Abstract In this paper, we propose a first second-order scheme based on arbitrary non-Euclidean norms, incorporated by Bregman distances. They are introduced directly in the Newton iterate with regularization parameter proportional to square root of norm current gradient. For basic scheme, as applied composite convex optimization problem, establish global convergence rate order $$O(k^{-2})$$ <m...

In this paper, we investigate sparsity regularization for electrical impedance tomography (EIT). Here, we combine sparsity regularization with the energy functional approach. The main results of our paper is the well-posedness and convergence rates of the sparsity regularization method.