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- David L. Donoho, Xiaoming Huo, +13 authors S. Semmes
- 2001

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 dyadicallyorganized collection of line segments, occupying a range of dyadic locations and scales, and occurring at a range of orientations.… (More)

- Frank Natterer, Helmut Sielschott, Oliver Dorn, Thomas Dierkes, Victor Palamodov
- SIAM Journal of Applied Mathematics
- 2002

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… (More)

- Frank Natterer, Erik L. Ritman
- Int. J. Imaging Systems and Technology
- 2002

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. © 2002 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 12, 175–187, 2002; Published online in Wiley… (More)

- Frank Natterer
- 1997

- Frank Natterer, Frank Wübbeling
- Numerische Mathematik
- 2005

Since supp f ⊂ Ω, uθ satisfies the plain Helmholtz equation with constant wavenumber outside of Ω, the radiation condition and uθ|∂Ω = gθ. So by solving the exterior problem of the Helmholtz equation (analytically if Ω is a circle), uθ can be computed everywhere outside of Ω without prior knowledge of f . In particular, we can compute h = ∂uθ ∂ν on ∂Ω.… (More)

- Fredrik Andersson, Randolph L. Moses, Frank Natterer
- IEEE Trans. Aerospace and Electronic Systems
- 2012

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)

- Frank Natterer
- Physics in medicine and biology
- 2010

It is shown that a simple metal plate serving as a mirror decisively improves ultrasound mammography. A suitable reconstruction algorithm is described. A numerical example based on computer simulations is given.

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. (Some figures in this article are in colour only in the electronic version)

- Frank Natterer
- Handbook of Mathematical Methods in Imaging
- 2015

Different sets of conditions for an estimate of the form * '"«¿«i«.» «c max »r vr+i)n¿ ,n i °°x I' to hold are given. Here, y" is the Galerkin approximation to the solution v of a boundary value problem for an ordinary differential equation, the trial functions being polynomials of degree < r on the subintervals I¡ = [x¡, x,-+j] of length h¡. The sequence… (More)