Generalized Graph Signal Sampling by Difference-of-Convex Optimization

TL;DR

This paper introduces a novel flexible sampling operator for graph signals using difference-of-convex optimization, enabling robust sampling and recovery beyond bandlimited signals with improved accuracy.

Contribution

It formulates the design of a flexible sampling operator as a DC optimization problem, overcoming limitations of previous methods and ensuring robustness under arbitrary priors.

Findings

Outperforms existing methods in sampling and recovery accuracy.

Guarantees convergence to a critical point with the proposed solver.

Effective for non-bandlimited graph signals in experiments.

Abstract

We propose a desigining method of a flexible sampling operator for graph signals via a difference-of-convex (DC) optimization algorithm. A fundamental challenge in graph signal processing is sampling, especially for graph signals that are not bandlimited. In order to sample beyond bandlimited graph signals, there are studies to expand the generalized sampling theory for the graph setting. Vertex-wise sampling and flexible sampling are two main strategies to sample graph signals. Recovery accuracy of existing vertex-wise sampling methods is highly dependent on specific vertices selected to generate a sampled graph signal that may compromise the accurary especially when noise is generated at the vertices. In contrast, a flexible sampling mixes values at multiple vertices to generate a sampled signal for robust sampling; however, existing flexible sampling methods impose strict assumptions and aggressive relaxations. To address these limitations, we aim to design a flexible sampling operator without such strict assumptions and aggressive relaxations by introducing DC optimization. By formulating the problem of designing a flexible sampling operator as a DC optimization problem, our method ensures robust sampling for graph signals under arbitrary priors based on generalized sampling theory. We develop an efficient solver based on the general double-proximal gradient DC algorithm, which guarantees convergence to a critical point. Experimental results demonstrate the superiority of our method in sampling and recovering beyond bandlimited graph signals compared to existing approaches.