A new fuzzy c-means method with total variation regularization for segmentation of images with noisy and incomplete data

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).