Volume 26, 2009Mathematical methods for imaging and inverse problems
|Page(s)||55 - 64|
|Published online||25 April 2009|
Generalized Fourier Transforms, Inverse Problems, and Integrability in 4+2
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, CB3 0WA, UK
Three different types of generalized Fourier transforms are discussed, which appear in the following: (a) The medical imaging technique called Single Photon Emission Computerized Tomography (SPECT). (b) The solution of the Cauchy problem of integrable nonlinear evolution PDEs in 4+2, i.e. in four spatial and two temporal dimensions. (c) The characterization of the generalized Dirichlet to Neumann map for integrable nonlinear evolution PDEs in 1+1, i.e. in one spatial and one temporal dimensions.
Mathematics Subject Classification: 35R30
Key words: Generalized Fourier transforms / generalized Dirichlet to Neumann map / integrable nonlinear evolution PDEs / Single Photon Emission Computerized Tomography.
© EDP Sciences, ESAIM, 2009
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