Chapter 8: Regularization theory

In this chapter, we discuss the concept of ill-posedness (see Section 8.1) and discuss several regularization techniques. We motivate regularization techniques primarily within the context of linear inverse problems on Hilbert spaces. In that context, we discuss some aspects of the underlying mathematical theory as well as the key computational considerations. This is done in Section 8.2. Recall that a brief study of ill-posedness and regularization was presented in Chapter 2. A quick review of that chapter is advised before reading Sections 8.1 and 8.2. For the case of nonlinear inverse problems, we provide a brief summary of approaches within the framework of generalized Tikhonov regularization (see Section 8.3) and point the readers to suitable references for further reading.