# Low-Rank Regularized Convex-Non-Convex Problems for Image Segmentation or Completion

## TL;DR

This paper introduces a new convex-non-convex formulation for image segmentation and completion that combines low-rank and smoothness regularizations, solved efficiently with ADMM and validated through numerical experiments.

## Contribution

It presents a novel formulation integrating low-rank and smoothness regularizations for image tasks, with convergence analysis and empirical validation.

## Key findings

- Effective in image segmentation and completion tasks.
- Convergence of the ADMM algorithm is established.
- Numerical experiments demonstrate superior performance.

## Abstract

This work proposes a novel convex-non-convex formulation of the image segmentation and the image completion problems. The proposed approach is based on the minimization of a functional involving two distinct regularization terms: one promotes low-rank structure in the solution, while the other one enforces smoothness. To solve the resulting optimization problem, we employ the alternating direction method of multipliers (ADMM). A detailed convergence analysis of the algorithm is provided, and the performance of the methods is demonstrated through a series of numerical experiments.