Approximation of penalty terms in Tikhonov functional-theory and applications in inverse problems (Q2874802)

In this interesting work, the authors establish the convergence of approximations of general Tikhonov regularization from the viewpoint of gamma convergence from variational calculus. The convergence is discussed for the general Tikhonov regularization, the regularization parameter (including discrepancy principle), and separable penalties. The discussion includes also the popular sparsity regularization, e.g., the Huber approximation to the \(\ell^1\) penalty. Finally, the theory is illustrated on an inverse medium scattering problem of recovering the refractive index from the scattered field, using a sparse reconstruction approach.