Graduation date: 2007Achieving sharpened (enhanced detail) features of a multi-dimensional data source using the linear prediction (LP) bandwidth extrapolation (BWE) technique in the transform domain is the main objective of this research. The evolution of sensor technology has provided acquisition scenarios in which the data format is inherently multi-dimensional, including hyperspectral imaging (HSI), interferometric synthetic aperture radar (IF-SAR) imaging, and radar space-time adaptive processing (STAP). In all these applications, fully multi-dimensional signal processing that has the capability (1) to enhance the resolution of the final multi-dimensional analysis result, and (2) to provide reduced-dimension parametric features of the multi-dimensional data for purposes of data encoding/compression is highly desirable. This thesis provides algorithmic techniques that achieve both capabilities using a novel 2-D BWE approach and its associated fast computational algorithms. Furthermore, 3-D LP fast algorithms were developed, as part of this research, that estimate 3-D AR parameters of the original 3-D sensor domain data, which are then used to produce high resolution 3-D AR spectral estimates. These new 3-D algorithms will become components of future research in 3-D BWE algorithms that sharpen features in 3-D data sources.