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This paper develops and compares the maximum a posteriori (MAP) and minimum mean-square error (MMSE) estimators for spherically contoured multivariate Laplace random vectors in additive white Gaussian noise. The MMSE estimator is expressed in closed-form using the generalized incomplete gamma function. We also find a computationally efficient yet accurate approximation for the MMSE estimator. In addition, this paper develops an expression for the MSE for any estimator of spherically contoured multivariate Laplace random vectors in additive white Gaussian noise (AWGN), the development of which again depends on the generalized incomplete gamma function. The estimators are motivated and tested on the problem of wavelet-based image denoising.