Multiple-domain image modeling and restoration

Several powerful, but heuristic techniques in recent image denoising literature have used multiple (typically overcomplete) image representations. This paper presents a framework for multiple-domain image modeling and restoration, based on fundamental statistical estimation principles. Information about image attributes from multiple wavelet transforms is incorporated as moment constraints on the underlying image prior. Our method constructs the maximum entropy distribution consistent with these moment constraints. A maximum a posteriori probability (MAP) image restoration algorithm based on this maximum entropy prior is developed. Unlike previous multiple-domain algorithms, ours satisfies certain desirable optimality properties and provides an information-theoretic figure of merit for the choice of domains. Simulation results show that the estimator is vastly superior to single-domain image restoration both in terms of mean squared error and perceptual quality.