Inverse problems in biomedical imaging: modeling and methods of solution

Imaging techniques are a powerful tool for the analysis of human organs and biological systems and they range from different kinds of tomography to different kinds of microscopy. Their common feature is that they require mathematical modeling of the acquisition process and numerical methods for the solution of the equations relating the data to the unknown object. These problems are usually named inverse problems and their main feature is that they are ill-posed in the sense of Hadamard, so that their solutions require special care. In this chapter we sketch the main issues which must be considered when treating inverse problems of interest in biomedical imaging.

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