An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, an inverse source problem for the time-fractional diffusion equationis investigated. The observational data is on the final time and the source termis assumed to be temporally independent and with a sparse structure. Here the sparsityis understood with respect to the pixel basis, i.e., the source has a small support.By an elastic-net regularization method, this inverse source problem is formulated intoan optimization problem and a semismooth Newton (SSN) algorithm is developedto solve it. A discretization strategy is applied in the numerical realization. Severalone- and two- dimensional numerical examples illustrate the efficiency of the proposedmethod.