Interpretation of Helioseismic Travel Times - Sensitivity to Sound Speed, Pressure, Density, and Flows

Time-distance helioseismology uses cross-covariances of wave motions on the solar surface to determine the travel times of wave packets moving from one surface location to another. We review the methodology to interpret travel-time measurements in terms of small, localized perturbations to a horizontally homogeneous reference solar model. Using the first Born approximation, we derive and compute 3D travel-time sensitivity (Fr\'echet) kernels for perturbations in sound-speed, density, pressure, and vector flows. While kernels for sound speed and flows had been computed previously, here we extend the calculation to kernels for density and pressure, hence providing a complete description of the effects of solar dynamics and structure on travel times. We treat three thermodynamic quantities as independent and do not assume hydrostatic equilibrium. We present a convenient approach to computing damped Green's functions using a normal-mode summation. The Green's function must be computed on a wavenumber grid that has sufficient resolution to resolve the longest lived modes. The typical kernel calculations used in this paper are computer intensive and require on the order of 600 CPU hours per kernel. Kernels are validated by computing the travel-time perturbation that results from horizontally-invariant perturbations using two independent approaches. At fixed sound-speed, the density and pressure kernels are approximately related through a negative multiplicative factor, therefore implying that perturbations in density and pressure are difficult to disentangle. Mean travel-times are not only sensitive to sound-speed, density and pressure perturbations, but also to flows, especially vertical flows. Accurate sensitivity kernels are needed to interpret complex flow patterns such as convection

Efficient Regularization of Squared Curvature

Curvature has received increased attention as an important alternative to length based regularization in computer vision. In contrast to length, it preserves elongated structures and fine details. Existing approaches are either inefficient, or have low angular resolution and yield results with strong block artifacts. We derive a new model for computing squared curvature based on integral geometry. The model counts responses of straight line triple cliques. The corresponding energy decomposes into submodular and supermodular pairwise potentials. We show that this energy can be efficiently minimized even for high angular resolutions using the trust region framework. Our results confirm that we obtain accurate and visually pleasing solutions without strong artifacts at reasonable run times.Comment: 8 pages, 12 figures, to appear at IEEE conference on Computer Vision and Pattern Recognition (CVPR), June 201

RIDI: Robust IMU Double Integration

This paper proposes a novel data-driven approach for inertial navigation, which learns to estimate trajectories of natural human motions just from an inertial measurement unit (IMU) in every smartphone. The key observation is that human motions are repetitive and consist of a few major modes (e.g., standing, walking, or turning). Our algorithm regresses a velocity vector from the history of linear accelerations and angular velocities, then corrects low-frequency bias in the linear accelerations, which are integrated twice to estimate positions. We have acquired training data with ground-truth motions across multiple human subjects and multiple phone placements (e.g., in a bag or a hand). The qualitatively and quantitatively evaluations have demonstrated that our algorithm has surprisingly shown comparable results to full Visual Inertial navigation. To our knowledge, this paper is the first to integrate sophisticated machine learning techniques with inertial navigation, potentially opening up a new line of research in the domain of data-driven inertial navigation. We will publicly share our code and data to facilitate further research

An Automated Method for Tracking Clouds in Planetary Atmospheres

We present an automated method for cloud tracking which can be applied to planetary images. The method is based on a digital correlator which compares two or more consecutive images and identifies patterns by maximizing correlations between image blocks. This approach bypasses the problem of feature detection. Four variations of the algorithm are tested on real cloud images of Jupiter’s white ovals from the Galileo mission, previously analyzed in Vasavada et al. [Vasavada, A.R., Ingersoll, A.P., Banfield, D., Bell, M., Gierasch, P.J., Belton, M.J.S., Orton, G.S., Klaasen, K.P., Dejong, E., Breneman, H.H., Jones, T.J., Kaufman, J.M., Magee, K.P., Senske, D.A. 1998. Galileo imaging of Jupiter’s atmosphere: the great red spot, equatorial region, and white ovals. Icarus, 135, 265, doi:10.1006/icar.1998.5984]. Direct correlation, using the sum of squared differences between image radiances as a distance estimator (baseline case), yields displacement vectors very similar to this previous analysis. Combining this distance estimator with the method of order ranks results in a technique which is more robust in the presence of outliers and noise and of better quality. Finally, we introduce a distance metric which, combined with order ranks, provides results of similar quality to the baseline case and is faster. The new approach can be applied to data from a number of space-based imaging instruments with a non-negligible gain in computing time

Bregman Voronoi Diagrams: Properties, Algorithms and Applications

The Voronoi diagram of a finite set of objects is a fundamental geometric structure that subdivides the embedding space into regions, each region consisting of the points that are closer to a given object than to the others. We may define many variants of Voronoi diagrams depending on the class of objects, the distance functions and the embedding space. In this paper, we investigate a framework for defining and building Voronoi diagrams for a broad class of distance functions called Bregman divergences. Bregman divergences include not only the traditional (squared) Euclidean distance but also various divergence measures based on entropic functions. Accordingly, Bregman Voronoi diagrams allow to define information-theoretic Voronoi diagrams in statistical parametric spaces based on the relative entropy of distributions. We define several types of Bregman diagrams, establish correspondences between those diagrams (using the Legendre transformation), and show how to compute them efficiently. We also introduce extensions of these diagrams, e.g. k-order and k-bag Bregman Voronoi diagrams, and introduce Bregman triangulations of a set of points and their connexion with Bregman Voronoi diagrams. We show that these triangulations capture many of the properties of the celebrated Delaunay triangulation. Finally, we give some applications of Bregman Voronoi diagrams which are of interest in the context of computational geometry and machine learning.Comment: Extend the proceedings abstract of SODA 2007 (46 pages, 15 figures