Frequency-dependent AVO attribute: theory and example

Fluid-saturated rocks generally have seismic velocities that depend upon frequency. Exploring this property may help us discriminate different fluids from seismic data. In this paper, we introduce a scheme to calculate a frequency-dependent AVO attribute in order to estimate seismic dispersion from pre-stack data, and apply it to North Sea data. The scheme essentially combines the two-term approximation of Smith and Gidlow (1987) with the method of spectral decomposition based on the Wigner-Ville distribution, which is used to achieve high resolution. The result suggests the potential of this method for detection of seismic dispersion due to fluid saturation

Principled Design and Implementation of Steerable Detectors

We provide a complete pipeline for the detection of patterns of interest in an image. In our approach, the patterns are assumed to be adequately modeled by a known template, and are located at unknown position and orientation. We propose a continuous-domain additive image model, where the analyzed image is the sum of the template and an isotropic background signal with self-similar isotropic power-spectrum. The method is able to learn an optimal steerable filter fulfilling the SNR criterion based on one single template and background pair, that therefore strongly responds to the template, while optimally decoupling from the background model. The proposed filter then allows for a fast detection process, with the unknown orientation estimation through the use of steerability properties. In practice, the implementation requires to discretize the continuous-domain formulation on polar grids, which is performed using radial B-splines. We demonstrate the practical usefulness of our method on a variety of template approximation and pattern detection experiments

Redshift-Space Enhancement of Line-of-Sight Baryon Acoustic Oscillations in the SDSS Main-Galaxy Sample

We show that redshift-space distortions of galaxy correlations have a strong effect on correlation functions with distinct, localized features, like the signature of the baryon acoustic oscillations (BAO). Near the line of sight, the features become sharper as a result of redshift-space distortions. We demonstrate this effect by measuring the correlation function in Gaussian simulations and the Millennium Simulation. We also analyze the SDSS DR7 main-galaxy sample (MGS), splitting the sample into slices 2.5 degrees on the sky in various rotations. Measuring 2D correlation functions in each slice, we do see a sharp bump along the line of sight. Using Mexican-hat wavelets, we localize it to (110 +/- 10) Mpc/h. Averaging only along the line of sight, we estimate its significance at a particular wavelet scale and location at 2.2 sigma. In a flat angular weighting in the (pi,r_p) coordinate system, the noise level is suppressed, pushing the bump's significance to 4 sigma. We estimate that there is about a 0.2% chance of getting such a signal anywhere in the vicinity of the BAO scale from a power spectrum lacking a BAO feature. However, these estimates of the significances make some use of idealized Gaussian simulations, and thus are likely a bit optimistic.Comment: 17 pages, 27 figures. Minor changes to match final version accepted to Ap

The Brera Multi-scale Wavelet (BMW) ROSAT HRI source catalog. II: application to the HRI and first results

The wavelet detection algorithm (WDA) described in the accompanying paper by Lazzati et al. is made suited for a fast and efficient analysis of images taken with the High Resolution Imager (HRI) instrument on board the ROSAT satellite. An extensive testing is carried out on the detection pipeline: HRI fields with different exposure times are simulated and analysed in the same fashion as the real data. Positions are recovered with few arcsecond errors, whereas fluxes are within a factor of two from their input values in more than 90% of the cases in the deepest images. At variance with the ``sliding-box'' detection algorithms, the WDA provides also a reliable description of the source extension, allowing for a complete search of e.g. supernova remnant or cluster of galaxies in the HRI fields. A completeness analysis on simulated fields shows that for the deepest exposures considered (~120 ks) a limiting flux of \~3x10^{-15} erg/cm2/s can be reached over the entire field of view. We test the algorithm on real HRI fields selected for their crowding and/or presence of extended or bright sources (e.g. cluster of galaxies and of stars, supernova remnants). We show that our algorithm compares favorably with other X-ray detection algorithms such as XIMAGE and EXSAS. A complete catalog will result from our analysis: it will consist of the Brera Multi-scale Wavelet Bright Source Catalog (BMW-BSC) with sources detected with a significance >4.5 sigma and of the Faint Source Catalog (BMW-FSC) with sources at >3.5 sigma. A conservative estimate based on the extragalactic log(N)-log(S) indicates that at least 16000 sources will be revealed in the complete analysis of the whole HRI dataset.Comment: 6 pages, 11 PostScript figures, 1 gif figure, ApJ in pres

A Wavelet-Based Algorithm for the Spatial Analysis of Poisson Data

Wavelets are scaleable, oscillatory functions that deviate from zero only within a limited spatial regime and have average value zero. In addition to their use as source characterizers, wavelet functions are rapidly gaining currency within the source detection field. Wavelet-based source detection involves the correlation of scaled wavelet functions with binned, two-dimensional image data. If the chosen wavelet function exhibits the property of vanishing moments, significantly non-zero correlation coefficients will be observed only where there are high-order variations in the data; e.g., they will be observed in the vicinity of sources. In this paper, we describe the mission-independent, wavelet-based source detection algorithm WAVDETECT, part of the CIAO software package. Aspects of our algorithm include: (1) the computation of local, exposure-corrected normalized (i.e. flat-fielded) background maps; (2) the correction for exposure variations within the field-of-view; (3) its applicability within the low-counts regime, as it does not require a minimum number of background counts per pixel for the accurate computation of source detection thresholds; (4) the generation of a source list in a manner that does not depend upon a detailed knowledge of the point spread function (PSF) shape; and (5) error analysis. These features make our algorithm considerably more general than previous methods developed for the analysis of X-ray image data, especially in the low count regime. We demonstrate the algorithm's robustness by applying it to various images.Comment: Accepted for publication in Ap. J. Supp. (v. 138 Jan. 2002). 61 pages, 23 figures, expands to 3.8 Mb. Abstract abridged for astro-ph submissio

Quantum Image Processing and Its Application to Edge Detection: Theory and Experiment

Processing of digital images is continuously gaining in volume and relevance, with concomitant demands on data storage, transmission and processing power. Encoding the image information in quantum-mechanical systems instead of classical ones and replacing classical with quantum information processing may alleviate some of these challenges. By encoding and processing the image information in quantum-mechanical systems, we here demonstrate the framework of quantum image processing, where a pure quantum state encodes the image information: we encode the pixel values in the probability amplitudes and the pixel positions in the computational basis states. Our quantum image representation reduces the required number of qubits compared to existing implementations, and we present image processing algorithms that provide exponential speed-up over their classical counterparts. For the commonly used task of detecting the edge of an image, we propose and implement a quantum algorithm that completes the task with only one single-qubit operation, independent of the size of the image. This demonstrates the potential of quantum image processing for highly efficient image and video processing in the big data era.Comment: 13 pages, including 9 figures and 5 appendixe

Exact reconstruction with directional wavelets on the sphere

A new formalism is derived for the analysis and exact reconstruction of band-limited signals on the sphere with directional wavelets. It represents an evolution of the wavelet formalism developed by Antoine & Vandergheynst (1999) and Wiaux et al. (2005). The translations of the wavelets at any point on the sphere and their proper rotations are still defined through the continuous three-dimensional rotations. The dilations of the wavelets are directly defined in harmonic space through a new kernel dilation, which is a modification of an existing harmonic dilation. A family of factorized steerable functions with compact harmonic support which are suitable for this kernel dilation is firstly identified. A scale discretized wavelet formalism is then derived, relying on this dilation. The discrete nature of the analysis scales allows the exact reconstruction of band-limited signals. A corresponding exact multi-resolution algorithm is finally described and an implementation is tested. The formalism is of interest notably for the denoising or the deconvolution of signals on the sphere with a sparse expansion in wavelets. In astrophysics, it finds a particular application for the identification of localized directional features in the cosmic microwave background (CMB) data, such as the imprint of topological defects, in particular cosmic strings, and for their reconstruction after separation from the other signal components.Comment: 22 pages, 2 figures. Version 2 matches version accepted for publication in MNRAS. Version 3 (identical to version 2) posted for code release announcement - "Steerable scale discretised wavelets on the sphere" - S2DW code available for download at http://www.mrao.cam.ac.uk/~jdm57/software.htm

Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images

We present a novel kernel regression framework for smoothing scalar surface data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel constructed from the eigenfunctions, we formulate a new bivariate kernel regression framework as a weighted eigenfunction expansion with the heat kernel as the weights. The new kernel regression is mathematically equivalent to isotropic heat diffusion, kernel smoothing and recently popular diffusion wavelets. Unlike many previous partial differential equation based approaches involving diffusion, our approach represents the solution of diffusion analytically, reducing numerical inaccuracy and slow convergence. The numerical implementation is validated on a unit sphere using spherical harmonics. As an illustration, we have applied the method in characterizing the localized growth pattern of mandible surfaces obtained in CT images from subjects between ages 0 and 20 years by regressing the length of displacement vectors with respect to the template surface.Comment: Accepted in Medical Image Analysi