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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 co 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. In this paper, a new transform, a localized Radon transform with a wavelet filter (LRTWF), is developed which accounts for both the linear and the chirp-like features of the internal n&e. This transform is then incorporated into optimal and sub-optimal detection schemes for images (with these features) which are contaminated by additive Gaussian noise.