We describe a novel method for the application of Convolutional Neural Networks (CNNs) to fields defined on the sphere, using the HEALPix tessellation scheme. Specifically, We have developed a pixel-based approach to implement convolutional layers on the spherical surface, similarly to what is commonly done for CNNs in Euclidian space. The algorithm is fully integrable with existing libraries for NNs (e.g., PyTorch or TensorFlow). We present two applications: (i) recognition of handwritten digits projected on the sphere; (ii) estimation of cosmological parameter from Cosmic Microwave Background (CMB) simulated maps. We have built a simple NN architecture, consisting in four convolutional+pooling layers, and have used it for all the applications explored herein. For what concerns the handwritten digits, our CNN reaches an accuracy of about 95%, comparable with other existing spherical CNNs. For CMB applications, we have tested the CNN on the estimation of a "mock" parameter, defining the angular scale at which the power spectrum of a Gaussian field projected on the sphere peaks. We have estimated this parameter directly from maps, in several cases: temperature and polarization, presence of noise and partial sky coverage. In all the cases, the NN performances are comparable with those from standard spectrum-based bayesian methods. We demonstrate, for the first time, the capability of CNNs to extract information from polarization fields and to distinguish between E and B-modes. Lastly, we have applied our CNN to the estimation of the Thomson scattering optical depth at reionization (tau) from simulated CMB maps. Even without any specific optimization of the NN architecture, we reach an accuracy comparable with standard bayesian methods. This work represents a first step towards the exploitation of NNs in CMB parameter estimation and demonstrates the feasibility of our approach.
The analysis of spatial observations on a sphere is important in areas such as geosciences, physics and embryo research, just to name a few. The purpose of the package rcosmo is to conduct efficient information processing, visualisation, manipulation and spatial statistical analysis of Cosmic Microwave Background (CMB) radiation and other spherical data. The package was developed for spherical data stored in the Hierarchical Equal Area isoLatitude Pixelation (Healpix) representation. rcosmo has more than 100 different functions. Most of them initially were developed for CMB, but also can be us…
Scientific exploitation of the ever increasing volumes of astronomical data requires efficient and practical methods for data access, visualisation, and analysis. Hierarchical sky tessellation techniques enable a multi-resolution approach to organising data on angular scales from the full sky down to the individual image pixels. Aims. We aim to show that the Hierarchical progressive survey (HiPS) scheme for describing astronomical images, source catalogues, and three-dimensional data cubes is a practical solution to managing large volumes of heterogeneous data and that it enables a new level o…
Swiss Data Science Center (SDSC)（瑞士数据科学中心）；EPFL（洛桑联邦理工学院）；ETH Zurich（苏黎世联邦理工学院）
Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those supporting images, audio, or video. Because of their success, CNN-based methods are becoming increasingly popular in Cosmology. Cosmological data often comes as spherical maps, which make the use of the traditional CNNs more complicated. The commonly used pixelization scheme for spherical maps is the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix). We pr…
We describe a hybrid Fourier/direct space convolution algorithm for compact radial (azimuthally symmetric) kernels on the sphere. For high resolution maps covering a large fraction of the sky, our implementation takes advantage of the inexpensive massive parallelism afforded by consumer graphics processing units (GPUs). Applications involve modeling of instrumental beam shapes in terms of compact kernels, computation of fine-scale wavelet transformations, and optimal filtering for the detection of point sources. Our algorithm works for any pixelization where pixels are grouped into isolatitude…
Recently, Minkowski Tensors (MT) have gained popularity for morphological analysis tasks. As opposed to the scalar Minkowski functionals (MF; in 2D given by area, perimeter and Euler characteristic), MT can characterize symmetry and orientation of a body. This has been used for a variety of tasks, e.g. to detect interstellar bubbles by tracing back the origins of filaments in HII-regions, or to search for alignment of structures in the CMB. I present a marching-square-based method for calculating MT and MF on the sphere for maps in the Healpix format. MT are calculated for a local neighborhood…
Deep Learning for CMB Foreground Removal and Beam Deconvolution: A U-Net GAN Approach
School of Physical Sciences, Indian Institute of Technology Mandi（印度技术学院曼迪分校物理科学学院）；Department of Physics, Indian Institute of Technology Delhi（印度技术学院德里分校物理系）；Oridigm Inc.（Oridigm公司）
Probing CMB Polarization Gaussianity with the Statistics of Unpolarized Points: Non-Gaussianity of Planck Data and Prospects for Future B-Mode Measurements
The maximum likelihood estimator for CMB map-making is optimal and unbiased as long as the data model is correct, but in practice it rarely is, with model errors including sub-pixel structure and instrumental problems like time-variable gain and pointing errors. In the presence of such errors, the solution is biased, with the local error in each pixel leaking outwards along the scanning pattern by a noise correlation length. The most important sources of such leakage are strong point sources, and for common scanning patterns the leakage manifests as an X around each such source. I discuss why …
We study the problem of EB-leakage that is associated with incomplete polarized CMB sky. In the blind case that assumes no additional information about the statistical properties and amplitudes of the signal from the missing sky region, we prove that the recycling method (Liu et al.~2018) gives the unique best estimate of the EB-leakage. Compared to the previous method, this method reduces the uncertainties in the BB power spectrum due to EB-leakage by more than one order of magnitude in the most interesting domain of multipoles, where $\ell$ is between $80$ and $200$. This work also provides …
With a single training image and using wavelet phase harmonic augmentation, we present polarized Cosmic Microwave Background (CMB) foreground marginalization in a high-dimensional likelihood-free (Bayesian) framework. We demonstrate robust foreground removal using only a single frequency of simulated data for a BICEP-like sky patch. Using Moment Networks we estimate the pixel-level posterior probability for the underlying {E,B} signal and validate the statistical model with a quantile-type test using the estimated marginal posterior moments. The Moment Networks use a hierarchy of U-Net convolu…
A great deal of experimental effort is currently being devoted to the precise measurements of the cosmic microwave background (CMB) sky in temperature and polarisation. Satellites, balloon-borne, and ground-based experiments scrutinize the CMB sky at multiple scales, and therefore enable to investigate not only the evolution of the early Universe, but also its late-time physics with unprecedented accuracy. The pipeline leading from time ordered data as collected by the instrument to the final product is highly structured. Moreover, it has also to provide accurate estimates of statistical and s…
Jet Propulsion Laboratory, California Institute of Technology（加州理工学院喷气推进实验室）；Scientific Computing and Imaging Institute, University of Utah（犹他大学科学计算与影像研究所）
The cosmic microwave background (CMB) is a significant source of knowledge about the origin and evolution of our universe. However, observations of the CMB are contaminated by foreground emissions, obscuring the CMB signal and reducing its efficacy in constraining cosmological parameters. We employ deep learning as a data-driven approach to CMB cleaning from multi-frequency full-sky maps. In particular, we develop a graph-based Bayesian convolutional neural network based on the U-Net architecture that predicts cleaned CMB with pixel-wise uncertainty estimates. We demonstrate the potential of t…
