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BNYQ Report Summary

Project ID: 646804
Funded under: H2020-EU.1.1.

Periodic Reporting for period 2 - BNYQ (Breaking the Nyquist Barrier: A New Paradigm in Data Conversion and Transmission)

Reporting period: 2017-02-01 to 2018-07-31

Summary of the context and overall objectives of the project

Digital signal processing (DSP) is a revolutionary paradigm shift enabling processing of physical data in the digital domain where design and implementation are considerably simplified. However, state-of-the-art analog-to-digital convertors (ADCs) preclude high-rate wideband sampling and pro- cessing with low cost and energy consumption, presenting a major bottleneck. This is mostly due to a traditional assumption that sampling must be performed at the Nyquist rate, that is, twice the signal bandwidth. Modern applications including communications, medical imaging, radar and more use signals with high bandwidth, resulting in prohibitively large Nyquist rates.
Our ambitious goal is to introduce a paradigm shift in ADC design that will enable systems capable of low-rate, wideband sensing and low-rate DSP. While DSP has a rich history in exploiting structure to reduce dimensionality and perform efficient parameter extraction, current ADCs do not exploit such knowledge. We challenge current practice that separates the sampling stage from the processing stage and exploit structure in analog signals already in the ADC, to drastically reduce the sampling and processing rates. Our preliminary data shows that this allows substantial savings in sampling and processing rates | we show rate reduction of 1/28 in ultrasound imaging, and 1/30 in radar detection.
To achieve our overreaching goal we focus on three interconnected objectives { developing the 1) theory 2) hardware and 3) applications of sub-Nyquist sampling. Our methodology ties together two areas on the frontier of signal processing: compressed sensing (CS), focused on finite length vectors, and analog sampling. Our research plan also inherently relies on advances in several other important areas within signal processing and combines multi-disciplinary research at the intersection of signal processing, information theory, optimization, estimation theory and hardware design.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

As one thrust in our research project we have been developing new methods for super-resolution imaging, in both fluorescence microscopy and contrast enhanced ultrasound imaging. Particular we developed novel methods which achieve a spatial resolution comparable to the 2014 Nobel winning method in chemistry PALM (and STORM), but has a two-orders of magnitude shorter exposure time. This dramatic improvement in the temporal resolution paves the way to both sub-diffraction live-cell imaging in microscopy and clinical sub-diffraction diagnosis in ultrasound. The microscopy implementation is called SPARCOM (sparsity-based super-resolution correlation microscopy), while the ultrasound implementation is referred to as SUSHI (sparsity-based ultrasound super-resolution hemodynamic imaging).in this topic we have written four papers. Another area we are working on is low-rate acquisition and processing framework based on frequency domain processing for 3D ultrasound imaging. The method was verified using numerous simulated scenarios as well as data acquired experimentally using a commercial imaging system. we have also looked development of computationally efficient processing method for ultrasound imaging with coded signals. The method allows obtaining optimal image quality with improved SNR and higher penetration depth, while keeping computational load low enough to enable real time implementation. The proposed method was implemented on Verasonics imaging system .We also considered a generalization of low-rate frequency domain processing for ultrafast ultrasound imaging based on coherent plane-wave compounding. The method was implemented and verified experimentally on simulated, experimental and in vivo acquisitions. The results are summarized in a paper submitted for publication. finally we have considered the development of statistical interpretation of beamforming, a basic processing step in ultrasound image formation. Our iterative scheme yields significantly improved contrast compared to standard processing method without severely increasing computational complexity or need for fine-tuning of parameters. The results are submitted for publication in. Another aspect we are working on in the area of ultrasound is improving quality and performance of medical ultrasound systemsusing a small number of antenna elements. Specifically we have considered the design of sparse arrays along with developing novel methods for beamforming that is the process producing the image. The work done is mainly concerned with providing better image quality in terms of resolution and contrast, and with improved performance in terms of power, cost and size by reducing the sampling rates, the number of transducer elements and required transmissions.We have published four papers in this area. .Moving on to more basic sampling paradigms, we have also explored-Sub-Nyquist sampling of correlated signals: A variety of interesting theories have been developed for sampling and reconstruction of individual signals with certain structure but very few results have been reported on sampling a set of signals with a certain underlying correlation. In information theory, Slepian-Wolf framework of lossless distributed source coding has been proposed where two or more sources are coded independently while decoding is achieved jointly. By exploring the correlation between the sources, the coders operates at conditional entropy rate rather than at the individual entropy rate of the sources. From a sampling theoretic perspective (in the discrete domain), distributed compressive sensing framework has been proposed by Baron et al.We are exploring the relations between these methods in order to develop new methods for sampling of correlated signals at low rates.
In the area of radar we have considered various methods to achieve high resolution radar using a small number of resources in time, space and frequency. Specifically,high Resolution FDMA MIMO Radar with Sub-Nyquist Sam

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

"As outlined above, we have made progress on many of the goals of this project, developing a wide array of systems. Improving power, size, speed, cost, data volume, performance.
The outcome of the research has been implemented in hardware and software demo systems, showing the advantages over traditional approach.This demos have been presented world wide in a large series of conferences.
Areas of interest:

• S. S. Ioushua, O. Yair, D. Cohen and Y. C. Eldar, ""CaSCADE: Compressed Carrier and DOA Estimation"", IEEE Transactions on Signal Processing, vol. 65, issue 10, pp. 2645-2658, May 2017.
• K. Aberman and Y. C. Eldar, ""Compressive Sensing of SAR Signals via Fourier Coefficients"" (EUSAR 2016).
• D. Cohen and Y. C. Eldar, ""Reduced Time-on-Target in Pulse Doppler Radar: Slow Time Domain Compressed Sensing"", IEEE Radar Conference (RadarCon 2016).
• D. Cohen, A. Dikopoltsev, R. Ifraimov and Y. C. Eldar, ""Towards Sub-Nyquist Cognitive Radar"", IEEE Radar Conference (RadarCon 2016).
• D. Cohen, D. Cohen, Y. C. Eldar and A. M. Haimovich, ""Sub-Nyquist Collocated MIMO Radar in Time and Space"", IEEE Radar Conference (RadarCon 2016).
• K. Aberman and Y. C. Eldar, ""Range Doppler Processing Via Fourier Coefficients:The Path to a Sub-Nyquist SAR"", IEEE Radar Conference (RadarCon 2016).
• K. V. Mishra, E. Shoshan, M. Namer, M. Meltsin, D. Cohen, R. Madmoni, S. Dror, R. Ifraimov and Y. C. Eldar, ""Cognitive Sub-Nyquist hardware prototype of a collocated MIMO radar"", Compressed Sensing Theory and its Applications to Radar, Sonar and Remote Sensing (CoSeRa), September 2016.
• D. Cohen, D. Cohen, Y. C. Eldar and A. M. Haimovich, ""Sub-Nyquist Pulse Doppler MIMO Radar"", The 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), March 2017.
• K. V. Mishra and Y. C. Eldar, ""Performance of Time Delay Estimation in a Cognitive Radar"", The 42nd IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), March 2017.
• D. Cohen, K. V. Mishra and Y. C. Eldar, “Spectral Coexistence in Radar using Xampling"", IEEE International Radar Conference (RadarCon), May 2017.
• D. Cohen, K. V. Mishra, D. Cohen, E. Ronen, Y. Grimovich and Y. C. Eldar, “Cognitive Sub-Nyquist MIMO Radar Prototype with Doppler Processing"", IEEE International Radar Conference (RadarCon), May 2017.
• K. Aberman, S. Aviv and Y. C. Eldar, ""Adaptive Frequency Allocation in Radar Imaging: Towards Cognitive SAR”, IEEE International Radar Conference (RadarCon), May 2017.
• K. Aberman and Y. C. Eldar, ""Sub-Nyquist SAR via Fourier Domain Range-Doppler Processing"", IEEE Transactions on Geoscience and Remote Sensing, vol. 55, issue 11, pp. 6228-6244, November 2017.


• D. Kogan, Y. C. Eldar and D. Oron, ""On The 2D Phase Retrieval Problem"", IEEE Transactions on Signal Processing, vol. 65, issue 4, pp. 1058-1067, February 2017.
• K. Huang, Y. C. Eldar and N. Sidiropoulos, ""On Convexity and Identifiability in 1-D Fourier Phase Retrieval"", The 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016).
• D. Cohen and Y. C. Eldar, ""Sub-Nyquist Cyclostationary Detection for Cognitive Radio"", IEEE Transactions on Signal Processing, vol. 65, issue 11, pp. 3004-3019, June 2017.
• D. Cohen, L. Pollak and Y. C. Eldar, ""Carrier Frequency and Bandwidth Estimation of Cyclostationary Multiband Signals"",The 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016).
• Koretz, A. Wiesel and Y. C. Eldar, ""Detection with phaseless measurements"",The 41st IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP 2016).
• Lavrenko, F. Roemer, S. S. Ioushua, D. Cohen, G. Del Galdo, R. S. Thomä and Y. C. Eldar, ""Spatially Resolved sub-Nyquist Sensing of Multiband Signals with Arbitrary Antenna Arrays"", (SPAWC 2016).
• G. Marques, G. Mateos, and Y. Eldar, “SIGIBE: Solving random bilinear equations via gradient desce"
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