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One of the most straightforward techniques for detecting changes in an image involves forming the difference between a test image and a reference image. Unfortunately, such a technique can give rise to a large number of false alarms due to the statistical variability of the underlying pixel values, as has been well established within the radar community over the years. One method for dealing with this large number of false alarms involves forming the ratio, rather than the difference, of two synthetic aperture radar (SAR) images. We introduce a modified version of the standard differencing technique to overcome problems associated with pixel value variability. The new (modified) differencing approach utilizes assumptions about the statistics of the image background and the object being sought (target) to reduce the number of false alarms due to highly variable background (clutter) regions, and it includes the standard ratio test as a special case. In fact, we find that the modified difference approach can also be viewed as a modified version of the ratio test with a threshold that varies as a function of the background clutter radar cross section (RCS). We also present an abridged, albeit suboptimal, version of this approach that eliminates assumptions regarding the target's probability distribution, and we analyze both of the approaches. We then compare these results with those obtained with a standard ratio test, and illustrate how the modified difference test reduces to the ratio test under certain operating conditions. The abridged version of the modified approach is applied to high resolution synthetic aperture radar imagery and compared with results obtained with the classical differencing technique, and following this, the modified difference technique is compared with the standard ratio test. Results suggest that under appropriate conditions the abridged, modified technique can successfully detect changes without the need for any image segmentation.