Reconstructing a continuous-time signal from a sequence of discrete-time samples is a common objective in signal processing. This can be accomplished especially efficiently for sparse signals, those which are contained in a lower dimensional subspace of the data space, through techniques such as compressive sensing. Sparse signals are present in many, but not all, data processing applications. We propose a broader definition of sparsity, in which data points occupy only a fraction of the volume of the data space and naturally cluster into distinguishable groups. We seek to verify that this type of sparsity exists in the datasets of useful applications, and will then focus on the development of clustering algorithms that would take advantage of it in data processing.

I have done research with the MIT Compact Muon Solenoid (CMS) Collaboration for over a year. This summer I worked on the measurement of the W and Z boson production cross-sections, contributing to the implementation of a more compact fitting framework. I gained experience in accounting for systematic and statistical uncertainties in a precision measurement and worked with both real and simulated datasets.