Big data : a compressed sensing approach

Abstract

In recent times Big Data has been talked about in many areas, ranging from information technology, to government and healthcare, and to business. Big Data is changing the world we live in in many respects, especially as data of the individual becomes available in forms which it has not been previously, for example, data about the behaviour of indiviuals tracked via mobile phones. We discuss Big Data and whether it is having the said affect, or if it is only an unsubstantiated hype about something old coated under a new name. Convinced that Big Data is indeed a phenomenon of our day worthy of spending time and money on, we investigate whether Compressed Sensing (CS), a new and exciting tool in the signal processing field, can provide sensible solutions to Big Data problems. CS proposes a framework in which we simultaneously acquire and compress a signal of interest. However, for this to work, the way in which we acquire the signal needs to adhere to some uncertainty principles and the signal of interest need to be sparse in some basis representation. We argue that because Big Data many times exhibit sparsity and generally poses challenges to the storage capacity of different devices and systems, CS can be a useful tool in addressing challenges in the Big Data era and should be considered as a potential research area. This mini-dissertation provides an overview of CS and is by no means a full in-depth mathematical treatment of CS. It is written to provide the statistician with the necessary background and building blocks of CS, for use in the Big Data environment, and herein, CS is presented in a simple and clear manner for a statistician not familiar with the field. The literature review, however, provides all the texts required should the reader want the specific mathematical details. The document aims to thus link CS in the statistical and engineering fields.