Sparsity and Parallel Acquisition: Optimal Uniform and Nonuniform Recovery Guarantees

The problem of multiple sensors simultaneously acquiring measurements of a single object can be found in many applications. In this paper, we present the optimal recovery guarantees for the recovery of compressible signals from multi-sensor measurements using compressed sensing. In the first half of the paper, we present both uniform and nonuniform recovery guarantees for the conventional sparse signal model in a so-called distinct sensing scenario. In the second half, using the so-called sparse and distributed signal model, we present nonuniform recovery guarantees which effectively broaden the class of sensing scenarios for which optimal recovery is possible, including to the so-called identical sampling scenario. To verify our recovery guarantees we provide several numerical results including phase transition curves and numerically-computed bounds.Comment: 13 pages and 3 figure

Compressed Sensing and Parallel Acquisition

Parallel acquisition systems arise in various applications in order to moderate problems caused by insufficient measurements in single-sensor systems. These systems allow simultaneous data acquisition in multiple sensors, thus alleviating such problems by providing more overall measurements. In this work we consider the combination of compressed sensing with parallel acquisition. We establish the theoretical improvements of such systems by providing recovery guarantees for which, subject to appropriate conditions, the number of measurements required per sensor decreases linearly with the total number of sensors. Throughout, we consider two different sampling scenarios -- distinct (corresponding to independent sampling in each sensor) and identical (corresponding to dependent sampling between sensors) -- and a general mathematical framework that allows for a wide range of sensing matrices (e.g., subgaussian random matrices, subsampled isometries, random convolutions and random Toeplitz matrices). We also consider not just the standard sparse signal model, but also the so-called sparse in levels signal model. This model includes both sparse and distributed signals and clustered sparse signals. As our results show, optimal recovery guarantees for both distinct and identical sampling are possible under much broader conditions on the so-called sensor profile matrices (which characterize environmental conditions between a source and the sensors) for the sparse in levels model than for the sparse model. To verify our recovery guarantees we provide numerical results showing phase transitions for a number of different multi-sensor environments.Comment: 43 pages, 4 figure

Uniform Recovery from Subgaussian Multi-Sensor Measurements

Parallel acquisition systems are employed successfully in a variety of different sensing applications when a single sensor cannot provide enough measurements for a high-quality reconstruction. In this paper, we consider compressed sensing (CS) for parallel acquisition systems when the individual sensors use subgaussian random sampling. Our main results are a series of uniform recovery guarantees which relate the number of measurements required to the basis in which the solution is sparse and certain characteristics of the multi-sensor system, known as sensor profile matrices. In particular, we derive sufficient conditions for optimal recovery, in the sense that the number of measurements required per sensor decreases linearly with the total number of sensors, and demonstrate explicit examples of multi-sensor systems for which this holds. We establish these results by proving the so-called Asymmetric Restricted Isometry Property (ARIP) for the sensing system and use this to derive both nonuniversal and universal recovery guarantees. Compared to existing work, our results not only lead to better stability and robustness estimates but also provide simpler and sharper constants in the measurement conditions. Finally, we show how the problem of CS with block-diagonal sensing matrices can be viewed as a particular case of our multi-sensor framework. Specializing our results to this setting leads to a recovery guarantee that is at least as good as existing results.Comment: 37 pages, 5 figure

Advanced sparse sampling techniques for accelerating structural and quantitative MRI

Magnetic Resonance Imaging (MRI) has become a routine clinical procedure for the screening, diagnosis and treatment monitoring of various clinical conditions. Although MRI has highly desirable properties such as being completely non-ionizing and providing excellent soft tissue contrast which has resulted in its widespread usage across the gamut of clinical applications, it is limited by a slow data acquisition process. Several techniques have been developed over the years that have considerably improved the speed of MRI but there is still a clinical need to further accelerate MRI for many clinical applications. This thesis focuses on two recent advances in MRI acceleration to reduce the overall patient scan time. The first part of the thesis describes the development of a fast 3D neuroimaging methodology that has been implemented in a clinical Magnetic Resonance (MR) sequence which was accelerated using a combination of compressed sensing and sampling order optimization of acquired measurements. This methodology reduced the overall scan time by more than 60% compared to the normal scan time while also producing images of acceptable quality for clinical diagnosis. The clinical utility of accelerated neuroimaging is demonstrated by conducting a healthy volunteer study on eight subjects using this fast 3D MRI method. The results of the radiological diagnostic quality assessments that were carried out on the accelerated human brain MR images by four experienced neuroradiologists are presented. The results show that accelerated MR neuroimaging retained sufficient clinical diagnostic value for certain clinical applications. The second part of the thesis describes the development of an accelerated Cartesian sampling scheme for a rapid quantitative MR method called Magnetic Resonance Fingerprinting (MRF). This method was able to simultaneously generate quantitative multi-parametric maps such as T1, T2 and proton density (PD) maps in a very short scan duration that is clinically acceptable. The developed Cartesian sampling method using Echo Planar Imaging (EPI) is compared with conventional spiral sampling that is generally used for MR fingerprinting. The ability of novel iterative reconstruction techniques to improve the multi-parametric estimation accuracy is also demonstrated. The results show that accelerated Cartesian MR fingerprinting can be an alternative to conventional spiral MR fingerprinting

2022 Review of Data-Driven Plasma Science

Data-driven science and technology offer transformative tools and methods to science. This review article highlights the latest development and progress in the interdisciplinary field of data-driven plasma science (DDPS), i.e., plasma science whose progress is driven strongly by data and data analyses. Plasma is considered to be the most ubiquitous form of observable matter in the universe. Data associated with plasmas can, therefore, cover extremely large spatial and temporal scales, and often provide essential information for other scientific disciplines. Thanks to the latest technological developments, plasma experiments, observations, and computation now produce a large amount of data that can no longer be analyzed or interpreted manually. This trend now necessitates a highly sophisticated use of high-performance computers for data analyses, making artificial intelligence and machine learning vital components of DDPS. This article contains seven primary sections, in addition to the introduction and summary. Following an overview of fundamental data-driven science, five other sections cover widely studied topics of plasma science and technologies, i.e., basic plasma physics and laboratory experiments, magnetic confinement fusion, inertial confinement fusion and high-energy-density physics, space and astronomical plasmas, and plasma technologies for industrial and other applications. The final section before the summary discusses plasma-related databases that could significantly contribute to DDPS. Each primary section starts with a brief introduction to the topic, discusses the state-of-the-art developments in the use of data and/or data-scientific approaches, and presents the summary and outlook. Despite the recent impressive signs of progress, the DDPS is still in its infancy. This article attempts to offer a broad perspective on the development of this field and identify where further innovations are required

Advances in Image Processing, Analysis and Recognition Technology

For many decades, researchers have been trying to make computers’ analysis of images as effective as the system of human vision is. For this purpose, many algorithms and systems have previously been created. The whole process covers various stages, including image processing, representation and recognition. The results of this work can be applied to many computer-assisted areas of everyday life. They improve particular activities and provide handy tools, which are sometimes only for entertainment, but quite often, they significantly increase our safety. In fact, the practical implementation of image processing algorithms is particularly wide. Moreover, the rapid growth of computational complexity and computer efficiency has allowed for the development of more sophisticated and effective algorithms and tools. Although significant progress has been made so far, many issues still remain, resulting in the need for the development of novel approaches

Imaging Sensors and Applications

In past decades, various sensor technologies have been used in all areas of our lives, thus improving our quality of life. In particular, imaging sensors have been widely applied in the development of various imaging approaches such as optical imaging, ultrasound imaging, X-ray imaging, and nuclear imaging, and contributed to achieve high sensitivity, miniaturization, and real-time imaging. These advanced image sensing technologies play an important role not only in the medical field but also in the industrial field. This Special Issue covers broad topics on imaging sensors and applications. The scope range of imaging sensors can be extended to novel imaging sensors and diverse imaging systems, including hardware and software advancements. Additionally, biomedical and nondestructive sensing applications are welcome

Gaze-Based Human-Robot Interaction by the Brunswick Model

We present a new paradigm for human-robot interaction based on social signal processing, and in particular on the Brunswick model. Originally, the Brunswick model copes with face-to-face dyadic interaction, assuming that the interactants are communicating through a continuous exchange of non verbal social signals, in addition to the spoken messages. Social signals have to be interpreted, thanks to a proper recognition phase that considers visual and audio information. The Brunswick model allows to quantitatively evaluate the quality of the interaction using statistical tools which measure how effective is the recognition phase. In this paper we cast this theory when one of the interactants is a robot; in this case, the recognition phase performed by the robot and the human have to be revised w.r.t. the original model. The model is applied to Berrick, a recent open-source low-cost robotic head platform, where the gazing is the social signal to be considered