Application of wavelet and radon-based techniques to the internal wake problem in synthetic aperture radar images

One problem of interest to the oceanic engineering community is the detection and enhancement of internal wakes in open water synthetic aperture radar (SAR) images. Internal wakes, which occur when a ship travels in a stratified medium, have a "V" shape extending from the ship, and a chirp-like feature across each arm. The Radon transform has been applied to the detection and the enhancement problems in internal wake images to account for the linear features while the wavelet transform has been applied to the enhancement problem in internal wake images to account for the chirp-like features. Although the Radon transform accentuates linear features, there have been several difficulties applying this transform to the wake detection and enhancement problem because the transform is not localized. In a recent article by Copeland et. al., a localized Radon transform (LRT) was developed and was shown to reduce the speckle noise. In this dissertation, another derivation of the LRT is obtained which shows that this transform is equivalent to the Radon transform with a rectangular window function. Several properties not considered in the article are derived using the new formulation. Another transform which has been applied to internal wake images is the wavelet transform. In a recent paper by Teti et. al., the wavelet transform was applied to slices through internal wakes in SAR images. Although the wavelet transform reduced the speckle noise in SAR wake images, it required extracting a line from the image. In this dissertation, a wavelet localized Radon transform is developed which performs the wavelet transform on all lines in an image without explicitly extracting slices of the image. The fundamental theory for this transform is developed and several examples are considered. This transform is then expanded to include features which occur over a region with a significant length. The fundamental theory for this new transform, a localized Radon transform with a wavelet filter, is developed and several examples are provided. These new transforms are then incorporated into optimal and sub-optimal detection schemes for images with linear features, including ship wakes, which are contaminated by additive Gaussian noise.