Abstract
The problem of inverse source problem is considered in this paper. The main aim of this problem is to determine the source density function from the state function which is corrupted by uniform noise. Under the framework of maximum a posteriori estimator, the problem can be converted into an optimization problem where the objective function is composed of an \(L_\infty \) norm and a total variation (TV) regularization term. By introducing an auxiliary variable, the optimization problem is further converted into a minimax problem. Then first order primal-dual method is applied to find the saddle point of the minimax problem. Numerical examples are given to demonstrate that our proposed method outperforms the other testing methods.
This work is supported by NSFC Grant No. 11871210, the Construct Program of the Key Discipline in Hunan Province, the SRF of Hunan Provincial Education Department (No.17A128)
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Pan, H., Wen, YW. (2021). A Total Variation Regularization Method for Inverse Source Problem with Uniform Noise. In: Tai, XC., Wei, S., Liu, H. (eds) Mathematical Methods in Image Processing and Inverse Problems. IPIP 2018. Springer Proceedings in Mathematics & Statistics, vol 360. Springer, Singapore. https://doi.org/10.1007/978-981-16-2701-9_5
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