Physics-Aware Linearized ADMM and Its Unrolling
2026-06-01 • Computer Vision and Pattern Recognition
Computer Vision and Pattern Recognition
AI summaryⓘ
The authors developed a new algorithm called PA-LADMM to solve problems where measurements come from processes described by partial differential equations (PDEs), which are usually slow to compute. Their method simplifies part of the problem using a linear approximation, making it faster by requiring only one PDE solve and its gradient per step. They also integrated this algorithm with deep learning techniques to improve its performance using training data. They tested their method on tasks involving signal recovery in optical fiber communication and image cleaning, showing it works effectively.
Partial Differential Equations (PDEs)Inverse ProblemsAlternating Direction Method of Multipliers (ADMM)LinearizationDeep UnfoldingGradient EvaluationCompressed SensingOptical Fiber CommunicationImage RestorationAnisotropic Diffusion
Authors
Satoshi Takabe, Shunta Arai, Tadashi Wadayama
Abstract
Recently, partial differential equations (PDEs) have been used to directly model the measurement process in signal processing, although their evaluation is costly. In this paper, we propose a novel alternating direction method of multipliers (ADMM)-based algorithm called physics-aware linearized ADMM (PA-LADMM) for inverse problems from PDE-based measurement processes. The key idea is the linearization of the subproblem with PDEs, leading to a cost-efficient update rule that calls only a PDE solver and its gradient evaluation per iteration. The algorithm has a theoretical convergence guarantee under certain conditions. In addition, we combine it with deep unfolding to unroll the PA-LADMM and train its internal parameters using supervised data. Two distinct experiments, compressed sensing with optical fiber communication and image restoration from noisy anisotropic diffusion, demonstrated the effectiveness of the proposed algorithms.