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Improved Sparse Signal Recovery via Adaptive Correlated Noise Model

Sparse signal recovery consists of employing a sparsity promoting regularizer to estimate the underlying signal from an incomplete set of measurements. Typical recovery approaches involve an alternating procedure where the estimate of the signal is progressively refined through filtering its degraded observation by a denoiser. The filter acts, implicitly, as a regularizer for the estimate. Hence, the implicit regularization is determined by the signal model underlying the denoising filter, as well as by the model of effective noise (i.e. degradation to be filtered) adopted by the filter. We improve the recovery by an adaptive stationary correlated noise model and the corresponding denoiser in place of the traditional filters for uncorrelated white noise. The effective noise can vary as the recovery progresses and we track these variations by estimating the noise correlation at every iteration. Competitive inverse problems are considered as benchmarks, including compressive spectral/temporal imaging and 2D/3D tomography. Analysis of the effective noise within each application demonstrates that it features various forms of correlation, which if leveraged by a denoiser lead to a better and faster signal recovery.