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
Mathematical Programming: Series A and B
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
The approximation power of moving least-squares
Mathematics of Computation
Geometric partial differential equations and image analysis
Geometric partial differential equations and image analysis
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
Total variation image restoration: numerical methods and extensions
ICIP '97 Proceedings of the 1997 International Conference on Image Processing (ICIP '97) 3-Volume Set-Volume 3 - Volume 3
Bilateral Filtering for Gray and Color Images
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Towards Ultimate Motion Estimation: Combining Highest Accuracy with Real-Time Performance
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision (ICCV'05) Volume 1 - Volume 01
International Journal of Computer Vision
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Image decomposition combining staircase reduction and texture extraction
Journal of Visual Communication and Image Representation
Local Adaptivity to Variable Smoothness for Exemplar-Based Image Regularization and Representation
International Journal of Computer Vision
Local and Nonlocal Discrete Regularization on Weighted Graphs for Image and Mesh Processing
International Journal of Computer Vision
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
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
Moving least squares response surface approximation: Formulation and metal forming applications
Computers and Structures
IEEE Transactions on Image Processing
Generalised Nonlocal Image Smoothing
International Journal of Computer Vision
Nonlinear image upsampling method based on radial basis function interpolation
IEEE Transactions on Image Processing - Special section on distributed camera networks: sensing, processing, communication, and implementation
Variational optic flow on the Sony PlayStation 3
Journal of Real-Time Image Processing
Total Variation for Image Restoration with Smooth Area Protection
Journal of Signal Processing Systems
A Unified Primal-Dual Algorithm Framework Based on Bregman Iteration
Journal of Scientific Computing
Improved Total Variation-Type Regularization Using Higher Order Edge Detectors
SIAM Journal on Imaging Sciences
Bregmanized Nonlocal Regularization for Deconvolution and Sparse Reconstruction
SIAM Journal on Imaging Sciences
SIAM Journal on Imaging Sciences
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
SIAM Journal on Imaging Sciences
Cardinal exponential splines: part I - theory and filtering algorithms
IEEE Transactions on Signal Processing
Non-local Methods with Shape-Adaptive Patches (NLM-SAP)
Journal of Mathematical Imaging and Vision
On the origin of the bilateral filter and ways to improve it
IEEE Transactions on Image Processing
Superresolution and noise filtering using moving least squares
IEEE Transactions on Image Processing
Kernel Regression for Image Processing and Reconstruction
IEEE Transactions on Image Processing
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering
IEEE Transactions on Image Processing
Efficient Nonlocal Means for Denoising of Textural Patterns
IEEE Transactions on Image Processing
Hi-index | 0.00 |
In this paper, we propose a computational framework to incorporate regularization terms used in regularity based variational methods into least squares based methods. In the regularity based variational approach, the image is a result of the competition between the fidelity term and a regularity term, while in the least squares based approach the image is computed as a minimizer to a constrained least squares problem. The total variation minimizing denoising scheme is an exemplary scheme of the former approach with the total variation term as the regularity term, while the moving least squares method is an exemplary scheme of the latter approach. Both approaches have appeared in the literature of image processing independently. By putting schemes from both approaches into a single framework, the resulting scheme benefits from the advantageous properties of both parties. As an example, in this paper, we propose a new denoising scheme, where the total variation minimizing term is adopted by the moving least squares method. The proposed scheme is based on splitting methods, since they make it possible to express the minimization problem as a linear system. In this paper, we employed the split Bregman scheme for its simplicity. The resulting denoising scheme overcomes the drawbacks of both schemes, i.e., the staircase artifact in the total variation minimizing based denoising and the noisy artifact in the moving least squares based denoising method. The proposed computational framework can be utilized to put various combinations of both approaches with different properties together.