Abstract
The problem of reconstructing images from measurements at the boundary of a domain belong to the class of inverse problems. In practice, these measurements are incomplete and inaccurate leading to ill-posed problems. This means that ’exact’ reconstructions are usually not possible. In this Introduction the reader will find some applications in which the main ideas about stability and resolution in image reconstruction are discussed. We will see that although different applications or imaging modalities work under different physical principles and map different physical parameters, they all share the same mathematical foundations and the tools used to create the images have a great deal in common. Current imaging problems deal with understanding the trade off between data size, the quality of the image and the computational tools used to create the image. In many cases, these tools represent the performance bottleneck due to the high operational count and the memory cost. © 2008 Springer-Verlag Berlin Heidelberg.
