Variational Bayes Image Restoration With Compressive Autoencoders.

Area of Science:

• Computational Imaging
• Machine Learning
• Bayesian Inference

Background:

• Regularization is crucial for solving inverse problems in computational imaging.
• Neural networks offer powerful data-driven regularizers, with plug-and-play (PnP) methods using implicit regularization from denoisers.
• Bayesian approaches use explicit regularization via Maximum A Posteriori (MAP) estimation in generative models, but these are data-intensive and complex.

Purpose of the Study:

• To propose compressive autoencoders as a more efficient alternative to complex deep generative models for regularization.
• To introduce the Variational Bayes Latent Estimation (VBLE) algorithm for efficient latent estimation using variational inference.
• To enable fast and accurate uncertainty quantification in inverse problems.

Main Methods:

• Utilized compressive autoencoders, a type of variational autoencoder with a flexible latent prior, for network training.
• Developed the Variational Bayes Latent Estimation (VBLE) algorithm employing variational inference for latent estimation.
• Implemented a simple yet efficient parameterization for the variational posterior to facilitate rapid posterior sampling.

Main Results:

• VBLE achieved performance comparable to state-of-the-art plug-and-play (PnP) methods on BSD and FFHQ image datasets.
• VBLE demonstrated significantly faster uncertainty quantification compared to existing posterior sampling techniques.
• Compressive autoencoders proved smaller and easier to train than traditional deep generative models.

Conclusions:

• VBLE offers a computationally efficient and effective approach for regularization in inverse problems.
• The method provides a viable alternative to existing PnP and Bayesian techniques, especially when data is limited or computational resources are constrained.
• VBLE successfully balances performance with speed in uncertainty quantification for imaging applications.