Computational electromagnetic problems are becoming exceedingly complex and traditional computation methods are simply no longer good enough for our technologically advancing world. Compressive sensing theory states that signals, such as those used in computational electromagnetic problems have a property known as sparseness. It has been proven that through under sampling, computation runtimes ...

High signal to noise ratio (SNR) consistency of model selection criteria in linear regression models has attracted a lot of attention recently. However, most of the existing literature on high SNR consistency deals with model order selection. Further, the limited literature available on the high SNR consistency of subset selection procedures (SSPs) is applicable to linear regression with full r...

Visual tracking is an important component of many video surveillance systems. Specifically, visual tracking refers to the inference of physical object properties (e.g., spatial position or velocity) from video data. This is a well-established problem that has received a great deal of attention from the research community (see, e.g., the survey (Yilmaz et al., 2006)). Classical techniques often ...

A combinatorial approach to compressive sensing based on a deterministic column replacement technique is proposed. Informally, it takes as input a pattern matrix and ingredient measurement matrices, and results in a larger measurement matrix by replacing elements of the pattern matrix with columns from the ingredient matrices. This hierarchical technique yields great flexibility in sparse signa...

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a few components. However, the theory of CS framework including random sampling has been focused on exa...

This thesis is dedicated to the development of new acquisition and processing methods in diffusion MRI (dMRI) to characterize the diffusion of water molecules in white matter fiber bundles at the scale of a voxel. In particular, we focus our attention on the accurate recovery of the Ensemble Average Propagator (EAP), which represents the full 3D displacement of water molecule diffusion. Diffusi...

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming probability when incoming data can be sparsely represented with a fixed number of components, which is one of the drawbacks of CS frameworks because the signal sparsit...

Compressive sensing (CS) is a technique to sample a sparse signal below the Nyquist-Shannon limit, yet still enabling its reconstruction. As such, CS permits an extremely parsimonious way to store and transmit large and important classes of signals and images that would be far more data intensive should they be sampled following the prescription of the Nyquist-Shannon theorem. CS has found appl...

BACKGROUND Magnetic Resonance Imaging (MRI) is a crucial medical imaging technology for the screening and diagnosis of frequently occurring cancers. However, image quality may suffer from long acquisition times for MRIs due to patient motion, which also leads to patient discomfort. Reducing MRI acquisition times can reduce patient discomfort leading to reduced motion artifacts from the acquisit...

Optical sensing and imaging applications often suffer from a combination of low resolution object reconstructions and a large number of sensors which, depending on frequency, can be quite expensive or bulky. It is therefore desirable to minimize the number of sensors (which reduces cost) for a given target resolution level (image quality) and permissible total sensor array size (compactness). E...