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.
