Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Feature-oriented image enhancement using shock filters
SIAM Journal on Numerical Analysis
Image selective smoothing and edge detection by nonlinear diffusion. II
SIAM Journal on Numerical Analysis
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
Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
International Journal of 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
Recovery of blocky images from noisy and blurred data
SIAM Journal on Applied Mathematics
A fast level set based algorithm for topology-independent shape modeling
Journal of Mathematical Imaging and Vision - Special issue on topology and geometry in computer vision
International Journal of Computer Vision
A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration
SIAM Journal on Scientific Computing
Linear and Nonlinear Image Deblurring: A Documented Study
SIAM Journal on Numerical Analysis
Journal of Computational Physics
SIAM Journal on Scientific Computing
Image segmentation by reaction-diffusion bubbles
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Active contours driven by local image fitting energy
Pattern Recognition
Active contours with selective local or global segmentation: A new formulation and level set method
Image and Vision Computing
PDE-based deconvolution with forward-backward diffusivities and diffusion tensors
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems
IEEE Transactions on Signal Processing
A computational algorithm for minimizing total variation in image restoration
IEEE Transactions on Image Processing
A unified approach to noise removal, image enhancement, and shape recovery
IEEE Transactions on Image Processing
Total variation blind deconvolution
IEEE Transactions on Image Processing
Fast, robust total variation-based reconstruction of noisy, blurred images
IEEE Transactions on Image Processing
Image segmentation and selective smoothing by using Mumford-Shah model
IEEE Transactions on Image Processing
Bayesian Restoration Using a New Nonstationary Edge-Preserving Image Prior
IEEE Transactions on Image Processing
Variational Bayesian Image Restoration Based on a Product of -Distributions Image Prior
IEEE Transactions on Image Processing
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Image deblurring and denoising are fundamental problems in the field of image processing with numerous applications. This paper presents a new nonlinear Partial Differential Equation (PDE) model based on curve evolution via level sets, for recovering images from their blurry and noisy observations. The proposed method integrates an image deconvolution process and a curve evolution based regularizing process to form a reaction-diffusion PDE. The regularization term in the proposed PDE is a combination of a diffusive image smoothing term and a reactive image enhancement term. The diffusive and reactive terms present in the model lead to effective suppression of noise with sharp restoration of image features. We present several numerical results for image restoration, with synthetic and real degradations and compare it to other state-of-the-art image restoration techniques. The experiments confirm the favorable performance of our method, both visually and in terms of Improvement in Signal-to-Noise-Ratio (ISNR) and Pratt's Figure Of Merit (FOM).