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We consider the minimization problem with the truncated quadraticregularization with gradient operator, which is a nonsmooth and nonconvexproblem. We cooperated the classical preconditioned iterations for linearequations into the nonlinear difference of convex functions algorithms withextrapolation. Especially, our preconditioned framework can deal with the largelinear system efficiently which is usually expensive for computations. Globalconvergence is guaranteed and local linear convergence rate is given based onthe analysis of the Kurdyka-\L ojasiewicz exponent of the minimizationfunctional. The proposed algorithm with preconditioners turns out to be veryefficient for image restoration and is also appealing for image segmentation.

A Preconditioned Difference of Convex Algorithm for Truncated Quadratic Regularization with Application to Imaging