GCN-based proximal unrolling matrix completion for piecewise smooth signal recovery

Abstract

Time-varying piecewise-smooth signal recovery is an important task in computer vision, image processing and environmental monitoring. The performance of many methods degrades dramatically in extreme scenario of sparse observations, a common case in these fields. In this extreme case, how to accurately recover time-varying piecewise-smooth signals is still a challenge. In this paper, we aim to batch recovery of the time-varying piecewise-smooth signals accurately. We first propose a graph signal matrix completion model based on piecewise smoothness, and use alternating direction method of multipliers (ADMM) to solve it, which is Low Rank and Piecewise Smoothness based recovery method (LRPS). To accelerate convergence, we further propose a proximal unrolling method based on LRPS (Pro-Un LRPS), where a denoising graph convolutional network (GCN) is used to replace the proximal operation in the ADMM framework. The Pro-Un LRPS can converge to a critical-point of the original optimization model. We interpret the embedded network as a subgradient-estimator from the optimization perspective. Finally, experimental results on several datasets demonstrate superior recovery performance of our methods when known entries are sparse, compared with existing matrix completion approaches. The convergence rate of Pro-Un LRPS is faster than that of LRPS, illustrating the effectiveness of the unrolling scheme.