All the analyses of Cosmic Microwave Background (CMB) temperature maps up–to–date show that CMB anisotropies follow a Gaussian distribution. On the other hand, astrophysical foregrounds which hamper the detection of the CMB angular power spectrum, are not Gaussian distributed on the sky. Therefore, they should give a sizeable contribution to the CMB bispectrum. In fact, the first year data of t...

We study the spherically averaged bispectrum of 21-cm signal from Epoch Reionization (EoR). This metric provides a quantitative measurement level non-Gaussianity which is expected to be high. focus on impact light-cone effect and its detectability with future SKA-Low telescope. Our investigation based single reionization model an ensemble 50 realisations estimate cosmic variance errors. calcula...

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters τNL and gNL. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that τNL is always positive and roughly equals to ( 6 5 fNL) 2 for the low scale inflation, but gNL can be negative or positive and its order ...

When we have observations of a discrete deterministic signal (physical object) in colored Gaussian noise, it is possible to obtain asymptotically unbiased estimates of the bispectrum of the signal only at frequency pairs (al, w2) which do not satisfy any of the following: wI = 0, w 2 = 0, and o1 + w2 = 0. Several approaches reported in the literature that deal with magnitude reconstruction from...

We derive a fast way for measuring primordial non-Gaussianity in a nearly full-sky map of the cosmic microwave background. We find a cubic combination of sky maps combining bispectrum configurations to capture a quadratic term in primordial fluctuations. Our method takes only N3/2 operations rather than N5/2 of the bispectrum analysis (1000 times faster for l = 512), retaining the same sensitiv...

Whenever we have a group acting on a class of functions by translation, the bispectrum offers a principled and lossless way of representing such functions invariant to the action. Unfortunately, computing the bispectrum is often costly and complicated. In this paper we propose a unitarily equivalent, but easier to compute set of invariants, which we call the skew spectrum. For functions on homo...

In this paper we propose two algorithms for the restoration of images based on the bispectrum. The bispectrum of a signal is the Fourier transform of its triple correlation. While second-order statistics (e.g., correlation function, power spectrum, etc.) do not provide any information about the phase of the signal, third-order statistics (e.g., triple correlation, bispectrum, etc.) allow the re...

Most biological signals are non-Gaussian, reflecting their origins in highly nonlinear physiological systems. A versatile set of techniques for studying non-Gaussian signals relies on the spectral representations of higher moments, known as polyspectra, which describe forms of cross-frequency dependence that do not arise in time-invariant Gaussian signals. The most commonly used of these employ...