As one can see from reading Nuit Blanche, it is becoming clear that Compressive Sensing has affected in some fashion or another the way we think and aim to solve problems when there are plenty of data. Subjects like Advanced Matrix Factorization or Randomized Numerical Linear Algebra (RandNLA) are examples of that. Today, we have a few review papers that provide this bird's eye view. It is as much useful to the newcomers as it is for the practicing researcher or Machine Learning professional. Some of the subjects mentioned here are barely mentioned in textbooks but eventually will.

Modeling and Optimization for Big Data Analytics by Konstantinos Slavakis, Georgios B. Giannakis, and Gonzalo Mateos

With the pervasive sensors continuously collecting and storing massive amounts of information, there is no doubt this is an era of data deluge. Learning from these large volumes of data is expected to bring significant science and engineering advances along with improvements in quality of life. However, with such a big blessing come big challenges. Running analytics on voluminous data sets by central processors and storage units seems infeasible, and with the advent of streaming data sources, learning must often be performed in real time, typically without a chance to revisit past entries. “Work-horse” signal processing (SP) and statistical learning tools have to be re-examined in today’s high-dimensional data regimes. This article contributes to the ongoing cross-disciplinary efforts in data science by putting forth encompassing models capturing a wide range of SP-relevant data analytic tasks, such as principal component analysis (PCA), dictionary learning (DL), compressive sampling (CS), and subspace clustering. It offers scalable architectures and optimization algorithms for decentralized and online learning problems, while revealing fundamental insights into the various analytic and implementation tradeoffs involved. Extensions of the encompassing models to timely data-sketching, tensor- and kernel-based learning tasks are also provided. Finally, the close connections of the presented framework with several big data tasks, such as network visualization, decentralized and dynamic estimation, prediction, and imputation of network link load traffic, as well as imputation in tensor-based medical imaging are highlighted.

Convex Optimization for Big Data: Scalable, randomized, and parallel algorithms for big data analytics

by Cevher, V., Becker, S. ; Schmidt, M.

This article reviews recent advances in convex optimization algorithms for big data, which aim to reduce the computational, storage, and communications bottlenecks. We provide an overview of this emerging field, describe contemporary approximation techniques such as first-order methods and randomization for scalability, and survey the important role of parallel and distributed computation. The new big data algorithms are based on surprisingly simple principles and attain staggering accelerations even on classical problems.

Mathematics of sparsity (and a few other things) by Emmanuel Cand es

In the last decade, there has been considerable interest in understanding when it is possible to nd structured solutions to underdetermined systems of linear equations. This paper surveys some of the mathematical theories, known as compressive sensing and matrix completion, that have been developed to nd sparse and low-rank solutions via convex programming techniques. Our exposition emphasizes the important role of the concept of incoherence.

Less is more: compressive sensing in optics and image science by Damber Thapa, Kaamran Raahemifar and Vasudevan Lakshminarayanan

We review an emerging sampling theory, namely compressive sampling, which reproduces signals or images from a much smaller set of samples than that required by the Nyquist–Shannon criterion. This review article outlines the main theoretical concepts surrounding compressive sensing and discusses the relationship among compressive sensing, signal sparsity, and sensing modalities. We also describe the applications of compressive sensing in the field of optics and image science.

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