Linear and nonlinear inverse problems with practical applications - Mueller, Jennifer; Siltanen, Samuli (Philadelphia Society for Industrial and Applied Mathematics, 2012)
Naive reconstruction and inverse crimes -- Ill-posedness in inverse problems -- Truncated singular value decomposition -- Tikhonov regularization -- Total variation regularization -- Besov space regularization using wavelets -- Discretization-invariance -- Practical X-ray tomography with limited data -- Projects -- Nonlinear inverse problems -- Nonlinear inversion -- Electrical impedance tomography -- Simulation of noisy EIT data -- Complex geometrical optics solutions -- A regularized D-bar method for direct EIT -- Other direct solution methods for EIT -- Projects -- Banach spaces and Hilbert spaces -- Mappings and compact operators -- Fourier transform and Sobolev spaces -- Iterative solution of linear equation
Includes bibliographical references (pages 311-347) and index.
Keywords: Inverse problems (Differential equation)