Generalized Fourier transforms, their nonlinearization and the imaging of the brain. (English) Zbl 1076.42004

Summary: The authors show how the Fourier transform can be generalized and nonlinearized and how these in turn can be used to solve certain nonlinear partial differential equations as well as to analytically invert certain integrals. As an application of the latter, the authors consider single particle emission computerized tomography (SPECT) as used in brain imaging.


42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
68U01 General topics in computing methodologies
92C55 Biomedical imaging and signal processing
35Q55 NLS equations (nonlinear Schrödinger equations)
Full Text: Link