DC programming and algorithm for nonconvex log total variation image reconstruction

In this paper, a nonconvex variational model with log total variation is proposed to investigate robust image reconstruction from a certain number of measurements.Due to the form of the new model, the difference of convex functions (DC) programming is presented and a DC algorithm (DCA) is adopted.The specific DCA subproblem can be solved by the alternating direction method of multipliers (ADMM).Theoretically, we prove the sequence generated by the DCA converges to a stationary point.The experimental results demonstrate that the new method outperforms the competitive methods when the measurement is limited or the noise level is significant.