Sparse Array Design via Fractal Geometries

Sparse sensor arrays have attracted considerable attention in various fields such as radar, array processing, ultrasound imaging and communications. In the context of correlation-based processing, such arrays enable to resolve more uncorrelated sources than physical sensors. This property of sparse arrays stems from the size of their difference coarrays, defined as the differences of element locations. Thus, the design of sparse arrays with large difference coarrays is of great interest. In addition, other array properties such as symmetry, robustness and array economy are important in different applications. Numerous studies have proposed diverse sparse geometries, focusing on certain properties while lacking others. Incorporating multiple properties into the design task leads to combinatorial problems which are generally NP-hard. For small arrays these optimization problems can be solved by brute force, however, in large scale they become intractable. In this paper, we propose a scalable systematic way to design large sparse arrays considering multiple properties. To that end, we introduce a fractal array design in which a generator array is recursively expanded according to its difference coarray. Our main result states that for an appropriate choice of the generator such fractal arrays exhibit large difference coarrays. Furthermore, we show that the fractal arrays inherit their properties from their generators. Thus, a small generator can be optimized according to desired requirements and then expanded to create a fractal array which meets the same criteria. This approach paves the way to efficient design of large arrays of hundreds or thousands of elements with specific properties.Comment: 16 pages, 9 figures, 1 Tabl

Learning Sub-Sampling and Signal Recovery with Applications in Ultrasound Imaging

Limitations on bandwidth and power consumption impose strict bounds on data rates of diagnostic imaging systems. Consequently, the design of suitable (i.e. task- and data-aware) compression and reconstruction techniques has attracted considerable attention in recent years. Compressed sensing emerged as a popular framework for sparse signal reconstruction from a small set of compressed measurements. However, typical compressed sensing designs measure a (non)linearly weighted combination of all input signal elements, which poses practical challenges. These designs are also not necessarily task-optimal. In addition, real-time recovery is hampered by the iterative and time-consuming nature of sparse recovery algorithms. Recently, deep learning methods have shown promise for fast recovery from compressed measurements, but the design of adequate and practical sensing strategies remains a challenge. Here, we propose a deep learning solution termed Deep Probabilistic Sub-sampling (DPS), that learns a task-driven sub-sampling pattern, while jointly training a subsequent task model. Once learned, the task-based sub-sampling patterns are fixed and straightforwardly implementable, e.g. by non-uniform analog-to-digital conversion, sparse array design, or slow-time ultrasound pulsing schemes. The effectiveness of our framework is demonstrated in-silico for sparse signal recovery from partial Fourier measurements, and in-vivo for both anatomical image and tissue-motion (Doppler) reconstruction from sub-sampled medical ultrasound imaging data

Addressing Spectrum Congestion by Spectrally-Cooperative Radar design

This dissertation attempts to address a significant challenge that is encountered by the users of the Radio Frequency (RF) Spectrum in recent years. The challenge arises due to the need for greater RF spectrum by wireless communication industries such as mobile telephony, cable/satellite and wireless internet as a result of growing con-sumer base and demands. As such, it has led to the issue of spectrum congestion as radar systems have traditionally maintain the largest share of the RF spectrum. To resolve the spectrum congestion problem, it has become even necessary for users from both radar and communication systems to coexist within a finite spectrum allocation. However, this then leads to other problems such as the increased likelihood of mutual interference experienced by all systems that are coexisting within the finite spectrum.. In order to address this challenge, the dissertation will seek to resolve it via a two-step approach that are described as follows. For the first step of this approach, it will present a structured and meticulous approach to design a sparse spectrum allocation optimization scheme that will lead to the release of valuable spectrum previously allocated to radar applications for reallocation to other players such as the wireless video-on-demand and telecommunication industries while maintaining the range resolution performance of these radar applications. This sparse bandwidth allocation scheme is implemented using an optimization process utilizing the Marginal Fisher information (MFI) measure as the main metric for optimization. Although the MFI approach belongs to the class of greedy optimization methods that cannot guarantee global convergence, the results obtained indicated that this approach is able to produce a locally optimal solution. For the second step of this approach, it will present on the design of a spectral efficient waveform that can be used to ensure that the allocated spectrum limits will not be violated due to poor spectral emission containment. The design concept of this waveform is based on the joint implementation of the first and higher orders of the Poly-phase coded Frequency Modulated (PCFM) waveform that expands previous research on first order PCFM waveform. As any waveform generated using the PCFM framework possesses good spectral containment and is amenable to high power transmit operations such as radar due to its constant modulus property, thus the combined-orders of PCFM waveform is a very suitable candidate that can be used in conjunction with the sparse bandwidth allocation scheme in the first step for any radar application such that the waveform will further mitigate the issue of interference experienced by other users coexisting within the same band

Theory and Algorithms for Reliable Multimodal Data Analysis, Machine Learning, and Signal Processing

Modern engineering systems collect large volumes of data measurements across diverse sensing modalities. These measurements can naturally be arranged in higher-order arrays of scalars which are commonly referred to as tensors. Tucker decomposition (TD) is a standard method for tensor analysis with applications in diverse fields of science and engineering. Despite its success, TD exhibits severe sensitivity against outliers —i.e., heavily corrupted entries that appear sporadically in modern datasets. We study L1-norm TD (L1-TD), a reformulation of TD that promotes robustness. For 3-way tensors, we show, for the first time, that L1-TD admits an exact solution via combinatorial optimization and present algorithms for its solution. We propose two novel algorithmic frameworks for approximating the exact solution to L1-TD, for general N-way tensors. We propose a novel algorithm for dynamic L1-TD —i.e., efficient and joint analysis of streaming tensors. Principal-Component Analysis (PCA) (a special case of TD) is also outlier responsive. We consider Lp-quasinorm PCA (Lp-PCA) for

Sparse Linear Antenna Arrays: A Review

Linear sparse antenna arrays have been widely studied in array processing literature. They belong to the general class of non-uniform linear arrays (NULAs). Sparse arrays need fewer sensor elements than uniform linear arrays (ULAs) to realize a given aperture. Alternately, for a given number of sensors, sparse arrays provide larger apertures and higher degrees of freedom than full arrays (ability to detect more source signals through direction-of-arrival (DOA) estimation). Another advantage of sparse arrays is that they are less affected by mutual coupling compared to ULAs. Different types of linear sparse arrays have been studied in the past. While minimum redundancy arrays (MRAs) and minimum hole arrays (MHAs) existed for more than five decades, other sparse arrays such as nested arrays, co-prime arrays and super-nested arrays have been introduced in the past decade. Subsequent to the introduction of co-prime and nested arrays in the past decade, many modifications, improvements and alternate sensor array configurations have been presented in the literature in the past five years (2015–2020). The use of sparse arrays in future communication systems is promising as they operate with little or no degradation in performance compared to ULAs. In this chapter, various linear sparse arrays have been compared with respect to parameters such as the aperture provided for a given number of sensors, ability to provide large hole-free co-arrays, higher degrees of freedom (DOFs), sharp angular resolutions and susceptibility to mutual coupling. The chapter concludes with a few recommendations and possible future research directions

Parallelization and improvement of beamforming process in synthetic aperture systems for real-time ultrasonic image generation

Tesis inédita de la Universidad Complutense de Madrid, Facultad de Informática, Departamento de Arquitectura de Computadores y Automática, leída el 9-02-2016La ecografía es hoy en día uno de los métodos de visualización más populares para examinar el interior de cuerpos opacos. Su aplicación es especialmente significativa tanto en el campo del diagnóstico médico como en las aplicaciones de evaluación no destructiva en el ámbito industrial, donde se evalúa la integridad de un componente o una estructura. El desarrollo de sistemas ecográficos de alta calidad y con buenas prestaciones se basa en el empleo de sistemas multisensoriales conocidos como arrays que pueden estar compuestos por varias decenas de elementos. El desarrollo de estos dispositivos tiene asociada una elevada complejidad, tanto por el número de sensores y la electrónica necesaria para la adquisición paralela de señales, como por la etapa de procesamiento de los datos adquiridos que debe operar en tiempo real. Esta etapa de procesamiento de señal trabaja con un elevado flujo de datos en paralelo y desarrolla, además de la composición de imagen, otras sofisticadas técnicas de medidas sobre los datos (medida de elasticidad, flujo, etc). En este sentido, el desarrollo de nuevos sistemas de imagen con mayores prestaciones (resolución, rango dinámico, imagen 3D, etc) está fuertemente limitado por el número de canales en la apertura del array. Mientras algunos estudios se han centrado en la reducción activa de sensores (sparse arrays como ejemplo), otros se han centrado en analizar diferentes estrategias de adquisiciónn que, operando con un número reducido de canales electrónicos en paralelo, sean capaz por multiplexación emular el funcionamiento de una apertura plena. A estas últimas técnicas se las agrupa mediante el concepto de Técnicas de Apertura Sintética (SAFT). Su interés radica en que no solo son capaces de reducir los requerimientos hardware del sistema (bajo consumo, portabilidad, coste, etc) sino que además permiten dentro de cierto compromiso la mejora de la calidad de imagen respecto a los sistemas convencionales...Ultrasound is nowadays one of the most popular visualization methods to examine the interior of opaque objects. Its application is particularly significant in the field of medical diagnosis as well as non-destructive evaluation applications in industry. The development of high performance ultrasound imaging systems is based on the use of multisensory systems known as arrays, which may be composed by dozens of elements. The development of these devices has associated a high complexity, due to the number of sensors and electronics needed for the parallel acquisition of signals, and for the processing stage of the acquired data which must operate on real-time. This signal processing stage works with a high data flow in parallel and develops, besides the image composition, other sophisticated measure techniques (measure of elasticity, flow, etc). In this sense, the development of new imaging systems with higher performance (resolution, dynamic range, 3D imaging, etc) is strongly limited by the number of channels in array’s aperture. While some studies have been focused on the reduction of active sensors (i.e. sparse arrays), others have been centered on analysing different acquisition strategies which, operating with reduced number of electronic channels in parallel, are able to emulate by multiplexing the behavior of a full aperture. These latest techniques are grouped under the term known as Synthetic Aperture Techniques (SAFT). Their interest is that they are able to reduce hardware requirements (low power, portability, cost, etc) and also allow to improve the image quality over conventional systems...Depto. de Arquitectura de Computadores y AutomáticaFac. de InformáticaTRUEunpu