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Feature matching is a key, underlying component in many approaches to object detection, localization, and recognition. In many cases, feature matching is accomplished by nearest neighbor methods on extracted feature descriptors. This methodology works well for clean, out-of-water images; however, when imaging underwater, even an image of the same object can be drastically different due to varying water conditions. As a result, descriptors of the same point on an object may be completely different between the clean and underwater images, and between different underwater images taken under varying imaging conditions. This makes feature matching between such images a very challenging problem. In this paper, we present a new method for feature matching by first synthetically constructing a feature codebook for all template features by simulating different underwater imaging conditions. We then approximate the target feature by a sparse linear combination of the features in the constructed codebook. The optimal sparse linear combination is found by compressive sensing algorithms. In the experiments, we show that the proposed method can produce better feature matching performance than the nearest neighbor approach and associated naïve extensions.