Titlebook: Handbook of Mathematical Methods in Imaging; Otmar Scherzer Living reference work 20200th edition

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Differential Methods for Multidimensional Visual Data Analysis,or fields given on 2D, 3D, and 4D domains, the objective is to reduce this complexity to two-dimensional images comprehensible to the human visual system. Various mathematical fields such as in particular differential geometry, topology (theory of discretized manifolds), differential topology, linea

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Electrical Impedance Tomography,ity (or conductivity and permittivity) of the interior of a body from knowledge of electrical stimulation and measurements on its surface. This problem is also known as the inverse conductivity problem and its mathematical formulation is due to A. P. Calderón, who wrote in 1980, the first mathematic

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EM Algorithms from a Non-stochastic Perspective,nguage, relying on conditional expectations to obtain a method for estimating parameters in statistics, the essence of the EM algorithm is not stochastic. The conventional formulation of the EM algorithm given in many texts and papers on the subject is inadequate. A new formulation is given here bas

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Imaging in Random Media,tures (inhomogeneities). We describe the challenges of imaging in random media and discuss the coherent interferometric (CINT) imaging approach. It is designed to image with partially coherent waves, so it works at distances that do not exceed a transport mean-free path. The waves are incoherent whe

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Iterative Solution Methods,ve algorithms such as Kaczmarz, expectation maximization, and Bregman iterations. Our intention here is to cite convergence results in the sense of regularization and to provide further references to the literature.

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Local Smoothing Neighborhood Filters,rhood filters are usually preferred. These filters perform an average of neighboring pixels, but only under the condition that their gray level is close enough to the one of the pixel in restoration. This very popular method unfortunately creates shocks and staircasing effects. It also excessivelly

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Mathematical Methods in PET and SPECT Imaging,e used in PET and SPECT image reconstruction, respectively. Using a new method for deriving transform pairs in one and two dimensions, we derive the inverse Radon transform and the IART. Furthermore, we discuss an alternative approach for computing the Hilbert transform using cubic splines. This new