A nonconvex total variational model for the joint image segmentation and restoration of images corrupted by Rician noise

In this paper, a novel variational model is proposed for image segmentation via joint restoration of images corrupted by blurring and Rician noise. The proposed model is built upon the piecewise constant Mumford–Shah framework and combines an appropriate data fidelity term with nonconvex total variation (NTV) regularization. The NTV regularization effectively denoises homogeneous regions while accurately preserving object boundaries to facilitate robust segmentation. To solve the resulting nonconvex optimization problem, a proximal alternating minimization algorithm is employed. In addition, an iteratively reweighted $ \ell_1 $ algorithm and the alternating direction method of multipliers are adopted to efficiently handle the corresponding subproblems. Numerical experiments demonstrate the effectiveness of the proposed model in achieving accurate and robust segmentation performance when compared with several state-of-the-art methods.