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We investigate a class of prior models, called Gamma chains, for modelling depedicies in time-frequency representations of signals. We assume transform coefficients are drawn independently from Gaussians where the latent variances are coupled using Markov chains of inverse Gamma random variables. Exact inference is not feasible but this model class is conditionally conjugate, so standard approximate inference methods like Gibbs sampling, variational Bayes or sequential Monte Carlo can be applied effectively and efficiently. We show how hyperparameters, that determine the coupling between prior variances of transform coefficients, can be optimised. We discuss the pros and cons of various inference schemata (variational Bayes, Gibbs sampler and Sequential Monte Carlo) in terms of complexity and optimisation performance for this model class. We illustrate the effectiveness of our approach in audio denoising and single channel audio source separation applications.