Fast Scalable Image Restoration Using Total Variation Priors and Expectation Propagation

Area of Science:

• Computational imaging
• Statistical signal processing
• Bayesian inference

Background:

• Image restoration tasks like denoising and deconvolution are crucial in various scientific fields.
• Traditional methods often rely on maximum a posteriori (MAP) estimation, which may not fully capture uncertainty.
• Existing Bayesian approaches can be computationally intensive, limiting their scalability.

Purpose of the Study:

• To develop a scalable approximate Bayesian method for image restoration.
• To provide accurate uncertainty quantification (pixel-wise variances) without Monte Carlo sampling.
• To enable efficient image restoration for large-scale problems.

Main Methods:

• Utilizes the Expectation Propagation (EP) framework to approximate minimum mean squared error (MMSE) estimates.
• Employs Gaussian approximating densities with diagonal covariance matrices for parallelizable computations.
• Incorporates an Expectation Maximization (EM) iterative scheme for automatic regularization parameter tuning in Total Variation (TV) priors.

Main Results:

• Achieves posterior estimates comparable to sampling-based methods but with significantly reduced computational cost.
• Demonstrates scalability to large images for denoising, deconvolution, and compressive sensing (CS).
• EP method shows reduced underestimation of posterior variances compared to variational Bayes alternatives.

Conclusions:

• The proposed scalable approximate Bayesian method using EP offers an efficient and accurate approach to image restoration.
• It provides valuable uncertainty quantification, crucial for reliable scientific interpretation of restored images.
• This method presents a computationally advantageous alternative to traditional optimization and sampling-based techniques.