We are living in a world in which the growth rate of the data generated every year is almost exponential. A significant problem is how we can store this amount of data. Compressive sensing is giving us a clue about how we can reconstruct images and signals from frequency data, by having less samples compared to the conventional ways of data acquisition, which somehow helps us with the storage problem and gives us some other benefits that we try to present in this thesis. The basic principle of Nyquist sampling theory has been one of the conventional ways in data acquisition and reconstruction signals and images. This so-called principle, introduces a minimum rate at which a signal can be sampled to be reconstructed without any errors. On the other side of this subject, compressive sensing introduces an efficient framework that enables us to derive exact reconstruction of a sparse signal from less measurements. In this thesis we provide a few notes on mathematical insight related to this new theory which involves some proofs about the desired properties of the sampling matrix and explain how we approach the problem of constructing this class of matrices and at last we move on to the recovery algorithm.
Level of Degree
Mathematics & Statistics
Pereyra, Maria Cristina
First Committee Member (Chair)
Second Committee Member
compressive sensing, image processing, transform coding, sampling theorem
Mehraban, Sara. "Some Notes on Compressive Sensing." (2016). https://digitalrepository.unm.edu/math_etds/29