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A smoothing algorithm to identify sharp discontinuities and peaks for a backward heat conduction problem

Yixin Dou, Hengshan Hu, Bo Han


We propose an l1-norm regularization with a smoothing algorithm for a backward heat conduction problem(BHCP). This approach can allow us to identify sharp discontinuities and peaks. We find that the proposed method can improve the accuracy of the reconstruction. In numerical experiments, we consider a moving average filter as a smoothing operator. Due to the non-differentiability of an l1-norm regularization, we employ a second-order cone program (SOCP) to minimize an l1-norm. The SOCP is solved with a generic log-barrier algorithm. We test three numerical experiments with sharp discontinuities and peaks to investigate our proposed method, as well as provide some interesting discussions.


l1-norm regularization, smoothing algorithm, backward heat conduction prob- lem, sharp discontinuities, peaks

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