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We introduce a new method of Bayesian wavelet shrinkage for reconstructing asignal when we observe a noisy version. Rather than making the commonassumption that the wavelet coefficients of the signal are independent, weallow for the possibility that they are locally correlated in both location(time) and scale (frequency). This leads us to a prior structure which isanalytically intractable, but it is possible to draw independent samples from aclose approximation to the posterior distribution by an approach based onCoupling From The Past.

Perfect simulation for Bayesian wavelet thresholding with correlated coefficients