Color Image Restoration in the Low Photon-Count Regime Using Expectation Propagation

In this paper, a new Expectation Propagation (EP) algorithm using ℓ
1
-norm total variation (ℓ
1
-TV) prior is proposed for color image restoration in the low photon-count regime. Different from most color image restoration methods proposed for the restoration of color images from observations that are already color images with some missing pixels and/or are usually corrupted by Gaussian noise, the observations considered in this paper are only a single channel grayscale image without color information and are corrupted by Poisson noise, making the color image restoration problem more difficult. To address the problem, a new efficient EP algorithm is proposed to estimate the RGB values of each pixel from such observations and simultaneously provide uncertainty quantification of the estimates. Moreover, by coupling the EP algorithm with a variational Expectation Maximization (EM) approach, the ℓ
1-
TV prior hyperparameter can be adjusted automatically with-out user supervision. Experiments on color image inpainting and compressive sensing (CS) reconstruction are conducted to illustrate the potential benefits of the proposed EP algorithm for color image restoration in the low photon-count regime.