Graph Spectral Image Processing

Recent advent of graph signal processing (GSP) has spurred intensive studies of signals that live naturally on irregular data kernels described by graphs (e.g., social networks, wireless sensor networks). Though a digital image contains pixels that reside on a regularly sampled 2D grid, if one can design an appropriate underlying graph connecting pixels with weights that reflect the image structure, then one can interpret the image (or image patch) as a signal on a graph, and apply GSP tools for processing and analysis of the signal in graph spectral domain. In this article, we overview recent graph spectral techniques in GSP specifically for image / video processing. The topics covered include image compression, image restoration, image filtering and image segmentation

An adaptive grid refinement strategy for the simulation of negative streamers

The evolution of negative streamers during electric breakdown of a non-attaching gas can be described by a two-fluid model for electrons and positive ions. It consists of continuity equations for the charged particles including drift, diffusion and reaction in the local electric field, coupled to the Poisson equation for the electric potential. The model generates field enhancement and steep propagating ionization fronts at the tip of growing ionized filaments. An adaptive grid refinement method for the simulation of these structures is presented. It uses finite volume spatial discretizations and explicit time stepping, which allows the decoupling of the grids for the continuity equations from those for the Poisson equation. Standard refinement methods in which the refinement criterion is based on local error monitors fail due to the pulled character of the streamer front that propagates into a linearly unstable state. We present a refinement method which deals with all these features. Tests on one-dimensional streamer fronts as well as on three-dimensional streamers with cylindrical symmetry (hence effectively 2D for numerical purposes) are carried out successfully. Results on fine grids are presented, they show that such an adaptive grid method is needed to capture the streamer characteristics well. This refinement strategy enables us to adequately compute negative streamers in pure gases in the parameter regime where a physical instability appears: branching streamers.Comment: 46 pages, 19 figures, to appear in J. Comp. Phy

Accelerated graph-based spectral polynomial filters

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.Comment: 6 pages, 6 figures. Accepted to the 2015 IEEE International Workshop on Machine Learning for Signal Processin

Structure of the Current Sheet in the 11 July 2017 Electron Diffusion Region Event.

The structure of the current sheet along the Magnetospheric Multiscale (MMS) orbit is examined during the 11 July 2017 Electron Diffusion Region (EDR) event. The location of MMS relative to the X-line is deduced and used to obtain the spatial changes in the electron parameters. The electron velocity gradient values are used to estimate the reconnection electric field sustained by nongyrotropic pressure. It is shown that the observations are consistent with theoretical expectations for an inner EDR in 2-D reconnection. That is, the magnetic field gradient scale, where the electric field due to electron nongyrotropic pressure dominates, is comparable to the gyroscale of the thermal electrons at the edge of the inner EDR. Our approximation of the MMS observations using a steady state, quasi-2-D, tailward retreating X-line was valid only for about 1.4 s. This suggests that the inner EDR is localized; that is, electron outflow jet braking takes place within an ion inertia scale from the X-line. The existence of multiple events or current sheet processes outside the EDR may play an important role in the geometry of reconnection in the near-Earth magnetotail

Depth Estimation via Affinity Learned with Convolutional Spatial Propagation Network

Depth estimation from a single image is a fundamental problem in computer vision. In this paper, we propose a simple yet effective convolutional spatial propagation network (CSPN) to learn the affinity matrix for depth prediction. Specifically, we adopt an efficient linear propagation model, where the propagation is performed with a manner of recurrent convolutional operation, and the affinity among neighboring pixels is learned through a deep convolutional neural network (CNN). We apply the designed CSPN to two depth estimation tasks given a single image: (1) To refine the depth output from state-of-the-art (SOTA) existing methods; and (2) to convert sparse depth samples to a dense depth map by embedding the depth samples within the propagation procedure. The second task is inspired by the availability of LIDARs that provides sparse but accurate depth measurements. We experimented the proposed CSPN over two popular benchmarks for depth estimation, i.e. NYU v2 and KITTI, where we show that our proposed approach improves in not only quality (e.g., 30% more reduction in depth error), but also speed (e.g., 2 to 5 times faster) than prior SOTA methods.Comment: 14 pages, 8 figures, ECCV 201

Comment on Calculation of Positron Flux from Galactic Dark Matter

Energetic positrons produced in annihilation or decay of dark matter particles in the Milky Way can serve as an important indirect signature of dark matter. Computing the positron flux expected in a given dark matter model involves solving transport equations, which account for interaction of positrons with matter and galactic magnetic fields. Existing calculations solve the equations inside the diffusion zone, where galactic magnetic fields confine positrons, and assume vanishing positron density on the boundaries of this zone. However, in many models, a substantial fraction of the dark matter halo lies outside the diffusion zone. Positrons produced there can then enter the diffusion zone and get trapped, potentially reaching the Earth and increasing the expected flux. We calculate this enhancement for a variety of models. We also evaluate the expected enhancement of the flux of energetic photons produced by the inverse Compton scattering of the extra positrons on starlight and cosmic microwave background. We find maximal flux enhancements of order 20% in both cases.Comment: 18 pages, 6 figures. Final version accepted for publication in Physical Review