Current wavelet-based statistical signal and image processing techniques such as shrinkage and filtering treat the wavelet coefficients as though they were statistically independent. This assumption is unrealistic; considering the statistical dependencies between wavelet coefficients can yield substantial performance improvements. In this paper we develop a new framework for wavelet-based signal processing that employs hidden Markov models to characterize the dependencies between wavelet coefficients. To illustrate the power of the new framework, we derive a new signal denoising algorithm that outperforms current scalar shrinkage techniques.