on Scientific Computing
Structure-Texture Image Decomposition--Modeling, Algorithms, and Parameter Selection

International Journal of Computer Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)

Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
A Fast $\ell$1-TV Algorithm for Image Restoration

SIAM Journal on Scientific Computing
Efficient Reconstruction of Piecewise Constant Images Using Nonsmooth Nonconvex Minimization

SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

SIAM Journal on Imaging Sciences
Inversion of large-support ill-posed linear operators using a piecewise Gaussian MRF

IEEE Transactions on Image Processing
Markovian reconstruction using a GNC approach

IEEE Transactions on Image Processing
Simulated annealing, acceleration techniques, and image restoration

IEEE Transactions on Image Processing
Deblurring of Color Images Corrupted by Impulsive Noise

IEEE Transactions on Image Processing
A Stochastic Continuation Approach to Piecewise Constant Reconstruction

IEEE Transactions on Image Processing
Nonlinear image recovery with half-quadratic regularization

IEEE Transactions on Image Processing

Alternating Krylov subspace image restoration methods

Journal of Computational and Applied Mathematics
Fast communication: Nonconvex compressed sensing with partially known signal support

Signal Processing
Nonconvex sparse regularizer based speckle noise removal

Pattern Recognition
Local joint entropy based non-rigid multimodality image registration

Pattern Recognition Letters
A superlinearly convergent R-regularized Newton scheme for variational models with concave sparsity-promoting priors

Computational Optimization and Applications
A coupled variational model for image denoising using a duality strategy and split Bregman

Multidimensional Systems and Signal Processing

Quantified Score

Hi-index	0.01

Visualization

Abstract

Nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges. However, its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization. In this paper, we deal with nonconvex nonsmooth minimization methods for image restoration and reconstruction. Our theoretical results show that the solution of the nonconvex nonsmooth minimization problem is composed of constant regions surrounded by closed contours and neat edges. The main goal of this paper is to develop fast minimization algorithms to solve the nonconvex nonsmooth minimization problem. Our experimental results show that the effectiveness and efficiency of the proposed algorithms.