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

arXiv: https://arxiv.org/abs/2001.01268 · HTML: https://mlsanity.com/paper/2001.01268/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Taming Nonconvexity with Epigraph Lifting](https://mlsanity.com/paper/2610.16429/) (2026)

## Abstract (arXiv)

We consider the minimization problem with the truncated quadratic regularization with gradient operator, which is a nonsmooth and nonconvex problem. We cooperated the classical preconditioned iterations for linear equations into the nonlinear difference of convex functions algorithms with extrapolation. Especially, our preconditioned framework can deal with the large linear system efficiently which is usually expensive for computations. Global convergence is guaranteed and local linear convergence rate is given based on the analysis of the Kurdyka-L ojasiewicz exponent of the minimization functional. The proposed algorithm with preconditioners turns out to be very efficient for image restoration and is also appealing for image segmentation.