Interpolation of Sparse Graph Signals by Sequential Adaptive Thresholds

TL;DR

This paper introduces IMATGI, an iterative adaptive thresholding algorithm for interpolating sparse graph signals, demonstrating superior performance over existing methods in signal reconstruction and recommendation system applications.

Contribution

The paper proposes a novel sparsity-based interpolation algorithm for graph signals, with proven convergence and improved performance over state-of-the-art methods.

Findings

IMATGI effectively reconstructs sparse graph signals.

IMATGI outperforms existing algorithms on benchmark datasets.

The algorithm converges analytically under certain conditions.

Abstract

This paper considers the problem of interpolating signals defined on graphs. A major presumption considered by many previous approaches to this problem has been lowpass/ band-limitedness of the underlying graph signal. However, inspired by the findings on sparse signal reconstruction, we consider the graph signal to be rather sparse/compressible in the Graph Fourier Transform (GFT) domain and propose the Iterative Method with Adaptive Thresholding for Graph Interpolation (IMATGI) algorithm for sparsity promoting interpolation of the underlying graph signal.We analytically prove convergence of the proposed algorithm. We also demonstrate efficient performance of the proposed IMATGI algorithm in reconstructing randomly generated sparse graph signals. Finally, we consider the widely desirable application of recommendation systems and show by simulations that IMATGI outperforms state-of-the-art algorithms on the benchmark datasets in this application.