Learn Graph Laplacian for Sparse Frequency Domain Representation

Abstract

"Learning of graph topology plays an important role in processing structure and unstructured data which can be represented as graph signals. Graph topology for a given graph signal is not always readily available from the given data and is also not unique. It is desirable to learn the graph topology for the graph signals such that the data admits the property or application. In this thesis we address the problem of estimating graph Laplacian matrix (graph topology) for signals with prior assumption that signals have sparse representation in frequency domain . This is done by first finding an optimal graph signal basis (eigenvectors of graph Laplacian matrix) and later knowing the eigenvectors, we try to estimate a sparse representation of the graph signals and its respective graph Laplacian matrix. Then we discuss the results of learning the graph for synthetic data. For application purpose, we propose a modification in an existing algorithm for image denoising and demonstrate the results for all the three class of images - natural, piece-wise smooth (depth map) and texture images. The performance is compared to that of other image denoising methods for various images and quality measures."