Mathematical Methods in Tomography: Proceedings of a Conference Held in Oberwolfach, Germany, 5-11 June, 1990

ISBN-13: 9783540549703 / Angielski / Miękka / 1992 / 270 str.

Gabor T. Herman; Alfred K. Louis; Frank Natterer

Opis

These conference proceedings are devoted to the discussion of present and future techniques in medical imaging, including 3D X-ray tomography, ultrasound and diffraction tomography and biomagnetic imaging. It treats the mathematical models and the development of algorithms.

Spis treści

Helgason's support theorem for Radon transforms — A new proof and a generalization.- Singular value decompositions for Radon transforms.- Image reconstruction in Hilbert space.- A problem of integral geometry for a family of rays with multiple reflections.- Inversion formulas for the three-dimensional ray transform.- Backscattered photons — Are they useful for a surface-near tomography?.- Mathematical framework of cone beam 3D reconstruction via the first derivative of the radon transform.- Diffraction tomography some applications and extension to 3-D ultrasound imaging.- Diffuse tomography: A refined model.- Three dimensional reconstructions in inverse obstacle scattering.- Mathematical questions of a biomagnetic imaging problem.- On variable block algebraic reconstruction techniques.- On Volterra-Lotka differential equations and multiplicative algorithms for monotone complementarity problems.- Constrained regularized least squares problems.- Multiplicative iterative methods in computed tomography.- Remark on the informative content of few measurements.- Theorems for the number of zeros of the projection radial modulators of the 2D exponential radon transform.- Evaluation of reconstruction algorithms.- Radon transform and analog coding.- Determination of the specific density of an aerosol through tomography.- Computed tomography and rockets.