arXiv subjects

Christopher A. Metzler

Publications and source records attributed to Christopher A. Metzler.

45 records · Page 3Linked to original sources

arXiv2017

Learned D-AMP: Principled Neural Network based Compressive Image Recovery

Compressive image recovery is a challenging problem that requires fast and accurate algorithms. Recently, neural networks have been applied to this problem with promising results. By exploiting massively parallel GPU processing architectures and oodles of training data, they can run orders of magnitude faster than existing techniques. However, these methods are largely unprincipled black boxes that are difficult to train and often-times specific to a single measurement matrix. It was recently demonstrated that iterative sparse-signal-recovery algorithms can be "unrolled" to form interpretable deep networks. Taking inspiration from this work, we develop a novel neural network architecture that mimics the behavior of the denoising-based approximate message passing (D-AMP) algorithm. We call this new network Learned D-AMP (LDAMP). The LDAMP network is easy to train, can be applied to a variety of different measurement matrices, and comes with a state-evolution heuristic that accurately predicts its performance. Most importantly, it outperforms the state-of-the-art BM3D-AMP and NLR-CS algorithms in terms of both accuracy and run time. At high resolutions, and when used with sensing matrices that have fast implementations, LDAMP runs over $50\times$ faster than BM3D-AMP and hundreds of times faster than NLR-CS.

stat.ML↗

arXiv2016

From Denoising to Compressed Sensing

A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, today's denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called Denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high performance denoiser for natural images, D-AMP offers state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.

cs.IT↗

arXiv2001

The Effect of the Cosmic Web on Cluster Weak Lensing Mass Estimates

In modern hierarchical theories of structure formation, rich clusters of galaxies form at the vertices of a weblike distribution of matter, with filaments emanating from them to large distances and with smaller objects forming and draining in along these filaments. The amount of mass contained in structure near the cluster can be comparable to the collapsed mass of the cluster itself. As the lensing kernel is quite broad along the line of sight around cluster lenses with typical redshifts near z=0.5, structures many Mpc away from the cluster are essentially at the same location as the cluster itself, when considering their effect on the cluster's weak lensing signal. We use large-scale numerical simulations of structure formation in a Lambda-dominated cold dark matter model to quantify the effect that large-scale structure near clusters has upon the cluster masses deduced from weak lensing analysis. A correction for the scatter in possible observed lensing masses should be included when interpreting mass functions from weak lensing surveys.

astro-ph↗

arXiv1999

Weak Gravitational Lensing and Cluster Mass Estimates

Hierarchical theories of structure formation predict that clusters of galaxies should be embedded in a web like structure, with filaments emanating from them to large distances. The amount of mass contained within such filaments near a cluster can be comparable to the collapsed mass of the cluster itself. Diffuse infalling material also contains a large amount of mass. Both these components can contribute to the cluster weak lensing signal. This ``projection bias'' is maximized if a filament lies close to the line-of-sight to a cluster. Using large--scale numerical simulations of structure formation in a cosmological constant dominated cold dark matter model, we show that the projected mass typically exceeds the actual mass by several tens of percent. This effect is significant for attempts to estimate cluster masses through weak lensing observations, and will affect weak lensing surveys aimed at constructing the cluster mass function.

astro-ph↗

arXiv1998

The Cluster SZ -- Mass Correlation

N-body + hydrodynamic simulations of galaxy clusters are used to demonstrate a correlation between galaxy cluster mass and the strength of the Sunyaev-Zel'dovich (SZ) effect induced by the cluster. The intrinsic scatter in the correlaton is larger than seen in the cluster mass -- X-ray temperature correlation, but smaller than seen in the correlation between mass (or temperature) and X-ray luminosity, as expected. Using the convergence to self-similarity of cluster structure at larger radii, a simple area-averaged SZ value derived from mock SZ maps also correlates well with mass; the intrinsic scatter in this correlation is comparable to that seen in simulations for the mass -- temperature correlation. Such a relation may prove a powerful tool for estimating cluster masses at higher redshifts.

astro-ph↗

arXiv1997

Simulations Of Galaxy Clusters With And Without Winds: I. The Structure Of Clusters

We use gas dynamic simulations to explore the effects of galactic winds on galaxy clusters. Two ensembles of 18 realizations, spanning a decade in temperature, are evolved with and without winds in an underlying biased CDM cosmology. Galaxies are identified as peaks in the initial density field, and are assumed to lose half their initial mass over a Hubble time in winds with an effective temperature of 8 keV. The energy input through winds boosts the entropy of the ICM above that generated by infall, resulting in a more extended density profile. The magnitude of this effect increases with decreasing mass or temperature, consistent with observations. The extended nature of the ICM with winds can lead to underestimates of the global baryon fraction, with low-temperature clusters particularly deficient. We calibrate the amplitude of this effect at density contrasts of 170 and 500. On the other hand, the final temperature of the gas is relatively unaffected; a similar mass-temperature relation exists with or without winds. The input wind energy is effectively consumed as work to lift the gas in the dark matter dominated potential. While the dark matter profile exhibits a self-similar form seen in other studies, the galaxy distribution is more centrally concentrated than either the dark matter or gas, and evidences a mild velocity bias. The gradient of galaxies with respect to primordial gas produces strong, negative radial gradients in metallicity within the ICM.

astro-ph↗

arXiv1995

Mass Estimates of X-Ray Clusters

We use cosmological gas dynamic simulations to investigate the accuracy of galaxy cluster mass estimates based on X-ray observations. The experiments follow the formation of clusters in different cosmological models and include the effects of gravity, pressure gradients, and hydrodynamical shocks. A subset of our ensemble also allows for feedback of mass and energy from galactic winds into the intracluster medium. We find that mass estimates based on the hydrostatic, isothermal beta-model are remarkably accurate when evaluated at radii where the cluster mean density is between 500-2500 times the critical density. Applied to 174 artificial ROSAT images constructed from the simulations, the distribution of the estimated-to-true mass ratio is nearly unbiased and has a standard deviation of 14-29%. The scatter can be considerably reduced (to 8-15%) by using an alternative mass estimator that exploits the tightness of the mass-temperature relation found in the simulations. The improvement over beta-model estimates is due to the elimination of the variance contributed by the gas outer slope parameter. We discuss these findings and their implications for recent measurements of cluster baryon fractions.

astro-ph↗

arXiv1995

The Velocity Dispersion -- Temperature Correlation from a Limited Cluster Sample

Most studies of correlations between X-ray and optical properties of galaxy clusters have used the largest samples of data available, regardless of the morphological types of clusters included. Given the increasing evidence that morphology is related to a cluster's degree of dynamical evolution, we approach the study of X-ray and optical correlations differently. We evaluate the relationship between velocity dispersion and temperature for a limited set of galaxy clusters taken from Bird (1994), which all possess dominant central galaxies and which have been explicitly corrected for the presence of substructure. We find that $σ_r \propto T^{0.61 \pm 0.13}$. We use a Monte Carlo computer routine to estimate the significance of this deviation from the $σ_r \propto T^{0.5}$ relationship predicted by the virial theorem. We find that the simulated correlation is steeper than the observed value only 4\% of the time, suggesting that the deviation is significant. The combination of protogalactic winds and dynamical friction reproduces nearly exactly the observed relationship between $σ_r$ and $T$.

astro-ph↗

arXiv1993

A Simulation of the Intracluster Medium with Feedback from Cluster Galaxies

The formation and evolution of an X--ray cluster is studied using a 3--D N-body + hydrodynamical simulation which includes feedback of energy and iron from cluster galaxies. The differences in evolution and final state between the simulation and a similar run without feedback are highlighted. We address the energetics of cluster gas; the distribution of dark matter, gas, and galaxies; the thermodynamic state of cluster gas, the beta model, and the beta discrepancy; x-ray evolution; the validity of estimates of the binding mass and of the baryon fraction of the cluster; dynamics of the galaxy population and velocity bias; and of the evolution of the iron abundance distribution in the cluster. We find that preheating by galactic winds results in a lower core density for the ICM, which in turn makes the simulated cluster fainter at high redshift and undergo rapid luminosity evolution to the present. A strong iron abundance gradient is present, even at high redshift. Velocity bias is present in the galaxy population; this bias combined with the preheating from winds drives the value of $β_{spec}\,=\,σ^{2}/\left(kT/μm_{p}\right)$ to values less than one. The two fluid simulation, modelling infall only, predicts $β_{spec}\,\geq\,1$, less in line with observation.

astro-ph↗