Computational Methods for Solving Inverse Problems in Imaging

Discrete linear and nonlinear inverse problems arise from many different imaging systems. These problems are ill-posed, which means, in most cases, that the solution is very sensitive to the data. Because the data usually contain errors produced by different imaging system parts (e.g., cameras, sensors, etc.), robust and reliable regularization methods need to be developed for computing meaningful solutions. In some imaging systems, massive amounts of data are produced making the data storage and computational cost of the inversion process intractable. In this talk, we will see different imaging systems, we will formulate the corresponding mathematical models, we will introduce regularization methods, and we will show some numerical results.