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The relation between random normal matrices and conformal map-pings discovered by Wiegmann and Zabrodin is made rigorous by restricting normal matrices to have spectrum in a bounded set. It is shown that for a suitable class of potentials the asymptotic density of eigenvalues is uniform with support in the interior domain of a simple smooth curve.

- Jérôme Boulanger, Charles Kervrann, Patrick Bouthemy, Peter Elbau, Jean-Baptiste Sibarita, Jean Salamero
- IEEE Trans. Med. Imaging
- 2010

We present a nonparametric regression method for denoising 3-D image sequences acquired via fluorescence microscopy. The proposed method exploits the redundancy of the 3-D+time information to improve the signal-to-noise ratio of images corrupted by Poisson-Gaussian noise. A variance stabilization transform is first applied to the image-data to remove the… (More)

- PETER ELBAU
- 2008

We show that in the large matrix limit, the eigenvalues of the normal matrix model for matrices with spectrum inside a compact domain with a special class of potentials homogeneously fill the interior of a polynomial curve uniquely defined by the area of its interior domain and its exterior harmonic moments which are all given as parameters of the… (More)

The literature on reconstruction formulas for photoacoustic tomography (PAT) is vast. The various reconstruction formulas differ by used measurement devices and geometry on which the data are sampled. In standard photoacoustic imaging (PAI), the object under investigation is illuminated uniformly. Recently, sectional photoacoustic imaging techniques, using… (More)

The integral quantum Hall effect can be explained either as resulting from bulk or edge currents (or, as it occurs in real samples, as a combination of both). This leads to different definitions of Hall conductance, which agree under appropriate hypotheses, as shown by Schulz-Baldes et al. by means of K-theory. We propose an alternative proof based on a… (More)

- Bernhard Moser, Frank Bauer, Peter Elbau, Bettina Heise, Holger Schöner
- Three-Dimensional Image Capture and Applications
- 2008

We establish a semi-group solution concept for morphological differential equations, such as the mean curvature flow equation. The proposed method consists in generating flows from generalized minimizers of non-convex energy functionals. We use relaxation and convexification to define generalized minimizers. The main part of this work consists in… (More)

- Peter Elbau, Otmar Scherzer
- SIAM J. Imaging Sciences
- 2015

To effectively use photoacoustic tomography to obtain cross-sectional images, a combination of a focused laser illumination and focusing acoustic detectors is used. In this work, we discuss how to incorporate cylindrically shaped focusing detectors in the mathematical modelling of photoacoustics and derive approximative reconstruction formulas. Moreover, we… (More)

- Peter Elbau, Leonidas Mindrinos, Otmar Scherzer
- Handbook of Mathematical Methods in Imaging
- 2015

In recent years, a series of convergence rates conditions for regularization methods has been developed. Mainly, the motivations for developing novel conditions came from the desire to carry over convergence rates results from the Hilbert space setting to generalized Tikhonov regularization in Banach spaces. For instance, variational source conditions have… (More)