Mathematics for medical imagery

Starting from basic knowledge, this book proposes an in-depth course on mathematical tools which are necessary for the elaboration of medical images. Thus, it addresses image reconstruction by means of deterministic or Bayesian methods, and also the implementation of simulations for radiotherapy. More precisely, after a general overview and presentation of techniques of medical imagery, it proposes detailed presentations of the Radon transform (derived from the Fourier transform), of the analytic reconstruction, of the Radon transform in R in n dimensions, of the discrete reconstruction, of matrix-based numerical methods (Kaczmarz, direct, iterative, and projective methods). It also addresses inverse problems, the regularization and algebraic iterative methods, the use of probabilistic methods, statistical iterative methods, Bayesian methods, Monte-Carlo simulation for radiotherapy, magnetic resonance imagery, issues related to image processing, and segmentation methods (threshold-based, contour-based, area-based, and stochastic optimization-based segmentation)