Generalized Gaussian Decompositions for Image Analysis and Synthesis

Abstract

This thesis presents a new technique for performing image analysis, synthesis, and modification using a generalized Gaussian model. The joint time-frequency characteristics of a generalized Gaussian are combined with the flexibility of the analysis-by-synthesis (ABS) decomposition technique to form the basis of the model. The good localization properties of the Gaussian make it an appealing basis function for image analysis, while the ABS process provides a more flexible representation with enhanced functionality. ABS was first explored in conjunction with sinusoidal modeling of speech and audio signals [George87]. A 2D extension of the ABS technique is developed here to perform the image decomposition. This model forms the basis for new approaches in image analysis and enhancement.

The major contribution is made in the resolution enhancement of images generated using coherent imaging modalities such as Synthetic Aperture Radar (SAR) and ultrasound. The ABS generalized Gaussian model is used to decouple natural image features from the speckle and facilitate independent control over feature characteristics and speckle granularity. This has the beneficial effect of increasing the perceived resolution and reducing the obtrusiveness of the speckle while preserving the edges and the definition of the image features. A consequence of its inherent flexibility, the model does not preclude image processing applications for non-coherent image data. This is illustrated by its application as a feature extraction tool for a FLIR imagery complexity measure.