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Register a new userCompressed sensing reconstruction of a string signal from interferometric observations of the cosmic microwave background
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We propose an algorithm for the reconstruction of the signal induced by cosmic strings in the cosmic microwave background (CMB), from radio-interferometric data at arcminute resolution. Radio interferometry provides incomplete and noisy Fourier measurements of the string signal, which exhibits sparse or compressible magnitude of the gradient due to the Kaiser-Stebbins (KS) effect. In this context the versatile framework of compressed sensing naturally applies for solving the corresponding inverse problem. Our algorithm notably takes advantage of a model of the prior statistical distribution of the signal fitted on the basis of realistic simulations. Enhanced performance relative to the standard CLEAN algorithm is demonstrated by simulated observations under noise conditions including primary and secondary CMB anisotropies.
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We investigate the impact of instrumental systematic errors in interferometric measurements of the cosmic microwave background (CMB) temperature and polarization power spectra. We simulate interferometric CMB observations to generate mock visibilities and estimate power spectra using the statistically optimal maximum likelihood technique. We define a quadratic error measure to determine allowable levels of systematic error that do not induce power spectrum errors beyond a given tolerance. As an example, in this study we focus on differential pointing errors. The effects of other systematics can be simulated by this pipeline in a straightforward manner. We find that, in order to accurately recover the underlying B-modes for r=0.01 at 28<l<384, Gaussian-distributed pointing errors must be controlled to 0.7^circ rms for an interferometer with an antenna configuration similar to QUBIC, in agreement with analytical estimates. Only the statistical uncertainty for 28<l<88 would be changed at ~10% level. With the same instrumental configuration, we find the pointing errors would slightly bias the 2-sigma upper limit of the tensor-to-scalar ratio r by ~10%. We also show that the impact of pointing errors on the TB and EB measurements is negligibly small.
Radio interferometers are well suited to studies of both total intensity and polarized intensity fluctuations of the cosmic microwave background radiation, and they have been used successfully in measurements of both the primary and secondary anisotropy. Recent observations with the Cosmic Background Imager operating in the Chilean Andes, the Degree Angular Scale Interferometer operating at the South Pole, and the Very Small Array operating in Tenerife have probed the primary anisotropy over a wide range of angular scales. The advantages of interferometers for microwave background observations of both total intensity and polarized radiation are discussed, and the cosmological results from these three instruments are presented. The results show that, subject to a reasonable value for the Hubble constant, which is degenerate with the geometry in closed models, the geometry of the Universe is flat to high precision (~5%) and the primordial fluctuation spectrum is very close to the scale-invariant Harrison-Zeldovich spectrum. Both of these findings are concordant with inflationary predictions. The results also show that the baryonic matter content is consistent with that found from primordial nucleosynthesis, while the cold dark matter component can account for no more than ~40% of the energy density of the Universe. It is a requirement of these observations, therefore, that ~60% of the energy content of the Universe is not related to matter, either baryonic or nonbaryonic. This dark energy component of the energy density is attributed to a nonzero cosmological constant.
We present results from an end-to-end simulation pipeline interferometric observations of cosmic microwave background polarization. We use both maximum-likelihood and Gibbs sampling techniques to estimate the power spectrum. In addition, we use Gibbs sampling for image reconstruction from interferometric visibilities. The results indicate the level to which various systematic errors (e.g., pointing errors, gain errors, beam shape errors, cross- polarization) must be controlled in order to successfully detect and characterize primordial B modes as well as other scientific goals. In addition, we show that Gibbs sampling is an effective method of image reconstruction for interferometric data in other astrophysical contexts.
Imaging by aperture synthesis from interferometric data is a well-known, but is a strong ill-posed inverse problem. Strong and faint radio sources can be imaged unambiguously using time and frequency integration to gather more Fourier samples of the sky. However, these imagers assumes a steady sky and the complexity of the problem increases when transients radio sources are also present in the data. Hopefully, in the context of transient imaging, the spatial and temporal information are separable which enable extension of an imager fit for a steady sky. We introduce independent spatial and temporal wavelet dictionaries to sparsely represent the transient in both spatial domain and temporal domain. These dictionaries intervenes in a new reconstruction method developed in the Compressed Sensing (CS) framework and using a primal-dual splitting algorithm. According to the preliminary tests in different noise regimes, this new Time-agile (or 2D-1D) method seems to be efficient in detecting and reconstructing the transients temporal dependence.
One way of imaging X-ray emission from solar flares is to measure Fourier components of the spatial X-ray source distribution. We present a new Compressed Sensing-based algorithm named VIS_CS, which reconstructs the spatial distribution from such Fourier components. We demonstrate the application of the algorithm on synthetic and observed solar flare X-ray data from the Reuven Ramaty High Energy Solar Spectroscopic Imager (RHESSI) satellite and compare its performance with existing algorithms. VIS_CS produces competitive results with accurate photometry and morphology, without requiring any algorithm- and X-ray source-specific parameter tuning. Its robustness and performance make this algorithm ideally suited for generation of quicklook images or large image cubes without user intervention, such as for imaging spectroscopy analysis.
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