Investigating Task-driven Latent Feasibility for Nonconvex Image Modeling

TL;DR

This paper introduces Task-driven Latent Feasibility (TLF), a flexible framework that incorporates task-specific constraints into nonconvex image modeling, ensuring convergence and improving performance in tasks like deblurring and rain removal.

Contribution

The paper proposes TLF, a novel approach that embeds designed and trained constraints into optimization for nonconvex image modeling, with proven convergence guarantees.

Findings

TLF effectively narrows solution space for image modeling tasks.

The method demonstrates superior performance over state-of-the-art approaches.

Theoretical convergence of the inference process is rigorously proven.

Abstract

Properly modeling latent image distributions plays an important role in a variety of image-related vision problems. Most exiting approaches aim to formulate this problem as optimization models (e.g., Maximum A Posterior, MAP) with handcrafted priors. In recent years, different CNN modules are also considered as deep priors to regularize the image modeling process. However, these explicit regularization techniques require deep understandings on the problem and elaborately mathematical skills. In this work, we provide a new perspective, named Task-driven Latent Feasibility (TLF), to incorporate specific task information to narrow down the solution space for the optimization-based image modeling problem. Thanks to the flexibility of TLF, both designed and trained constraints can be embedded into the optimization process. By introducing control mechanisms based on the monotonicity and boundedness conditions, we can also strictly prove the convergence of our proposed inference process. We demonstrate that different types of image modeling problems, such as image deblurring and rain streaks removals, can all be appropriately addressed within our TLF framework. Extensive experiments also verify the theoretical results and show the advantages of our method against existing state-of-the-art approaches.