Fast Poisson Noise Removal by Biorthogonal Haar Domain Hypothesis Testing

Methods based on hypothesis tests (HTs) in the Haar domain are widely used to denoise Poisson count data. Facing large datasets or real-time applications, Haar-based denoisers have to use the decimated transform to meet limited-memory or computation-time constraints. Unfortunately, for regular underlying intensities, decimation yields discontinuous estimates and strong "staircase" artifacts. In this paper, we propose to combine the HT framework with the decimated biorthogonal Haar (Bi-Haar) transform instead of the classical Haar. The Bi-Haar filter bank is normalized such that the p-values of Bi-Haar coefficients (pBH) provide good approximation to those of Haar (pH) for high-intensity settings or large scales; for low-intensity settings and small scales, we show that pBH are essentially upper-bounded by pH. Thus, we may apply the Haar-based HTs to Bi-Haar coefficients to control a prefixed false positive rate. By doing so, we benefit from the regular Bi-Haar filter bank to gain a smooth estimate while always maintaining a low computational complexity. A Fisher-approximation-based threshold imple- menting the HTs is also established. The efficiency of this method is illustrated on an example of hyperspectral-source-flux estimation

Inverse Compton scattering on solar photons, heliospheric modulation, and neutrino astrophysics

We study the inverse Compton scattering of solar photons by Galactic cosmic-ray electrons. We show that the gamma-ray emission from this process is substantial with the maximum flux in the direction of the Sun; the angular distribution of the emission is broad. This previously-neglected foreground should be taken into account in studies of the diffuse Galactic and extragalactic gamma-ray emission. Furthermore, observations by GLAST can be used to monitor the heliosphere and determine the electron spectrum as a function of position from distances as large as Saturn's orbit to close proximity of the Sun, thus enabling unique studies of solar modulation. This paves the way for the determination of other Galactic cosmic-ray species, primarily protons, near the solar surface which will lead to accurate predictions of gamma rays from pp-interactions in the solar atmosphere. These albedo gamma rays will be observable by GLAST, allowing the study of deep atmospheric layers, magnetic field(s), and cosmic-ray cascade development. The latter is necessary to calculate the neutrino flux from pp-interactions at higher energies (>1 TeV). Although this flux is small, it is a "guaranteed flux" in contrast to other astrophysical sources of neutrinos, and may be detectable by km^3 neutrino telescopes of the near future, such as IceCube. Since the solar core is opaque for very high-energy neutrinos, directly studying the mass distribution of the solar core may thus be possible.Comment: 4 pages, 4 figures, emulateapj.cls, final version; published in ApJ Letters, added an erratum; conclusions unchange

Developing the Galactic diffuse emission model for the GLAST Large Area Telescope

Diffuse emission is produced in energetic cosmic ray (CR) interactions, mainly protons and electrons, with the interstellar gas and radiation field and contains the information about particle spectra in distant regions of the Galaxy. It may also contain information about exotic processes such as dark matter annihilation, black hole evaporation etc. A model of the diffuse emission is important for determination of the source positions and spectra. Calculation of the Galactic diffuse continuum gamma-ray emission requires a model for CR propagation as the first step. Such a model is based on theory of particle transport in the interstellar medium as well as on many kinds of data provided by different experiments in Astrophysics and Particle and Nuclear Physics. Such data include: secondary particle and isotopic production cross sections, total interaction nuclear cross sections and lifetimes of radioactive species, gas mass calibrations and gas distribution in the Galaxy (H_2, H I, H II), interstellar radiation field, CR source distribution and particle spectra at the sources, magnetic field, energy losses, gamma-ray and synchrotron production mechanisms, and many other issues. We are continuously improving the GALPROP model and the code to keep up with a flow of new data. Improvement in any field may affect the Galactic diffuse continuum gamma-ray emission model used as a background model by the GLAST LAT instrument. Here we report about the latest improvements of the GALPROP and the diffuse emission model.Comment: 2 pages, 2 figures; to appear in the Proc. of the First Int. GLAST Symp. (Stanford, Feb. 5-8, 2007), eds. S.Ritz, P.F.Michelson, and C.Meegan, AIP Conf. Pro

Poisson noise removal in multivariate count data

International audienceThe Multi-scale Variance Stabilization Transform (MSVST) has recently been proposed for 2D Poisson data denoising.1 In this work, we present an extension of the MSVST with the wavelet transform to multivariate data-each pixel is vector-valued-, where the vector field dimension may be the wavelength, the energy, or the time. Such data can be viewed naively as 3D data where the third dimension may be time, wavelength or energy (e.g. hyperspectral imaging). But this naive analysis using a 3D MSVST would be awkward as the data dimensions have different physical meanings. A more appropriate approach would be to use a wavelet transform, where the time or energy scale is not connected to the spatial scale. We show that our multivalued extension of MSVST can be used advantageously for approximately Gaussianizing and stabilizing the variance of a sequence of independent Poisson random vectors. This approach is shown to be fast and very well adapted to extremely low-count situations. We use a hypothesis testing framework in the wavelet domain to denoise the Gaussianized and stabilized coefficients, and then apply an iterative reconstruction algorithm to recover the estimated vector field of intensities underlying the Poisson data. Our approach is illustrated for the detection and characterization of astrophysical sources of high-energy gamma rays, using realistic simulated observations. We show that the multivariate MSVST permits efficient estimation across the time/energy dimension and immediate recovery of spectral properties