An efficient maximum entropy technique for 2-D isotropic random fields

Title from cover.Bibliography: p. 24-25.Supported in part by the National Science Foundation under Grant ECS-83-12921 and in part by the Army Research Office under Grant DAAG-29-84-K-0005.Ahmed H. Tewfik, Bernard C. Levy and Alan S. Willsky

An efficient maximum entropy technique for 2-D isotropic random fields

Bibliography: p. 36-40.Supported by the National Science Foundation under grant no. ECS-83-12921 Supported by the Army Research Office under grant no. DAAG-84-K-0005Ahmed H. Tewfik, Bernard C. Levy, Alan S. Willsky

Efficient Wiener filtering without preconditioning

We present a new approach to calculate the Wiener filter solution of general data sets. It is trivial to implement, flexible, numerically absolutely stable, and guaranteed to converge. Most importantly, it does not require an ingenious choice of preconditioner to work well. The method is capable of taking into account inhomogeneous noise distributions and arbitrary mask geometries. It iteratively builds up the signal reconstruction by means of a messenger field, introduced to mediate between the different preferred bases in which signal and noise properties can be specified most conveniently. Using cosmic microwave background (CMB) radiation data as a showcase, we demonstrate the capabilities of our scheme by computing Wiener filtered WMAP7 temperature and polarization maps at full resolution for the first time. We show how the algorithm can be modified to synthesize fluctuation maps, which, combined with the Wiener filter solution, result in unbiased constrained signal realizations, consistent with the observations. The algorithm performs well even on simulated CMB maps with Planck resolution and dynamic range.Comment: 5 pages, 2 figures. Submitted to Astronomy and Astrophysics. Replaced to match published versio

Final report on estimation and statistical analysis of spatially distributed random processes

Includes bibliographical references.Final report;Supported by the NSF. ECS-8312921prepared by Alan S. Willsky, Bernard C. Levy, George C. Verghese

Detecting the orientation of magnetic fields in galaxy clusters

Clusters of galaxies, filled with hot magnetized plasma, are the largest bound objects in existence and an important touchstone in understanding the formation of structures in our Universe. In such clusters, thermal conduction follows field lines, so magnetic fields strongly shape the cluster's thermal history; that some have not since cooled and collapsed is a mystery. In a seemingly unrelated puzzle, recent observations of Virgo cluster spiral galaxies imply ridges of strong, coherent magnetic fields offset from their centre. Here we demonstrate, using three-dimensional magnetohydrodynamical simulations, that such ridges are easily explained by galaxies sweeping up field lines as they orbit inside the cluster. This magnetic drape is then lit up with cosmic rays from the galaxies' stars, generating coherent polarized emission at the galaxies' leading edges. This immediately presents a technique for probing local orientations and characteristic length scales of cluster magnetic fields. The first application of this technique, mapping the field of the Virgo cluster, gives a startling result: outside a central region, the magnetic field is preferentially oriented radially as predicted by the magnetothermal instability. Our results strongly suggest a mechanism for maintaining some clusters in a 'non-cooling-core' state.Comment: 48 pages, 21 figures, revised version to match published article in Nature Physics, high-resolution version available at http://www.cita.utoronto.ca/~pfrommer/Publications/pfrommer-dursi.pd

Automatic Renal Segmentation in DCE-MRI using Convolutional Neural Networks

Kidney function evaluation using dynamic contrast-enhanced MRI (DCE-MRI) images could help in diagnosis and treatment of kidney diseases of children. Automatic segmentation of renal parenchyma is an important step in this process. In this paper, we propose a time and memory efficient fully automated segmentation method which achieves high segmentation accuracy with running time in the order of seconds in both normal kidneys and kidneys with hydronephrosis. The proposed method is based on a cascaded application of two 3D convolutional neural networks that employs spatial and temporal information at the same time in order to learn the tasks of localization and segmentation of kidneys, respectively. Segmentation performance is evaluated on both normal and abnormal kidneys with varying levels of hydronephrosis. We achieved a mean dice coefficient of 91.4 and 83.6 for normal and abnormal kidneys of pediatric patients, respectively