Investigating Task-driven Latent Feasibility for Nonconvex Image Modeling
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Properly modeling the latent image distributions always plays a key role in a variety of low-level vision problems. Most existing approaches, such as Maximum A Posterior (MAP), aimed at establishing optimization models with prior regularization to address this task. However, designing sophisticated priors may lead to challenging optimization model and time-consuming iteration process. Recent studies tried to embed learnable network architectures into the MAP scheme. Unfortunately, for the MAP model with deeply trained priors, the exact behaviors and the inference process are actually hard to investigate, due to their inexact and uncontrolled nature. In this work, by investigating task-driven latent feasibility for the MAP-based model, we provide a new perspective to enforce domain knowledge and data distributions to MAP-based image modeling. Specifically, we first introduce an energy-based feasibility constraint to the given MAP model. By introducing the proximal gradient updating scheme to the objective and performing an adaptive averaging process, we obtain a completely new MAP inference process, named Proximal Average Optimization (PAO), for image modeling. Owning to the flexibility of PAO, we can also incorporate deeply trained architectures into the feasibility module. Finally, we provide a simple monotone descent-based control mechanism to guide the propagation of PAO. We prove in theory that the sequence generated by both our PAO and its learning-based extension can successfully converge to the critical point of the original MAP optimization task. We demonstrate how to apply our framework to address different vision applications. Extensive experiments verify the theoretical results and show the advantages of our method against existing state-of-the-art approaches.
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