Sub-Nyquist Sampling: Bridging Theory and Practice

Sampling theory encompasses all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark in the development of digital signal processing. In modern applications, an increasingly number of functions is being pushed forward to sophisticated software algorithms, leaving only those delicate finely-tuned tasks for the circuit level. In this paper, we review sampling strategies which target reduction of the ADC rate below Nyquist. Our survey covers classic works from the early 50's of the previous century through recent publications from the past several years. The prime focus is bridging theory and practice, that is to pinpoint the potential of sub-Nyquist strategies to emerge from the math to the hardware. In that spirit, we integrate contemporary theoretical viewpoints, which study signal modeling in a union of subspaces, together with a taste of practical aspects, namely how the avant-garde modalities boil down to concrete signal processing systems. Our hope is that this presentation style will attract the interest of both researchers and engineers in the hope of promoting the sub-Nyquist premise into practical applications, and encouraging further research into this exciting new frontier.Comment: 48 pages, 18 figures, to appear in IEEE Signal Processing Magazin

Common pulse retrieval algorithm: a fast and universal method to retrieve ultrashort pulses

We present a common pulse retrieval algorithm (COPRA) that can be used for a broad category of ultrashort laser pulse measurement schemes including frequency-resolved optical gating (FROG), interferometric FROG, dispersion scan, time domain ptychography, and pulse shaper assisted techniques such as multiphoton intrapulse interference phase scan (MIIPS). We demonstrate its properties in comprehensive numerical tests and show that it is fast, reliable and accurate in the presence of Gaussian noise. For FROG it outperforms retrieval algorithms based on generalized projections and ptychography. Furthermore, we discuss the pulse retrieval problem as a nonlinear least-squares problem and demonstrate the importance of obtaining a least-squares solution for noisy data. These results improve and extend the possibilities of numerical pulse retrieval. COPRA is faster and provides more accurate results in comparison to existing retrieval algorithms. Furthermore, it enables full pulse retrieval from measurements for which no retrieval algorithm was known before, e.g., MIIPS measurements

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Thirty Years of Machine Learning: The Road to Pareto-Optimal Wireless Networks

Future wireless networks have a substantial potential in terms of supporting a broad range of complex compelling applications both in military and civilian fields, where the users are able to enjoy high-rate, low-latency, low-cost and reliable information services. Achieving this ambitious goal requires new radio techniques for adaptive learning and intelligent decision making because of the complex heterogeneous nature of the network structures and wireless services. Machine learning (ML) algorithms have great success in supporting big data analytics, efficient parameter estimation and interactive decision making. Hence, in this article, we review the thirty-year history of ML by elaborating on supervised learning, unsupervised learning, reinforcement learning and deep learning. Furthermore, we investigate their employment in the compelling applications of wireless networks, including heterogeneous networks (HetNets), cognitive radios (CR), Internet of things (IoT), machine to machine networks (M2M), and so on. This article aims for assisting the readers in clarifying the motivation and methodology of the various ML algorithms, so as to invoke them for hitherto unexplored services as well as scenarios of future wireless networks.Comment: 46 pages, 22 fig

Review of small-angle coronagraphic techniques in the wake of ground-based second-generation adaptive optics systems

Small-angle coronagraphy is technically and scientifically appealing because it enables the use of smaller telescopes, allows covering wider wavelength ranges, and potentially increases the yield and completeness of circumstellar environment - exoplanets and disks - detection and characterization campaigns. However, opening up this new parameter space is challenging. Here we will review the four posts of high contrast imaging and their intricate interactions at very small angles (within the first 4 resolution elements from the star). The four posts are: choice of coronagraph, optimized wavefront control, observing strategy, and post-processing methods. After detailing each of the four foundations, we will present the lessons learned from the 10+ years of operations of zeroth and first-generation adaptive optics systems. We will then tentatively show how informative the current integration of second-generation adaptive optics system is, and which lessons can already be drawn from this fresh experience. Then, we will review the current state of the art, by presenting world record contrasts obtained in the framework of technological demonstrations for space-based exoplanet imaging and characterization mission concepts. Finally, we will conclude by emphasizing the importance of the cross-breeding between techniques developed for both ground-based and space-based projects, which is relevant for future high contrast imaging instruments and facilities in space or on the ground.Comment: 21 pages, 7 figure

GUARDIANS final report

Emergencies in industrial warehouses are a major concern for firefghters. The large dimensions together with the development of dense smoke that drastically reduces visibility, represent major challenges. The Guardians robot swarm is designed to assist fire fighters in searching a large warehouse. In this report we discuss the technology developed for a swarm of robots searching and assisting fire fighters. We explain the swarming algorithms which provide the functionality by which the robots react to and follow humans while no communication is required. Next we discuss the wireless communication system, which is a so-called mobile ad-hoc network. The communication network provides also one of the means to locate the robots and humans. Thus the robot swarm is able to locate itself and provide guidance information to the humans. Together with the re ghters we explored how the robot swarm should feed information back to the human fire fighter. We have designed and experimented with interfaces for presenting swarm based information to human beings

Development of self-organizing methods for radio spectrum sensing

A problem of wide-band radio spectrum analysis in real time was solved and presented in the dissertation. The goal of the work was to develop a spectrum sensing method for primary user emission detection in radio spectrum by investigating new signal feature extraction and intelligent decision making techniques. A solution of this problem is important for application in cognitive radio systems, where radio spectrum is analyzed in real time. In thesis there are reviewed currently suggested spectrum analysis methods, which are used for cognitive radio. The main purpose of these methods is to optimize spectrum description feature estimation in real-time systems and to select suitable classification threshold. For signal spectrum description analyzed methods used signal energy estimation, analyzed energy statistical difference in time and frequency. In addition, the review has shown that the wavelet transform can be used for signal pre-processing in spectrum sensors. For classification threshold selection in literature most common methods are based on statistical noise estimate and energy statistical change analysis. However, there are no suggested efficient methods, which let classification threshold to change adaptively, when RF environment changes. It were suggested signal features estimation modifications, which let to increase the efficiency of algorithm implementation in embedded system, by decreasing the amount of required calculations and preserving the accuracy of spectrum analysis algorithms. For primary signal processing it is suggested to use wavelet transform based features extraction, which are used for spectrum sensors and lets to increase accuracy of noisy signal detection. All primary user signal emissions were detected with lower than 1% false alarm ratio. In dissertation, there are suggested artificial neural network based methods, which let adaptively select classification threshold for the spectrum sensors. During experimental tests, there was achieved full signals emissions detection with false alarm ratio lower than 1%. It was suggested self organizing map structure modification, which increases network self-training speed up to 32 times. This self-training speed is achieved due to additional inner weights, which are added in to self organizing map structure. In self-training stage network structure changes especially fast and when topology, which is suited for given task, is reached, in further self-training iterations it can be disordered. In order to avoid this over-training, self-training process monitoring algorithms must be used. There were suggested original methods for self-training process control, which let to avoid network over-training and decrease self-training iteration quantity