A unified approach for a 1D generalized total variation problem
研究一维离散信号去噪问题，提出基于KKT条件的统一方法，适用于一般凸保真项和正则项，并给出快速算法，理论复杂度最优且实际速度优于现有求解器。
Abstract We study a 1-dimensional discrete signal denoising problem that consists of minimizing a sum of separable convex fidelity terms and convex regularization terms, the latter penalize the differences of adjacent signal values. This problem generalizes the total variation regularization problem. We provide here a unified approach to solve the problem for general convex fidelity and regularization functions that is based on the Karush–Kuhn–Tucker optimality conditions. This approach is shown here to lead to a fast algorithm for the problem with general convex fidelity and regularization functions, and a faster algorithm if, in addition, the fidelity functions are differentiable and the regularization functions are strictly convex. Both algorithms achieve the best theoretical worst case complexity over existing algorithms for the classes of objective functions studied here. Also in practice, our C++ implementation of the method is considerably faster than popular C++ nonlinear optimization solvers for the problem.