Multichannel Poisson denoising and deconvolution on the sphere: application to the Fermi Gamma-ray Space Telescope

  title={Multichannel Poisson denoising and deconvolution on the sphere: application to the Fermi Gamma-ray Space Telescope},
  author={Jeremy Schmitt and Jean-Luc Starck and Jean Marc Casandjian and Jalal M. Fadili and Isabelle A. Grenier},
  journal={Astronomy and Astrophysics},
A multiscale representation-based denoising method for spherical data contaminated with Poisson noise, the multiscale variance stabilizing transform on the sphere (MS-VSTS), has been recently proposed. This paper first extends this MS-VSTS to spherical 2D-1D, where the two first dimensions are longitude and latitude, and the third dimension is a meaningful physical index such as energy or time. Then we introduce a novel multichannel deconvolution built upon the 2D-1D MS-VSTS, which allows to… 
The denoised, deconvolved, and decomposed Fermi γ-ray sky - An application of the D3PO algorithm
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Denoising, deconvolving, and decomposing photon observations - Derivation of the D3PO algorithm
The D 3 PO algorithm addresses the inference problem of denoising, deconvolving, and decomposing photon observations and successfully denoised, deconvolved, and decomposed the data into a diuse and a point-like signal estimate for the respective photon flux components.
Deconvolution of poissonian images with the PURE-LET approach
Simulation experiments indicate that the proposed non-iterative image deconvolution algorithm outperforms current state-of-the-art techniques, in terms of both restoration quality and computational time.
Wavelet-Based Segmentation on the Sphere
Distinguishing Dark Matter from Unresolved Point Sources in the Inner Galaxy with Photon Statistics
Data from the Fermi Large Area Telescope suggests that there is an extended excess of GeV gamma-ray photons in the Inner Galaxy. Identifying potential astrophysical sources that contribute to this
Minimal spanning tree algorithm for γ-ray source detection in sparse photon images: cluster parameters and selection strategies
The results show that $\sqrt{M}$ is strongly correlated with other statistical significance parameters, derived from a wavelet based algorithm and maximum likelihood (ML) analysis, and that it can be used as a good estimator of statistical significance of MST detections.
3D sparse representations on the sphere and applications in astronomy
We present several 3D sparse decompositions based on wavelets on the sphere that are useful for different kind of data set such as regular 3D spherical measurements (r,θ, φ) and multichannel
Nonparametric noise estimation method for raw images.
An extensive cross-validation procedure is described to compare this new method with state-of-the-art parametric methods and with laboratory calibration methods giving a reliable ground truth, even for nonlinear detectors.
Second-Generation Curvelets on the Sphere
This work presents a new second-generation curvelet transform, where scale-discretized curvelets are constructed directly on the sphere, and presents an illustrative application demonstrating the effectiveness of curvelets for representing directional curve-like features in natural spherical images.
Mean curvature regularization-based Poisson image restoration
Experimental results show that the proposed approach to mean curvature-based regularization to address the Poisson noise image restoration problem can produce higher quality results and more natural images compared to some state of theart variational algorithms recently developed.


Poisson denoising on the sphere: application to the Fermi gamma ray space telescope
The Large Area Telescope (LAT), the main instrument of the Fermi gamma-ray Space telescope, detects high energy gamma rays with energies from 20 MeV to more than 300 GeV. The two main scientific
Source detection using a 3D sparse representation: application to the Fermi gamma-ray space telescope
The multiscale variance stabilization Transform (MSVST) has recently been proposed for Poisson data denoising. This procedure, which is nonparametric, is based on thresholding wavelet coefficients.
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal
A variance stabilizing transform (VST) is applied on a filtered discrete Poisson process, yielding a near Gaussian process with asymptotic constant variance, leading to multiscale VSTs (MS-VSTs) and nonlinear decomposition schemes.
HEALPix: A Framework for High-Resolution Discretization and Fast Analysis of Data Distributed on the Sphere
This paper considers the requirements and implementation constraints on a framework that simultaneously enables an efficient discretization with associated hierarchical indexation and fast analysis/synthesis of functions defined on the sphere and demonstrates how these are explicitly satisfied by HEALPix.
The Large Area Telescope on the Fermi Gamma-ray Space Telescope Mission
(Abridged) The Large Area Telescope (Fermi/LAT, hereafter LAT), the primary instrument on the Fermi Gamma-ray Space Telescope (Fermi) mission, is an imaging, wide field-of-view, high-energy gamma-ray
We present a catalog of high-energy gamma-ray sources detected by the Large Area Telescope (LAT), the primary science instrument on the Fermi Gamma-ray Space Telescope (Fermi), during the first 11
Threshold for Extended Emission in Short Gamma-ray Bursts
The initial pulse complex (IPC) in short gamma-ray bursts is sometimes accompanied by a softer, low-intensity extended emission (EE) component. In cases where such a component is not observed, it is
Wavelets, ridgelets and curvelets on the sphere
It is shown how these transforms can be used in denoising and especially in a Combined Filtering Method, which uses both the wavelet and the curvelet transforms, thus benefiting from the advantages of both transforms.
For most large underdetermined systems of linear equations the minimal 𝓁1‐norm solution is also the sparsest solution
The techniques include the use of random proportional embeddings and almost‐spherical sections in Banach space theory, and deviation bounds for the eigenvalues of random Wishart matrices.
Advances in Machine Learning and Data Mining for Astronomy
This book explores how advances in machine learning and data mining can solve current and future problems in astronomy and looks at how they could lead to the creation of entirely new algorithms within the data mining community.