Efficient parameter identification using nonsmooth and nonconvex regularization for inverse problem of diffuse...

To better reconstruct the piecewise constant optical coefficients in diffuse optical tomography, nonconvex and nonsmooth approximation of weak Mumford-Shah functional is considered in this paper. We theoretically analyze the existence of minimizers in piecewise constant finite element space and constrained finite dimensional subsets. However, optimizing such minimization problems presents a computational challenge due to the nonconvex and non-differentiable properties. To overcome these difficulties, we propose a fast graduated nonconvex alternative directional multiplier method to solve this numerical problem. Compared with graduated nonconvex Gaussian-Newton, [Formula: see text] Gaussian-Newton, and TV Gaussian-Newton, our simulations show that the proposed GNC-ADMM can well keep edges and values of the anomaly with fewer iteration steps and fewer measurements.