  In this paper we propose a new adaptive wavelet denoising methodology using
complex wavelets. The method is based on a fully Bayesian hierarchical model in
the complex wavelet domain that uses a bivariate mixture prior on the wavelet
coefficients. The heart of the procedure is computational, where the posterior
mean is computed through Markov chain Monte Carlo (MCMC) simulations. We show
that the method has good performance, as demonstrated by simulations on the
well-known test functions and by comparison to a well-established complex
wavelet-based denoising procedure. An application to real-life data set is also
considered.
