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This paper introduces a new non-Gaussian detection method for complex-valued synthetic aperture sonar (SAS) imagery. The detection method is based on a multivariate extension of the Laplace distribution derived using a scale mixture of Normal distributions. A goodness-of-fit test in the form of a likelihood ratio is then conducted on a sonar imagery data set consisting of high frequency (HF) and broadband (BB) images coregistered over the same region on the sea-floor showing the proposed model's applicability in sonar imagery. Detection based on testing the equality of parameters from two populations is then implemented and tested on the same sonar imagery data set using both the Normal and Laplace distributions. Detection performance in this paper is given in terms of Receiver-Operator Characteristic (ROC) curve attributes, probability of detection, and average false alarm rate.