Title: Unrolling Physics-Aware Linearized ADMM

Abstract:

While partial differential equations (PDEs) are increasingly utilized to directly model measurement processes in signal processing, their computational expense often poses a significant challenge. To address this, we introduce a new algorithm for solving inverse problems derived from PDE-based measurements, termed physics-aware linearized alternating direction method of multipliers (PA-LADMM). The core innovation lies in linearizing the PDE-containing subproblem, which yields a computationally efficient update mechanism that requires only a PDE solver and its gradient evaluation at each iteration. We establish theoretical convergence guarantees for the algorithm under specific conditions. Furthermore, we integrate deep unfolding techniques with PA-LADMM to unroll the process, allowing for the supervised training of its internal parameters. The efficacy of our proposed approach is validated through two case studies: compressed sensing in optical fiber communication and image restoration from noisy anisotropic diffusion.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC