An Inverse Source Problem with Sparsity Constraint for the Time-Fractional Diffusion Equation

In this paper,an inverse source problem for the time-fractional diffusion equation is investigated.The observational data is on the final time and the source term is assumed to be temporally independent and with a sparse structure.Here the sparsity is 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 into an optimization problem and a semismooth Newton(SSN)algorithm is developed to solve it.A discretization strategy is applied in the numerical realization.Several one and two dimensional numerical examples illustrate the efficiency of the proposed method.