Christoph Brune

Quantum Hall effect from the topological surface states of strained bulk HgTe.

We report transport studies on a three-dimensional, 70-nm-thick HgTe layer, which is strained by epitaxial growth on a CdTe substrate. The strain induces a band gap in the otherwise semimetallic HgTe, which thus becomes a three-dimensional topological insulator. Contributions from residual bulk carriers to the transport properties of the gapped HgTe layer are negligible at mK temperatures. As a result, the sample exhibits a quantized Hall effect that results from the 2D single cone Dirac-like topological surface states.

Single valley Dirac fermions in zero-gap HgTe quantum wells

Most of the notable properties of graphene are a result of the cone-like nature of the points in its electronic structure where its conduction and valance bands meet. Similar structures arise in 2D HgTe quantum wells, but without the spin- and valley-degeneracy of graphene; their properties are also likely to be easier to control.

Higher-Order TV Methods--Enhancement via Bregman Iteration

In this work we analyze and compare two recent variational models for image denoising and improve their reconstructions by applying a Bregman iteration strategy. One of the standard techniques in image denoising, the ROF-model (cf. Rudin et al. in Physicaxa0D 60:259–268, 1992), is well known for recovering sharp edges of a signal or image, but also for producing staircase-like artifacts. In order to overcome these model-dependent deficiencies, total variation modifications that incorporate higher-order derivatives have been proposed (cf. Chambolle and Lions in Numer. Math. 76:167–188, 1997; Bredies etxa0al. in SIAM J. Imaging Sci. 3(3):492–526, 2010). These models reduce staircasing for reasonable parameter choices. However, the combination of derivatives of different order leads to other undesired side effects, which we shall also highlight in several examples.The goal of this paper is to analyze capabilities and limitations of the different models and to improve their reconstructions in quality by introducing Bregman iterations. Besides general modeling and analysis we discuss efficient numerical realizations of Bregman iterations and modified versions thereof.

Accurate EM-TV algorithm in PET with low SNR

PET measurements of tracers with a lower dose rate or short radioactive half life suffer from extremely low SNRs. In these cases standard reconstruction methods (OSEM, EM, filtered backprojection) deliver unsatisfactory and noisy results. Here, we propose to introduce nonlinear variational methods into the reconstruction process to make an efficient use of a-priori information and to attain improved imaging results. We illustrate our technique by evaluating cardiac H215O measurements. The general approach can also be used for other specific goals allowing to incorporate a-priori information about the solution with Poisson distributed data.

Primal and Dual Bregman Methods with Application to Optical Nanoscopy

Measurements in nanoscopic imaging suffer from blurring effects modeled with different point spread functions (PSF). Some apparatus even have PSFs that are locally dependent on phase shifts. Additionally, raw data are affected by Poisson noise resulting from laser sampling and “photon counts” in fluorescence microscopy. In these applications standard reconstruction methods (EM, filtered backprojection) deliver unsatisfactory and noisy results. Starting from a statistical modeling in terms of a MAP likelihood estimation we combine the iterative EM algorithm with total variation (TV) regularization techniques to make an efficient use of a-priori information. Typically, TV-based methods deliver reconstructed cartoon images suffering from contrast reduction. We propose extensions to EM-TV, based on Bregman iterations and primal and dual inverse scale space methods, in order to obtain improved imaging results by simultaneous contrast enhancement. Besides further generalizations of the primal and dual scale space methods in terms of general, convex variational regularization methods, we provide error estimates and convergence rates for exact and noisy data. We illustrate the performance of our techniques on synthetic and experimental biological data.

Total Variation Processing of Images with Poisson Statistics

This paper deals with denoising of density images with bad Poisson statistics (low count rates), where the reconstruction of the major structures seems the only reasonable task. Obtaining the structures with sharp edges can also be a prerequisite for further processing, e.g. segmentation of objects. n nA variety of approaches exists in the case of Gaussian noise, but only a few in the Poisson case. We propose some total variation (TV) based regularization techniques adapted to the case of Poisson data, which we derive from approximations of logarithmic a-posteriori probabilities. In order to guarantee sharp edges we avoid the smoothing of the total variation and use a dual approach for the numerical solution. We illustrate and test the feasibility of our approaches for data in positron emission tomography, namely reconstructions of cardiac structures with 18F-FDG and H

Josephson radiation from gapless andreev bound states in HgTe-based topological junctions

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EM-TV Methods for Inverse Problems with Poisson Noise

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Backscattering of Dirac fermions in HgTe quantum wells with a finite gap.

Frequency analysis of the rf emission of oscillating Josephson supercurrent is a powerful passive way of probing properties of topological Josephson junctions. In particular, measurements of the Josephson emission enables to detect the expected presence of topological gapless Andreev bound states that give rise to emission at half the Josephson frequency

Terahertz quantum Hall effect of Dirac fermions in a topological insulator

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