This paper presents a scalable approximate Bayesian method for image restoration using total variation (TV) priors. In contrast to most optimization methods based on maximum a posteriori estimation, we use the expectation propagation (EP) framework to approximate minimum mean squared error (MMSE) estimators and marginal (pixel-wise) variances, without resorting to Monte Carlo sampling. For the classical anisotropic TV-based prior, we also propose an iterative scheme to automatically adjust the regularization parameter via expectation-maximization (EM). Using Gaussian approximating densities with diagonal covariance matrices, the resulting method allows highly parallelizable steps and can scale to large images for denoising, deconvolution and compressive sensing (CS) problems. The simulation results illustrate that such EP methods can provide a posteriori estimates on par with those obtained via sampling methods but at a fraction of the computational cost. Moreover, EP does not exhibit strong underestimation of posteriori variances, in contrast to variational Bayes alternatives.

翻译：本文介绍了一种使用全面变异(TV)前缀来进行图像恢复的可伸缩近似巴伊西亚方法。 与大多数基于事后估计的优化方法不同,我们使用预期传播框架来估计最小平均正方差(MMSE)估计值和边际(像素-像素-)差异,而不用蒙特卡洛取样。 对于以前以传统厌食电视为基础的古典厌食电视,我们还提议了一个迭接办法,通过预期-最大化(EM)来自动调整正规化参数。 与变异贝雅替代物相比,使用高氏相近密度和二对等同差矩阵,所产生的方法允许高度平行的步骤,并可以向大图像缩放,以缓解、分解变异和压缩问题。模拟结果表明,这种EP方法可以提供与通过抽样方法获得的相近的事后估计值,但只提供计算成本的一小部分。 此外, EP没有表现出对后种差异差异的强烈低估,与变异湾替代物的偏差。