Graph Signal Processing: Overview, Challenges and Applications

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.Comment: To appear, Proceedings of the IEE

Deep Markov Random Field for Image Modeling

Markov Random Fields (MRFs), a formulation widely used in generative image modeling, have long been plagued by the lack of expressive power. This issue is primarily due to the fact that conventional MRFs formulations tend to use simplistic factors to capture local patterns. In this paper, we move beyond such limitations, and propose a novel MRF model that uses fully-connected neurons to express the complex interactions among pixels. Through theoretical analysis, we reveal an inherent connection between this model and recurrent neural networks, and thereon derive an approximated feed-forward network that couples multiple RNNs along opposite directions. This formulation combines the expressive power of deep neural networks and the cyclic dependency structure of MRF in a unified model, bringing the modeling capability to a new level. The feed-forward approximation also allows it to be efficiently learned from data. Experimental results on a variety of low-level vision tasks show notable improvement over state-of-the-arts.Comment: Accepted at ECCV 201

Hierarchical Nearest-Neighbor Gaussian Process Models for Large Geostatistical Datasets

Spatial process models for analyzing geostatistical data entail computations that become prohibitive as the number of spatial locations become large. This manuscript develops a class of highly scalable Nearest Neighbor Gaussian Process (NNGP) models to provide fully model-based inference for large geostatistical datasets. We establish that the NNGP is a well-defined spatial process providing legitimate finite-dimensional Gaussian densities with sparse precision matrices. We embed the NNGP as a sparsity-inducing prior within a rich hierarchical modeling framework and outline how computationally efficient Markov chain Monte Carlo (MCMC) algorithms can be executed without storing or decomposing large matrices. The floating point operations (flops) per iteration of this algorithm is linear in the number of spatial locations, thereby rendering substantial scalability. We illustrate the computational and inferential benefits of the NNGP over competing methods using simulation studies and also analyze forest biomass from a massive United States Forest Inventory dataset at a scale that precludes alternative dimension-reducing methods

Non-homogeneous polygonal Markov fields in the plane: graphical representations and geometry of higher order correlations

We consider polygonal Markov fields originally introduced by Arak and Surgailis (1989). Our attention is focused on fields with nodes of order two, which can be regarded as continuum ensembles of non-intersecting contours in the plane, sharing a number of features with the two-dimensional Ising model. We introduce non-homogeneous version of polygonal fields in anisotropic enviroment. For these fields we provide a class of new graphical constructions and random dynamics. These include a generalised dynamic representation, generalised and defective disagreement loop dynamics as well as a generalised contour birth and death dynamics. Next, we use these constructions as tools to obtain new exact results on the geometry of higher order correlations of polygonal Markov fields in their consistent regime.Comment: 54 page

CT-SRCNN: Cascade Trained and Trimmed Deep Convolutional Neural Networks for Image Super Resolution

We propose methodologies to train highly accurate and efficient deep convolutional neural networks (CNNs) for image super resolution (SR). A cascade training approach to deep learning is proposed to improve the accuracy of the neural networks while gradually increasing the number of network layers. Next, we explore how to improve the SR efficiency by making the network slimmer. Two methodologies, the one-shot trimming and the cascade trimming, are proposed. With the cascade trimming, the network's size is gradually reduced layer by layer, without significant loss on its discriminative ability. Experiments on benchmark image datasets show that our proposed SR network achieves the state-of-the-art super resolution accuracy, while being more than 4 times faster compared to existing deep super resolution networks.Comment: Accepted to IEEE Winter Conf. on Applications of Computer Vision (WACV) 2018, Lake Tahoe, US