Sparse phase retrieval of structured signals by Prony's method

The phase retrieval problem consists in the recovery of a complex-valued signal from the magnitudes of its Fourier transform. Restricting ourselves to the case of sparse structured signals f, which can be represented as a linear combination of N arbitrary translations of a given generator function, we show that almost all f can be recovered from 𝒪 (N²) intensity measurements |ℱ[f](ω)| up to trivial ambiguities. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Determination of boron and hydrogen in materials for multicrystalline solar cell production with prompt gamma activation analysis

Journal of Radioanalytical and Nuclear Chemistry - For the optimization of the manufacturing process of multicrystalline silicon (mc-Si) for solar cells in order to reduce energy consumption and...     

Computation of Adaptive Fourier Series by Sparse Approximation of Exponential Sums

Journal of Fourier Analysis and Applications - In this paper, we study the convergence of adaptive Fourier sums for real-valued $$2\pi $$ -periodic functions. For this purpose, we approximate the...     

A deterministic sparse FFT algorithm for vectors with small support

In this paper we consider the special case where a signal x\({\in }\,\mathbb {C}^{N}\) is known to vanish outside a support interval of length m < N. If the support length m of x or a good bound of it is a-priori known we derive a sublinear deterministic algorithm to compute x from its discrete Fourier transform \(\widehat {\mathbf x}\,{\in }\,\mathbb {C}^{N}\). In case of exact Fourier measurements we require only \({\mathcal O}\)(m\(\log \)m) arithmetical operations. For noisy measurements, we propose a stable \({\mathcal O}\)(m\(\log \)N) algorithm.     

Ambiguities in one-dimensional phase retrieval of structured functions

Phase retrieval means that we wish to recover a complex-valued signal (discrete or continuous) from the magnitudes of its Fourier transform. Here we restrict ourselves to the recovery of structured functions, e.g. linear spline functions with equidistant knots. First, a complete characterization of the occurring ambiguities is presented. Moreover, we investigate additionally given moduli of the signal itself regarding their ability to reduce the set of ambiguities. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Two-scale symbol and autocorrelation symbol for B-splines with multiple knots

The Fourier transforms of B-splines with multiple integer knots are shown to satisfy a simple recursion relation. This recursion formula is applied to derive a generalized two-scale relation for B-splines with multiple knots. Furthermore, the structure of the corresponding autocorrelation symbol is investigated. In particular, it can be observed that the solvability of the cardinal Hermite spline interpolation problem for spline functions of degree 2m+1 and defectr, first considered by Lipow and Schoenberg [9], is equivalent to the Riesz basis property of our B-splines with degreem and defectr. In this way we obtain a new, simple proof for the assertion that the cardinal Hermite spline interpolation problem in [9] has a unique solution.     

Direct experimental limit on neutron-mirror-neutron oscillations

In case a mirror world with a copy of our ordinary particle spectrum would exist, the neutron n and its degenerate partner, the mirror neutron n', could potentially mix and undergo nn' oscillations. The interaction of an ordinary magnetic field with the ordinary neutron would lift the degeneracy between the mirror partners, diminish the n' amplitude in the n wave function and, thus, suppress its observability. We report an experimental comparison of ultracold neutron storage in a trap with and without superimposed magnetic field. No influence of the magnetic field is found and, assuming negligible mirror magnetic fields, a limit on the oscillation time taunn' > 103 s (95% C.L.) is derived.