Measure What Should be Measured: Progress and Challenges in Compressive Sensing

Is compressive sensing overrated? Or can it live up to our expectations? What will come after compressive sensing and sparsity? And what has Galileo Galilei got to do with it? Compressive sensing has taken the signal processing community by storm. A large corpus of research devoted to the theory and numerics of compressive sensing has been published in the last few years. Moreover, compressive sensing has inspired and initiated intriguing new research directions, such as matrix completion. Potential new applications emerge at a dazzling rate. Yet some important theoretical questions remain open, and seemingly obvious applications keep escaping the grip of compressive sensing. In this paper I discuss some of the recent progress in compressive sensing and point out key challenges and opportunities as the area of compressive sensing and sparse representations keeps evolving. I also attempt to assess the long-term impact of compressive sensing

Structured Sparsity: Discrete and Convex approaches

Compressive sensing (CS) exploits sparsity to recover sparse or compressible signals from dimensionality reducing, non-adaptive sensing mechanisms. Sparsity is also used to enhance interpretability in machine learning and statistics applications: While the ambient dimension is vast in modern data analysis problems, the relevant information therein typically resides in a much lower dimensional space. However, many solutions proposed nowadays do not leverage the true underlying structure. Recent results in CS extend the simple sparsity idea to more sophisticated {\em structured} sparsity models, which describe the interdependency between the nonzero components of a signal, allowing to increase the interpretability of the results and lead to better recovery performance. In order to better understand the impact of structured sparsity, in this chapter we analyze the connections between the discrete models and their convex relaxations, highlighting their relative advantages. We start with the general group sparse model and then elaborate on two important special cases: the dispersive and the hierarchical models. For each, we present the models in their discrete nature, discuss how to solve the ensuing discrete problems and then describe convex relaxations. We also consider more general structures as defined by set functions and present their convex proxies. Further, we discuss efficient optimization solutions for structured sparsity problems and illustrate structured sparsity in action via three applications.Comment: 30 pages, 18 figure

Biologically Inspired Approaches to Automated Feature Extraction and Target Recognition

Ongoing research at Boston University has produced computational models of biological vision and learning that embody a growing corpus of scientific data and predictions. Vision models perform long-range grouping and figure/ground segmentation, and memory models create attentionally controlled recognition codes that intrinsically cornbine botton-up activation and top-down learned expectations. These two streams of research form the foundation of novel dynamically integrated systems for image understanding. Simulations using multispectral images illustrate road completion across occlusions in a cluttered scene and information fusion from incorrect labels that are simultaneously inconsistent and correct. The CNS Vision and Technology Labs (cns.bu.edulvisionlab and cns.bu.edu/techlab) are further integrating science and technology through analysis, testing, and development of cognitive and neural models for large-scale applications, complemented by software specification and code distribution.Air Force Office of Scientific Research (F40620-01-1-0423); National Geographic-Intelligence Agency (NMA 201-001-1-2016); National Science Foundation (SBE-0354378; BCS-0235298); Office of Naval Research (N00014-01-1-0624); National Geospatial-Intelligence Agency and the National Society of Siegfried Martens (NMA 501-03-1-2030, DGE-0221680); Department of Homeland Security graduate fellowshi

Anticipatory Mobile Computing: A Survey of the State of the Art and Research Challenges

Today's mobile phones are far from mere communication devices they were ten years ago. Equipped with sophisticated sensors and advanced computing hardware, phones can be used to infer users' location, activity, social setting and more. As devices become increasingly intelligent, their capabilities evolve beyond inferring context to predicting it, and then reasoning and acting upon the predicted context. This article provides an overview of the current state of the art in mobile sensing and context prediction paving the way for full-fledged anticipatory mobile computing. We present a survey of phenomena that mobile phones can infer and predict, and offer a description of machine learning techniques used for such predictions. We then discuss proactive decision making and decision delivery via the user-device feedback loop. Finally, we discuss the challenges and opportunities of anticipatory mobile computing.Comment: 29 pages, 5 figure