Deep Proximal Unrolling: Algorithmic Framework, Convergence Analysis and Applications.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Optimization Theory

Background:

• Deep learning models are widely used but often lack mathematical rigor and interpretability.
• Existing methods for unrolling optimization into deep models face convergence issues due to dynamic parameters.

Purpose of the Study:

• To develop a generic paradigm for unrolling nonconvex optimization into deep models with proven convergence properties.
• To provide a mathematically sound foundation for deep model design.

Main Methods:

• Developed a proximally unrolled deep model paradigm.
• Provided theoretical proofs for global convergence to critical points.
• Extended the framework to handle multi-block optimization problems.

Main Results:

• The proposed deep model guarantees global convergence to the critical-point of the original optimization model.
• The framework enables training convergent deep propagations even with partial task information.
• Demonstrated superior performance on low-level vision tasks like deconvolution, dehazing, and low-light enhancement.

Conclusions:

• The generic paradigm offers a mathematically rigorous and convergent approach to deep model design.
• The framework is versatile, applicable to various real-world problems, including multi-block optimization.
• Outperforms existing state-of-the-art methods in low-level vision tasks.