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Interferometric phase (InPhase) estimation, that is, the denoising of modulo-<inline-formula> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula> phase images from sinusoidal <inline-formula> <tex-math notation="LaTeX">$2\pi $ </tex-math></inline-formula>-periodic and noisy observations, is a challenging inverse problem with wide applications in many coherent imaging techniques. This paper introduces a novel approach to InPhase restoration based on an external data set and importance sampling. In the proposed method, a class-specific data set of clean patches is clustered using a mixture of circular symmetric Gaussian (csMoG) distributions. For each noisy patch, a &#x201C;home-cluster&#x201D;, i.e., the closest cluster in the external data set, is identified. An InPhase estimator, termed as <italic>Shift-invariant Importance Sampling (SIS)</italic> estimator, is developed using the principles of importance sampling. The SIS estimator uses samples from the home-cluster to perform the denoising operation. Both the clustering mechanism and the estimation technique are developed for complex-valued signals by taking into account patch shift invariance, which is an important property for an efficient InPhase denoiser. The effectiveness of the proposed algorithm is shown using experiments conducted on a semi-real InPhase data set constructed using human face images and medical imaging applications involving real magnetic resonance imaging (MRI) data. It is observed that, in most of the experiments, the SIS estimator shows better results compared to the state-of-the-art algorithms, yielding a minimum improvement of 1 dB in peak signal-to-noise ratio (PSNR) for low to high noise levels.

Class-Specific Interferometric Phase Estimation Using Patch-Based Importance Sampling