**Publications**(41)

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We apply our method to a dataset of Euclid-like simulated PSFs (Point Spread Function). ESA's Euclid mission will cover a large area of the sky in order to accurately measure the shape of billions of galaxies. PSF estimation and correction is one of the main sources of systematic errors on those galaxy shape measurements. PSF variations across the field of view and with the incoming light's wavelength can be highly non-linear, while still retaining strong geometrical information, making the use of Optimal Transport distances an attractive prospect. We show that our representation does indeed succeed at capturing the PSF's variations.

^{1}we present a concept of a deployable annular telescope, named TALC for Thinned Aperture Light Collector, reaching 20m in diameter. Being annular, this telescope features a main beam width equivalent to that of a 27m telescope, i.e. an angular resolution of 0.92" at 100 μm. In this paper we focus on the science case of such a telescope as well on the aspects of unconventional data processing that come with this unconventional optical configuration. The principal science cases of TALC revolve around its imaging capacities, that allow resolving the Kuiper belt in extra-solar planetary systems, or the filamentary scale in star forming clouds all the way to the Galactic Center, or the Narrow Line Region in Active Galactic Nuclei of the Local Group, or breaking the confusion limit to resolve the Cosmic Infrared Background. Equipping this telescope with detectors capable of imaging polarimetry offers as well the extremely interesting perspective to study the influence of the magnetic field in structuring the interstellar medium. We will then present simulations of the optical performance of such a telescope. The main feature of an annular telescope is the small amount of energy contained in the main beam, around 30% for the studied configuration, and the presence of bright diffraction rings. Using simulated point spread functions for realistic broad-band filters, we study the observing performance of TALC in typical situations, i.e a field of point sources, and fields with emission power at every physical scales, taken to represent an extragalactic deep field observation and an interstellar medium observation. We investigate different inversion techniques to try and recover the information present in the input field. We show that techniques combining a forward modeling of the observation process and a reconstruction algorithm exploiting the concept of sparsity (i.e. related to the more general field of compressed sensing) represent a promising avenue to reach the angular resolution promised by the main beam of TALC.

^{2}minimization modeling the background as a low order polynomial on WMAP realistic simulations. If in noisy situations estimating more than a few parameter does not improve flux recovery, in the first WMAP channels the proposed method leads to lower biases (typically by factors of 2) and increased robustness.

^{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.

Multiscale analysis methods, including wavelet transforms, used for image enhancement, faint feature recognition, image content characterization and fusion are presented in this material. Embedded applications in object detection, image database operations, image and signal compression and transmission, and process control are also discussed. This course explains how image and signal processing methods are used in science operations, product development and visual inspection.

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