SOWAT: Speckle Observations With Alleviated Turbulence

Adaptive optics (AO) systems and image reconstruction algorithms are indispensable tools when it comes to high-precision astrometry. In this paper, we analyze the potential of combining both techniques, i.e. by applying image reconstruction on partially AO corrected short exposures. Therefore we simulate speckle clouds with and without AO corrections and create synthetic observations. We apply holographic image reconstruction to the obtained observations and find that (i) the residual wavefronts decorrelate slowlier and to a lower limit when AO systems are used, (ii) the same reference stars yield a better reconstruction, and (iii) using fainter reference stars we achieve a similar image quality. These results suggest that holographic imaging of speckle observations is feasible with 2-3 times longer integration times and 3mag fainter reference stars, to obtain diffraction-limited imaging from low-order AO systems that are less restricted in sky-coverage than typical high-order AO systems.Comment: 18 pages, 13 figures, and 3 table

Holographic Imaging of Crowded Fields: High Angular Resolution Imaging with Excellent Quality at Very Low Cost

We present a method for speckle holography that is optimised for crowded fields. Its two key features are an iterativ improvement of the instantaneous Point Spread Functions (PSFs) extracted from each speckle frame and the (optional) simultaneous use of multiple reference stars. In this way, high signal-to-noise and accuracy can be achieved on the PSF for each short exposure, which results in sensitive, high-Strehl re- constructed images. We have tested our method with different instruments, on a range of targets, and from the N- to the I-band. In terms of PSF cosmetics, stability and Strehl ratio, holographic imaging can be equal, and even superior, to the capabilities of currently available Adaptive Optics (AO) systems, particularly at short near-infrared to optical wavelengths. It outperforms lucky imaging because it makes use of the entire PSF and reduces the need for frame selection, thus leading to higher Strehl and improved sensitivity. Image reconstruction a posteriori, the possibility to use multiple reference stars and the fact that these reference stars can be rather faint means that holographic imaging offers a simple way to image large, dense stellar fields near the diffraction limit of large telescopes, similar to, but much less technologically demanding than, the capabilities of a multi-conjugate adaptive optics system. The method can be used with a large range of already existing imaging instruments and can also be combined with AO imaging when the corrected PSF is unstable.Comment: Accepted for publication in MNRAS on 15 Nov 201

Normal Factor Graphs and Holographic Transformations

This paper stands at the intersection of two distinct lines of research. One line is "holographic algorithms," a powerful approach introduced by Valiant for solving various counting problems in computer science; the other is "normal factor graphs," an elegant framework proposed by Forney for representing codes defined on graphs. We introduce the notion of holographic transformations for normal factor graphs, and establish a very general theorem, called the generalized Holant theorem, which relates a normal factor graph to its holographic transformation. We show that the generalized Holant theorem on the one hand underlies the principle of holographic algorithms, and on the other hand reduces to a general duality theorem for normal factor graphs, a special case of which was first proved by Forney. In the course of our development, we formalize a new semantics for normal factor graphs, which highlights various linear algebraic properties that potentially enable the use of normal factor graphs as a linear algebraic tool.Comment: To appear IEEE Trans. Inform. Theor

A Recursive Definition of the Holographic Standard Signature

We provide a recursive description of the signatures realizable on the standard basis by a holographic algorithm. The description allows us to prove tight bounds on the size of planar matchgates and efficiently test for standard signatures. Over finite fields, it allows us to count the number of n-bit standard signatures and calculate their expected sparsity.Comment: Fixed small typo in Section 3.

Robust particle outline extraction and its application to digital on-line holography

Peer reviewedPostprin

Massive MIMO is a Reality -- What is Next? Five Promising Research Directions for Antenna Arrays

Massive MIMO (multiple-input multiple-output) is no longer a "wild" or "promising" concept for future cellular networks - in 2018 it became a reality. Base stations (BSs) with 64 fully digital transceiver chains were commercially deployed in several countries, the key ingredients of Massive MIMO have made it into the 5G standard, the signal processing methods required to achieve unprecedented spectral efficiency have been developed, and the limitation due to pilot contamination has been resolved. Even the development of fully digital Massive MIMO arrays for mmWave frequencies - once viewed prohibitively complicated and costly - is well underway. In a few years, Massive MIMO with fully digital transceivers will be a mainstream feature at both sub-6 GHz and mmWave frequencies. In this paper, we explain how the first chapter of the Massive MIMO research saga has come to an end, while the story has just begun. The coming wide-scale deployment of BSs with massive antenna arrays opens the door to a brand new world where spatial processing capabilities are omnipresent. In addition to mobile broadband services, the antennas can be used for other communication applications, such as low-power machine-type or ultra-reliable communications, as well as non-communication applications such as radar, sensing and positioning. We outline five new Massive MIMO related research directions: Extremely large aperture arrays, Holographic Massive MIMO, Six-dimensional positioning, Large-scale MIMO radar, and Intelligent Massive MIMO.Comment: 20 pages, 9 figures, submitted to Digital Signal Processin