Seismic Fault Preserving Diffusion

This paper focuses on the denoising and enhancing of 3-D reflection seismic data. We propose a pre-processing step based on a non linear diffusion filtering leading to a better detection of seismic faults. The non linear diffusion approaches are based on the definition of a partial differential equation that allows us to simplify the images without blurring relevant details or discontinuities. Computing the structure tensor which provides information on the local orientation of the geological layers, we propose to drive the diffusion along these layers using a new approach called SFPD (Seismic Fault Preserving Diffusion). In SFPD, the eigenvalues of the tensor are fixed according to a confidence measure that takes into account the regularity of the local seismic structure. Results on both synthesized and real 3-D blocks show the efficiency of the proposed approach.Comment: 10 page

Evolution-Operator-Based Single-Step Method for Image Processing

This work proposes an evolution-operator-based single-time-step method for image and signal processing. The key component of the proposed method is a local spectral evolution kernel (LSEK) that analytically integrates a class of evolution partial differential equations (PDEs). From the point of view PDEs, the LSEK provides the analytical solution in a single time step, and is of spectral accuracy, free of instability constraint. From the point of image/signal processing, the LSEK gives rise to a family of lowpass filters. These filters contain controllable time delay and amplitude scaling. The new evolution operator-based method is constructed by pointwise adaptation of anisotropy to the coefficients of the LSEK. The Perona-Malik-type of anisotropic diffusion schemes is incorporated in the LSEK for image denoising. A forward-backward diffusion process is adopted to the LSEK for image deblurring or sharpening. A coupled PDE system is modified for image edge detection. The resulting image edge is utilized for image enhancement. Extensive computer experiments are carried out to demonstrate the performance of the proposed method. The major advantages of the proposed method are its single-step solution and readiness for multidimensional data analysis

Evidence of a Supermassive Black Hole in the Galaxy NGC 1023 from the Nuclear Stellar Dynamics

We analyze the nuclear stellar dynamics of the SB0 galaxy NGC 1023, utilizing observational data both from the Space Telescope Imaging Spectrograph aboard the Hubble Space Telescope and from the ground. The stellar kinematics measured from these long-slit spectra show rapid rotation (V = 70 km/s at a distance of 0.1 arcsec = 4.9 pc from the nucleus) and increasing velocity dispersion toward the nucleus (where sigma = 295 +/- 30 km/s). We model the observed stellar kinematics assuming an axisymmetric mass distribution with both two and three integrals of motion. Both modeling techniques point to the presence of a central dark compact mass (which presumably is a supermassive black hole) with confidence > 99%. The isotropic two-integral models yield a best-fitting black hole mass of (6.0 +/- 1.4) x 10^7 M_sun and mass-to-light ratio (M/L_V) of 5.38 +/- 0.08, and the goodness-of-fit (chi^2) is insensitive to reasonable values for the galaxy's inclination. The three-integral models, which non-parametrically fit the observed line-of-sight velocity distribution as a function of position in the galaxy, suggest a black hole mass of (3.9 +/- 0.4) x 10^7 M_sun and M/L_V of 5.56 +/- 0.02 (internal errors), and the edge-on models are vastly superior fits over models at other inclinations. The internal dynamics in NGC 1023 as suggested by our best-fit three-integral model shows that the velocity distribution function at the nucleus is tangentially anisotropic, suggesting the presence of a nuclear stellar disk. The nuclear line of sight velocity distribution has enhanced wings at velocities >= 600 km/s from systemic, suggesting that perhaps we have detected a group of stars very close to the central dark mass.Comment: 21 pages, 12 figures, accepted in the Astrophysical Journa

Dynamical Measurements of Black Hole Masses in Four Brightest Cluster Galaxies at 100 Mpc

We present stellar kinematics and orbit superposition models for the central regions of four Brightest Cluster Galaxies (BCGs), based upon integral-field spectroscopy at Gemini, Keck, and McDonald Observatories. Our integral-field data span radii from < 100 pc to tens of kpc. We report black hole masses, M_BH, of 2.1 +/- 1.6 x 10^10 M_Sun for NGC 4889, 9.7 + 3.0 - 2.6 x 10^9 M_Sun for NGC 3842, and 1.3 + 0.5 - 0.4 x 10^9 M_Sun for NGC 7768. For NGC 2832 we report an upper limit of M_BH < 9 x 10^9 M_Sun. Stellar orbits near the center of each galaxy are tangentially biased, on comparable spatial scales to the galaxies' photometric cores. We find possible photometric and kinematic evidence for an eccentric torus of stars in NGC 4889, with a radius of nearly 1 kpc. We compare our measurements of M_BH to the predicted black hole masses from various fits to the relations between M_BH and stellar velocity dispersion, luminosity, or stellar mass. The black holes in NGC 4889 and NGC 3842 are significantly more massive than all dispersion-based predictions and most luminosity-based predictions. The black hole in NGC 7768 is consistent with a broader range of predictions.Comment: 24 pages, 18 figures. Accepted for publication in Ap

Optical Dual Laser Based Sensor Denoising for OnlineMetal Sheet Flatness Measurement Using Hermite Interpolation

Flatness sensors are required for quality control of metal sheets obtained from steel coils by roller leveling and cutting systems. This article presents an innovative system for real-time robust surface estimation of flattened metal sheets composed of two line lasers and a conventional 2D camera. Laser plane triangulation is used for surface height retrieval along virtual surface fibers. The dual laser allows instantaneous robust and quick estimation of the fiber height derivatives. Hermite cubic interpolation along the fibers allows real-time surface estimation and high frequency noise removal. Noise sources are the vibrations induced in the sheet by its movements during the process and some mechanical events, such as cutting into separate pieces. The system is validated on synthetic surfaces that simulate the most critical noise sources and on real data obtained from the installation of the sensor in an actual steel mill. In the comparison with conventional filtering methods, we achieve at least a 41% of improvement in the accuracy of the surface reconstruction