The book contains presentations of recent and ongoing research on inverse problems and its application to engineering and physical sciences. The articles are structured around three closely related topics: Inverse scattering problems, inverse boundary value problems, and inverse spectral problems. The applications range from quantum and electromagnetic scattering to medical imaging, geophysical sounding of the Earth, and non-destructive material evaluation. The book gives an up-to-date presentation of the most recent developments in these rapidlychanging and evolving fields of applied research. The contributors of the volume give extra emphysis to the pedagogical aspects of their presentation to make this collection eysily accessible to graduate students as well as to people working on nearby fields of research.

The once esoteric idea of embedding scientific computing into a probabilistic framework, mostly along the lines of the Bayesian paradigm, has recently enjoyed wide popularity and found its way into numerous applications. This book provides an insider's view of how to combine two mature fields, scientific computing and Bayesian inference, into a powerful language leveraging the capabilities of both components for computational efficiency, high resolution power and uncertainty quantification ability. The impact of Bayesian scientific computing has been particularly significant in the area of computational inverse problems where the data are often scarce or of low quality, but some characteristics of the unknown solution may be available a priori. The ability to combine the flexibility of the Bayesian probabilistic framework with efficient numerical methods has contributed to the popularity of Bayesian inversion, with the prior distribution being the counterpart of classical regularization. However, the interplay between Bayesian inference and numerical analysis is much richer than providing an alternative way to regularize inverse problems, as demonstrated by the discussion of time dependent problems, iterative methods, and sparsity promoting priors in this book. The quantification of uncertainty in computed solutions and model predictions is another area where Bayesian scientific computing plays a critical role. This book demonstrates that Bayesian inference and scientific computing have much more in common than what one may expect, and gradually builds a natural interface between these two areas.