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Register a new userAn application of the Independent Component Analysis methodology to gamma ray astrophysical imaging
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Independent Component Analysis (ICA) is a statistical method often used to decompose a complex dataset in its independent sub-parts. It is a powerful technique to solve a typical Blind Source Separation problem. A fast calculation of the gamma ray sky observed by GLAST, assuming the expected instrumental response, has been implemented. The simulated images were used to test the capability of the ICA method in identifying the sources.
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We apply the independent component analysis (ICA) to the real data from a gravitational wave detector for the first time. Specifically we use the iKAGRA data taken in April 2016, and calculate the correlations between the gravitational wave strain channel and 35 physical environmental channels. Using a couple of seismic channels which are found to be strongly correlated with the strain, we perform ICA. Injecting a sinusoidal continuous signal in the strain channel, we find that ICA recovers correct parameters with enhanced signal-to-noise ratio, which demonstrates usefulness of this method. Among the two implementations of ICA used here, we find the correlation method yields the optimal result for the case environmental noises act on the strain channel linearly.
We present a new, fast, algorithm for the separation of astrophysical components superposed in maps of the sky, based on the fast Independent Component Analysis technique (FastICA). It allows to recover both the spatial pattern and the frequency scalings of the emissions from statistically independent astrophysical processes, present along the line-of-sight, from multi-frequency observations. We apply FastICA to simulated observations of the microwave sky with angular resolution and instrumental noise at the mean nominal levels for the Planck satellite, containing the most important known diffuse signals: the Cosmic Microwave Background (CMB), Galactic synchrotron, dust and free-free emissions. A method for calibrating the reconstructed maps of each component at each frequency has been devised. The spatial pattern of all the components have been recovered on all scales probed by the instrument. In particular, the CMB angular power spectra is recovered at the percent level up to $ell_{max}simeq 2000$. Frequency scalings and normalization have been recovered with better than percent precision for all the components at frequencies and in sky regions where their signal-to-noise ratio exceeds 1.5; the error increases at ten percent level for signal-to-noise ratios about 1. Runs have been performed on a Pentium III 600 MHz computer; FastICA typically took a time of the order of 10 minutes for all-sky simulations with 3.5 arcminutes pixel size. We conclude that FastICA is an extremly promising technique for analyzing the maps that will be obtained by the forthcoming high resolution CMB experiments.
There are several cutting edge applications needing PCA methods for data on tori and we propose a novel torus-PCA method with important properties that can be generally applied. There are two existing general methods: tangent space PCA and geodesic PCA. However, unlike tangent space PCA, our torus-PCA honors the cyclic topology of the data space whereas, unlike geodesic PCA, our torus-PCA produces a variety of non-winding, non-dense descriptors. This is achieved by deforming tori into spheres and then using a variant of the recently developed principle nested spheres analysis. This PCA analysis involves a step of small sphere fitting and we provide an improved test to avoid overfitting. However, deforming tori into spheres creates singularities. We introduce a data-adaptive pre-clustering technique to keep the singularities away from the data. For the frequently encountered case that the residual variance around the PCA main component is small, we use a post-mode hunting technique for more fine-grained clustering. Thus in general, there are three successive interrelated key steps of torus-PCA in practice: pre-clustering, deformation, and post-mode hunting. We illustrate our method with two recently studied RNA structure (tori) data sets: one is a small RNA data set which is established as the benchmark for PCA and we validate our method through this data. Another is a large RNA data set (containing the small RNA data set) for which we show that our method provides interpretable principal components as well as giving further insight into its structure.
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a straightforward estimate based on the efficient score function by using B-spline approximations. The estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ICA methods in a variety of simulations.
This paper offers a new point of view on component separation, based on a model of additive components which enjoys a much greater flexibility than more traditional linear component models. This flexibility is needed to process the complex full-sky observations of the CMB expected from the Planck space mission, for which it was developed, but it may also be useful in any context where accurate component separation is needed.
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