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Interpretable Deep Image Decomposition via Hierarchical Bayesian Modeling

A framework that decomposes an image into low-rank, sparse, and noise components by casting the problem as hierarchical Bayesian inference, solving it with variational inference, and realizing the inference as an architecture-modularized deep neural network whose modules mirror the graphical model. A PAC-Bayesian bound ties the training loss to the generalization error and motivates a test-time adaptation step for out-of-distribution inputs.