Novel Numerical Approximation Techniques for Non-Standard Sampling Regimes Novel Numerical Approximation Techniques for Non-Standard Sampling Regimes Data collection techniques in a variety of applications are becoming increasingly more sophisti- cated, giving new meaning to the fundamental concept of numerical approximation. Standard algorithms have been significantly improved by the explosion of computational methods and re- sources. Many user friendly software packages allow disciplinary scientists to successfully diagnose, predict, model, and determine important characteristics from a plethora of collected data. Re- searchers have successfully modified their numerical algorithms to improve results specific to their area of interest, often heuristically. Research and practical results, however, also continually show limitations of some heuristic techniques. Magnetic resonance imaging (MRI) provides a prototyp- ical example where scientists have pragmatically modified numerical reconstruction algorithms to manage complicated data sampling patterns. Modern MRI machines implement data acquisition strategies designed to reduce cost and time by collecting data non-uniformly in the Fourier domain, often resulting in sparse sampling of high frequencies. Many practical image reconstruction and segmentation algorithms have been designed to handle the resulting data discrepancies. The PIs own recent investigations into a variety of these methods have clearly demonstrated shortcomings that arise when such pragmatic modifications are used without considering fundamental numerical analysis issues such as accuracy, robustness, and efficiency. Of course methods that only take into consideration these fundamental issues are often not practical for real data. This project extends the PIs prior research and addresses the development of novel approximation and data inversion techniques for handling issues associated with extracting functional and feature information from data acquired by non-standard sampling protocols.
|Effective start/end date||9/1/12 → 8/31/16|
- National Science Foundation (NSF): $336,853.00
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