3D Velocity and Density Reconstructions of the Local Universe with Cosmicflows-1

This paper presents an analysis of the local peculiar velocity field based on the Wiener Filter reconstruction method. We used our currently available catalog of distance measurements containing 1,797 galaxies within 3000 km/s: Cosmicflows-1. The Wiener Filter method is used to recover the full 3D peculiar velocity field from the observed map of radial velocities and to recover the underlying linear density field. The velocity field within a data zone of 3000 km/s is decomposed into a local component that is generated within the data zone and a tidal one that is generated by the mass distribution outside that zone. The tidal component is characterized by a coherent flow toward the Norma-Hydra-Centaurus (Great Attractor) region while the local component is dominated by a flow toward the Virgo Cluster and away from the Local Void. A detailed analysis shows that the local flow is predominantly governed by the Local Void and the Virgo Cluster plays a lesser role. The analysis procedure was tested against a mock catalog. It is demonstrated that the Wiener Filter accurately recovers the input velocity field of the mock catalog on the scale of the extraction of distances and reasonably recovers the velocity field on significantly larger scales. The Bayesian Wiener Filter reconstruction is carried out within the ?CDM WMAP5 framework. The Wiener Filter reconstruction draws particular attention to the importance of voids in proximity to our neighborhood. The prominent structure of the Local Supercluster is wrapped in a horseshoe collar of under density with the Local Void as a major component.Comment: Accepted for ApJ, August 6, 201

Stochastic Wiener Filter in the White Noise Space

In this paper we introduce a new approach to the study of filtering theory by allowing the system's parameters to have a random character. We use Hida's white noise space theory to give an alternative characterization and a proper generalization to the Wiener filter over a suitable space of stochastic distributions introduced by Kondratiev. The main idea throughout this paper is to use the nuclearity of this spaces in order to view the random variables as bounded multiplication operators (with respect to the Wick product) between Hilbert spaces of stochastic distributions. This allows us to use operator theory tools and properties of Wiener algebras over Banach spaces to proceed and characterize the Wiener filter equations under the underlying randomness assumptions

One Signal-Noise Separation based Wiener Filter for Magnetogastrogram

Magnetogastrogram (MGG) signal frequency is about 0.05 Hz, the low-frequency environmental noise interference is serious and can be several times stronger in magnitude than the signals of interest and may severely impede the extraction of relevant information. Wiener filter is one classic denoising solution for biomagnetic applications. Since the reference channels are usually placed not far enough from the biomagnetic sources under test, they will inevitably detect the signals and the Wiener filters may produce ill-conditioned solutions. Considering the solutions to improve the signal-to-noise ratio (SNR) of Wiener filter output, there are few methods to separate the signals from the noises of the reference signal at the filter input. In this paper, a new signal processing framework called signal-noise separation based Wiener filter (SNSWF) is proposed that it separates the main noise as the input signal of the filter to improve the output SNR of Wiener filter. The filter was successfully applied to the noise suppression for MGG signal detection. Using the SNSWF, the filter SNR is 16.7 dB better than the classic Wiener filter

3D Reconstruction of the Density Field: An SVD Approach to Weak Lensing Tomography

We present a new method for constructing three-dimensional mass maps from gravitational lensing shear data. We solve the lensing inversion problem using truncation of singular values (within the context of generalized least squares estimation) without a priori assumptions about the statistical nature of the signal. This singular value framework allows a quantitative comparison between different filtering methods: we evaluate our method beside the previously explored Wiener filter approaches. Our method yields near-optimal angular resolution of the lensing reconstruction and allows cluster sized halos to be de-blended robustly. It allows for mass reconstructions which are 2-3 orders-of-magnitude faster than the Wiener filter approach; in particular, we estimate that an all-sky reconstruction with arcminute resolution could be performed on a time-scale of hours. We find however that linear, non-parametric reconstructions have a fundamental limitation in the resolution achieved in the redshift direction.Comment: 11 pages, 6 figures. Accepted for publication in Ap

Adaptive acoustooptic filter

A new adaptive filter utilizing acoustooptic devices in a space integrating architecture is described. Two configurations are presented; one of them, suitable for signal estimation, is shown to approximate the Wiener filter, while the other, suitable for detection, is shown to approximate the matched filter

Ringing effects reduction by improved deconvolution algorithm Application to A370 CFHT image of gravitational arcs

We develop a self-consistent automatic procedure to restore informations from astronomical observations. It relies on both a new deconvolution algorithm called LBCA (Lower Bound Constraint Algorithm) and the use of the Wiener filter. In order to explore its scientific potential for strong and weak gravitational lensing, we process a CFHT image of the galaxies cluster Abell 370 which exhibits spectacular strong gravitational lensing effects. A high quality restoration is here of particular interest to map the dark matter within the cluster. We show that the LBCA turns out specially efficient to reduce ringing effects introduced by classical deconvolution algorithms in images with a high background. The method allows us to make a blind detection of the radial arc and to recover morphological properties similar to thoseobserved from HST data. We also show that the Wiener filter is suitable to stop the iterative process before noise amplification, using only the unrestored data.Comment: A&A in press 9 pages 9 figure

Linear Reconstruction of Non-Stationary Image Ensembles Incorporating Blur and Noise Models

Two new linear reconstruction techniques are developed to improve the resolution of images collected by ground-based telescopes imaging through atmospheric turbulence. The classical approach involves the application of constrained least squares (CLS) to the deconvolution from wavefront sensing (DWFS) technique. The new algorithm incorporates blur and noise models to select the appropriate regularization constant automatically. In all cases examined, the Newton-Raphson minimization converged to a solution in less than 10 iterations. The non-iterative Bayesian approach involves the development of a new vector Wiener filter which is optimal with respect to mean square error (MSE) for a non-stationary object class degraded by atmospheric turbulence and measurement noise. This research involves the first extension of the Wiener filter to account properly for shot noise and an unknown, random optical transfer function (OTF). The vector Wiener filter provides superior reconstructions when compared to the traditional scalar Wiener filter for a non-stationary object class. In addition, the new filter can provide a superresolution capability when the object\u27s Fourier domain statistics are known for spatial frequencies beyond the OTF cutoff. A generalized performance and robustness study of the vector Wiener filter showed that MSE performance is fundamentally limited by object signal-to-noise ratio (SNR) and correlation between object pixels