The purpose of this course is to introduce and to understand theory and solution for linear and nonlinear inverse problems with emphasis on regularization techniques and parameter estimation, and the course also aims to gain the ability of researching using modern approaches in this field in both theoretically and practically.

Overview of inverse problems, and some examples of direct problems, the definition of ill-posed and ill-conditioned problems, the deconvolution problem, Tikhonov regularization, Truncated Fourier decomposition, Regularization parameter selection, generalized Tikhonov regularization with Bayesian perspective, ill-posedness and regularization of linear operators in function spaces, compact operators, Singular value decomposition (SVD), Least squares solution, Minimization of quadractic functionals, Truncated SVD, Generalized Tikhonov /Bayesian regularization, some inverse problems and their applications.