相关论文: Solving Jigsaw Puzzles By the Graph Connection Lap…

Partitioning a graph into three pieces, with two of them large and connected, and the third a small ``separator'' set, is useful for improving the performance of a number of combinatorial algorithms. This is done using the second…

We consider the simultaneous deblurring of a set of noisy images whose point spread functions are different but known and spatially invariant, and the noise is Gaussian. Currently available iterative algorithms that are typically used for…

We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…

The purpose of this paper is to infer a global (collective) model of time-varying responses of a set of nodes as a dynamic graph, where the individual time series are respectively observed at each of the nodes. The motivation of this work…

The original contributions of this paper are twofold: a new understanding of the influence of noise on the eigenvectors of the graph Laplacian of a set of image patches, and an algorithm to estimate a denoised set of patches from a noisy…

For a given graph $G$, we aim to determine the possible realizable spectra for a generalized (or sometimes referred to as a weighted) Laplacian matrix associated with $G$. This new specialized inverse eigenvalue problem is considered for…

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously…

In this paper we introduce new types of square-piece jigsaw puzzles, where in addition to the unknown location and orientation of each piece, a piece might also need to be flipped. These puzzles, which are associated with a number of real…

Large graphs commonly appear in social networks, knowledge graphs, recommender systems, life sciences, and decision making problems. Summarizing large graphs by their high level properties is helpful in solving problems in these settings.…

Graph learning methods have recently been receiving increasing interest as means to infer structure in datasets. Most of the recent approaches focus on different relationships between a graph and data sample distributions, mostly in…

Graph sampling with noise is a fundamental problem in graph signal processing (GSP). Previous works assume an unbiased least square (LS) signal reconstruction scheme and select samples greedily via expensive extreme eigenvector computation.…

This paper studies the problem of learning the large-scale Gaussian graphical models that are multivariate totally positive of order two ($\text{MTP}_2$). By introducing the concept of bridge, which commonly exists in large-scale sparse…

Tensor decomposition has emerged as a prominent technique to learn low-dimensional representation under the supervision of reconstruction error, primarily benefiting data inference tasks like completion and imputation, but not…

Matrix completion algorithms fill missing entries in a large matrix given a subset of observed samples. However, how to best pre-select informative matrix entries given a sampling budget is largely unaddressed. In this paper, we propose a…

This paper is concerned with the numerical computation of scattering resonances of the Laplacian for Dirichlet obstacles with rough boundary. We prove that under mild geometric assumptions on the obstacle there exists an algorithm whose…

We introduce a new notion of graph sparsificaiton based on spectral similarity of graph Laplacians: spectral sparsification requires that the Laplacian quadratic form of the sparsifier approximate that of the original. This is equivalent to…

Spectral clustering is a novel clustering method which can detect complex shapes of data clusters. However, it requires the eigen decomposition of the graph Laplacian matrix, which is proportion to $O(n^3)$ and thus is not suitable for…

We introduce a data-adaptive inversion method that integrates classical or deep learning-based approaches with iterative graph Laplacian regularization, specifically targeting acoustic impedance inversion - a critical task in seismic…

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in…

We report a new algorithm to generate Laplacian Growth Patterns using iterated conformal maps. The difficulty of growing a complete layer with local width proportional to the gradient of the Laplacian field is overcome. The resulting growth…