Overlearning in marginal distribution-based ICA: analysis and solutions

The present paper is written as a word of caution, with users of independent component analysis (ICA) in mind, to overlearning phenomena that are often observed.\\ We consider two types of overlearning, typical to high-order statistics based ICA. These algorithms can be seen to maximise the negentropy of the source estimates. The first kind of overlearning results in the generation of spike-like signals, if there are not enough samples in the data or there is a considerable amount of noise present. It is argued that, if the data has power spectrum characterised by $1/f$ curve, we face a more severe problem, which cannot be solved inside the strict ICA model. This overlearning is better characterised by bumps instead of spikes. Both overlearning types are demonstrated in the case of artificial signals as well as magnetoencephalograms (MEG). Several methods are suggested to circumvent both types, either by making the estimation of the ICA model more robust or by including further modelling of the data

Sunyaev-Zel'dovich clusters reconstruction in multiband bolometer camera surveys

We present a new method for the reconstruction of Sunyaev-Zel'dovich (SZ) galaxy clusters in future SZ-survey experiments using multiband bolometer cameras such as Olimpo, APEX, or Planck. Our goal is to optimise SZ-Cluster extraction from our observed noisy maps. We wish to emphasize that none of the algorithms used in the detection chain is tuned on prior knowledge on the SZ -Cluster signal, or other astrophysical sources (Optical Spectrum, Noise Covariance Matrix, or covariance of SZ Cluster wavelet coefficients). First, a blind separation of the different astrophysical components which contribute to the observations is conducted using an Independent Component Analysis (ICA) method. Then, a recent non linear filtering technique in the wavelet domain, based on multiscale entropy and the False Discovery Rate (FDR) method, is used to detect and reconstruct the galaxy clusters. Finally, we use the Source Extractor software to identify the detected clusters. The proposed method was applied on realistic simulations of observations. As for global detection efficiency, this new method is impressive as it provides comparable results to Pierpaoli et al. method being however a blind algorithm. Preprint with full resolution figures is available at the URL: w10-dapnia.saclay.cea.fr/Phocea/Vie_des_labos/Ast/ast_visu.php?id_ast=728Comment: Submitted to A&A. 32 Pages, text onl

Neural networks and separation of Cosmic Microwave Background and astrophysical signals in sky maps

The Independent Component Analysis (ICA) algorithm is implemented as a neural network for separating signals of different origin in astrophysical sky maps. Due to its self-organizing capability, it works without prior assumptions on the signals, neither on their frequency scaling, nor on the signal maps themselves; instead, it learns directly from the input data how to separate the physical components, making use of their statistical independence. To test the capabilities of this approach, we apply the ICA algorithm on sky patches, taken from simulations and observations, at the microwave frequencies, that are going to be deeply explored in a few years on the whole sky, by the Microwave Anisotropy Probe (MAP) and by the {\sc Planck} Surveyor Satellite. The maps are at the frequencies of the Low Frequency Instrument (LFI) aboard the {\sc Planck} satellite (30, 44, 70 and 100 GHz), and contain simulated astrophysical radio sources, Cosmic Microwave Background (CMB) radiation, and Galactic diffuse emissions from thermal dust and synchrotron. We show that the ICA algorithm is able to recover each signal, with precision going from 10% for the Galactic components to percent for CMB; radio sources are almost completely recovered down to a flux limit corresponding to $0.7\sigma_{CMB}$, where $\sigma_{CMB}$ is the rms level of CMB fluctuations. The signal recovering possesses equal quality on all the scales larger then the pixel size. In addition, we show that the frequency scalings of the input signals can be partially inferred from the ICA outputs, at the percent precision for the dominant components, radio sources and CMB.Comment: 15 pages; 6 jpg and 1 ps figures. Final version to be published in MNRA

No-reference Image Denoising Quality Assessment

A wide variety of image denoising methods are available now. However, the performance of a denoising algorithm often depends on individual input noisy images as well as its parameter setting. In this paper, we present a no-reference image denoising quality assessment method that can be used to select for an input noisy image the right denoising algorithm with the optimal parameter setting. This is a challenging task as no ground truth is available. This paper presents a data-driven approach to learn to predict image denoising quality. Our method is based on the observation that while individual existing quality metrics and denoising models alone cannot robustly rank denoising results, they often complement each other. We accordingly design denoising quality features based on these existing metrics and models and then use Random Forests Regression to aggregate them into a more powerful unified metric. Our experiments on images with various types and levels of noise show that our no-reference denoising quality assessment method significantly outperforms the state-of-the-art quality metrics. This paper also provides a method that leverages our quality assessment method to automatically tune the parameter settings of a denoising algorithm for an input noisy image to produce an optimal denoising result.Comment: 17 pages, 41 figures, accepted by Computer Vision Conference (CVC) 201

Bayesian blind component separation for Cosmic Microwave Background observations

We present a technique for the blind separation of components in CMB data. The method uses a spectral EM algorithm which recovers simultaneously component templates, their emission law as a function of wavelength, and noise levels. We test the method on Planck HFI simulated observations featuring 3 astrophysical components.Comment: 15 pages, 5 figures, to appear in the Proceedings of the MAXENT 2001 international worksho