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
Active shape models—their training and application
Computer Vision and Image Understanding
IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Spatial models for fuzzy clustering
Computer Vision and Image Understanding
A Unified Continuous Optimization Framework for Center-Based Clustering Methods
The Journal of Machine Learning Research
Regularized fuzzy c-means method for brain tissue clustering
Pattern Recognition Letters
Efficient projections onto the l1-ball for learning in high dimensions
Proceedings of the 25th international conference on Machine learning
The Split Bregman Method for L1-Regularized Problems
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
A Spatial Regularization Approach for Vector Quantization
Journal of Mathematical Imaging and Vision
SIAM Journal on Imaging Sciences
On vector and matrix median computation
Journal of Computational and Applied Mathematics
Fuzzy order statistics and their application to fuzzy clustering
IEEE Transactions on Fuzzy Systems
Relative entropy fuzzy c-means clustering
Information Sciences: an International Journal
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The objective function of the original (fuzzy) c-mean method is modified by a regularizing functional in the form of total variation (TV) with regard to gradient sparsity, and a regularization parameter is used to balance clustering and smoothing. An alternating direction method of multipliers in conjunction with the fast discrete cosine transform is used to solve the TV-regularized optimization problem. The new algorithm is tested on both synthetic and real data, and is demonstrated to be effective and robust in treating images with noise and missing data (incomplete data).