Semantic web technologies (Hitzler, Krötzsch, and Rudolph 2010) are meant to deal with these issues, and indeed since the advent of linked data (Bizer, Heath, and Berners-Lee 2009) a few years ago, they have become central to mainstream semantic web research and development. We can easily understand linked data as being a part of the greater big data landscape, as many of the challenges are the same (Hitzler and Janowicz 2013). The linking component of linked data, however, puts an additional focus on the integration and conflation of data across multiple sources. This issue of AI Magazine is a followup from that meeting and contains significantly extended, enhanced, and updated contributions. We summarize the articles in the following paragraphs.
Deploying AI systems on the Web provides tangible evidence of the power and utility of AI techniques. Next time you encounter AI bashing, wouldn't it be satisfying to counter with a handful of well-chosen URLs? At the conference, Jude Shavlik asked me to edit a special issue of AI Magazine describing AI systems that have the Web as their domain. Indeed, the authors of each article included in this special issue have promised to create and maintain a URL pointing to a working prototype. Now, almost a year later, we have the fruit of this labor.
There are more than a trillion sensors in the world today and according to some estimates there will be about 50 trillion cameras worldwide within the next 5 years, all collecting data either sporadically or around the clock. With such explosive growth of available data and computing resources, recent advances in machine learning and data analytics have yielded transformative results across diverse scientific disciplines, including image recognition, natural language processing, cognitive science, and genomics. However, in many engineering applications, quality and error-free data is not easy to obtain, e.g., for system dynamics characterized by bifurcations and instabilities, hysteresis, delayed responses, and often irreversible responses. Admittedly, as in all everyday applications, in engineering problems, the volume of data has increased substantially compared to even a decade ago but analyzing big data is expensive and time-consuming. Data-driven methods, which have been enabled in the past decade by the availability of sensors, data storage, and computational resources, are taking center stage across many disciplines (physical and information) of science.
In this survey, we provide a detailed review of recent advances in the recovery of continuous domain multidimensional signals from their few nonuniform (multichannel) measurements using structured low-rank matrix completion formulation. This framework is centered on the fundamental duality between the compactness (e.g., sparsity) of the continuous signal and the rank of a structured matrix, whose entries are functions of the signal. This property enables the reformulation of the signal recovery as a low-rank structured matrix completion, which comes with performance guarantees. We will also review fast algorithms that are comparable in complexity to current compressed sensing methods, which enables the application of the framework to large-scale magnetic resonance (MR) recovery problems. The remarkable flexibility of the formulation can be used to exploit signal properties that are difficult to capture by current sparse and low-rank optimization strategies. We demonstrate the utility of the framework in a wide range of MR imaging (MRI) applications, including highly accelerated imaging, calibration-free acquisition, MR artifact correction, and ungated dynamic MRI. The slow nature of signal acquisition in magnetic resonance imaging (MRI), where the image is formed from a sequence of Fourier samples, often restricts the achievable spatial and temporal resolution in multidimensional static and dynamic imaging applications. Discrete compressed sensing (CS) methods provided a major breakthrough to accelerate the magnetic resonance (MR) signal acquisition by reducing the sampling burden. As described in an introductory article in this special issue  these algorithms exploited the sparsity of the discrete signal in a transform domain to recover the images from a few measurements. In this paper, we review a continuous domain extension of CS using a structured low-rank (SLR) framework for the recovery of an image or a series of images from a few measurements using various compactness assumptions -. The general strategy of the SLR framework starts with defining a lifting operation to construct a structured matrix, whose entries are functions of the signal samples. The SLR algorithms exploit the dual relationships between the signal compactness properties (e.g. This dual relationship allows recovery of the signal from a few samples in the measurement domain as an SLR optimization problem. MJ and MM are with the University of Iowa, Iowa City, IA 52242 (emails: email@example.com,firstname.lastname@example.org). JCY is with the Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea (email: email@example.com).