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We describe a framework for multiscale image analysis in which line segments play a role analogous to the role played by points in wavelet analysis. The framework has five key components. The beamlet dictionary is a dyadically-organized collection of line segments, occupying a range of dyadic locations and scales, and occurring at a range of orientations.… (More)
In many inverse problems a functional of u is given by measurements where u solves a partial differential equation of the type L(p)u + Su = q. Here, q is a known source term and L(p), S are operators with p as unknown parameter of the inverse problem. For the numerical reconstruction of p often the heuristically derived Fréchet derivative R of the mapping R… (More)
We give a short account of the history of CT from motion tomography in the early 1930's to sprial CT. We discuss the physical and the mathematical background. Finally we give an outlook on possible future developments of CT and related techniques. I. INTRODUCTION In 1895, Röntgen first indicated that X-rays could be used to image internal structures such as… (More)
In synthetic aperture radar one wishes to reconstruct the reflectivity function of a region on the ground from a set of radar measurements taken at several angles. The ground reflectivity is found by interpolating measured samples, which typically lie on a polar grid in frequency space, to an equally spaced rectangular grid in frequency space, then… (More)
Radar imaging and x-ray computed tomography (CT) are both based on inverting the Radon transform. Yet radar imaging can make images from as little as two degrees of aperture while x-ray CT typically requires an aperture of at least 120 •. Our discussion addresses this phenomenon.
Articles 1. Einschließungen für die großen Eigenwerte bei gewöhnlichen Differen-tialgleichungen zweiter und vierter Ordnung.