Emanuele Salerno

Component separation methods for the PLANCK mission

Context. The PLANCK satellite will map the full sky at nine frequencies from 30 to 857 GHz. The CMB intensity and polarization that are its prime targets are contaminated by foreground emission. Aims. The goal of this paper is to compare proposed methods for separating CMB from foregrounds based on their different spectral and spatial characteristics, and to separate the foregrounds into “components” with different physical origins (Galactic synchrotron, free-free and dust emissions; extra-galactic and far-IR point sources; Sunyaev-Zeldovich effect, etc.) Methods. A component separation challenge has been organised, based on a set of realistically complex simulations of sky emission. Several methods including those based on internal template subtraction, maximum entropy method, parametric method, spatial and harmonic cross correlation methods, and independent component analysis have been tested. Results. Different methods proved to be effective in cleaning the CMB maps of foreground contamination, in reconstructing maps of diffuse Galactic emissions, and in detecting point sources and thermal Sunyaev-Zeldovich signals. The power spectrum of the residuals is, on the largest scales, four orders of magnitude lower than the input Galaxy power spectrum at the foreground minimum. The CMB power spectrum was accurately recovered up to the sixth acoustic peak. The point source detection limit reaches 100 mJy, and about 2300 clusters are detected via the thermal SZ effect on two thirds of the sky. We have found that no single method performs best for all scientific objectives. Conclusions. We foresee that the final component separation pipeline for PLANCK will involve a combination of methods and iterations between processing steps targeted at different objectives such as diffuse component separation, spectral estimation, and compact source extraction.

All-sky astrophysical component separation with Fast Independent Component Analysis (FASTICA)

We present a new, fast, algorithm for the separation of astrophysical components superposed in maps of the sky. The algorithm, based on the Independent Component Analysis (ICA) technique, is aimed at recovering 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, without any a priori assumption on properties of the components to be separated, except that all of them, but at most one, must have non-Gaussian distributions. The analysis starts from very simple toy-models of the sky emission in order to assess the quality of the reconstruction when inputs are well known and controlled. In particular we study the dependence of the results of separation conducted on and off the Galactic plane independently, showing that optimal separation is achieved for sky regions where components are smoothly distributed. Then we move to more realistic applications on simulated observations of the microwave sky with angular resolution and instrumental noise at the mean nominal levels for the Planck satellite. We consider several Planck observation channels 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 lmax ≃ 2000. Frequency scalings and normalization have been recovered with better than 1% precision for all the components at frequencies and in sky regions where their signalto-noise ratio > ∼ 1.5; the error increases at ∼ 10% level for signal-to-noise ratios ≃ 1.

Fast correction of bleed-through distortion in grayscale documents by a blind source separation technique

Ancient documents are usually degraded by the presence of strong background artifacts. These are often caused by the so-called bleed-through effect, a pattern that interferes with the main text due to seeping of ink from the reverse side. A similar effect, called show-through and due to the nonperfect opacity of the paper, may appear in scans of even modern, well-preserved documents. These degradations must be removed to improve human or automatic readability. For this purpose, when a color scan of the document is available, we have shown that a simplified linear pattern overlapping model allows us to use very fast blind source separation techniques. This approach, however, cannot be applied to grayscale scans. This is a serious limitation, since many collections in our libraries and archives are now only available as grayscale scans or microfilms. We propose here a new model for bleed-through in grayscale document images, based on the availability of the recto and verso pages, and show that blind source separation can be successfully applied in this case too. Some experiments with real-ancient documents arepresented and described.

An acoustic pyrometer system for tomographic thermal imaging in power plant boilers

The paper presents an acoustic pyrometry method for the reconstruction of temperature maps inside power plant boilers. It is based on measuring times-of-flight of acoustic waves along a number of straight paths in a cross-section of the boiler; via an integral relationship, these times depend on the temperature of the gaseous medium along the paths. On this basis, 2D temperature maps can be reconstructed using suitable inversion techniques. The structure of a particular system for the measurement of the times-of-flight is described, and two classes of reconstruction algorithms are presented. The algorithms proposed have been applied to both simulated and experimental data measured in power plants of the Italian National Electricity Board (ENEL). The results obtained appear fairly satisfactory, considering the small data sets that it was possible to acquire in the tested boilers.

Independent component analysis for document restoration

Abstract.We propose a novel approach to restoring digital document images, with the aim of improving text legibility and OCR performance. These are often compromised by the presence of artifacts in the background, derived from many kinds of degradations, such as spots, underwritings, and show-through or bleed-through effects. So far, background removal techniques have been based on local, adaptive filters and morphological-structural operators to cope with frequent low-contrast situations. For the specific problem of bleed-through/show-through, most work has been based on the comparison between the front and back pages. This, however, requires a preliminary registration of the two images. Our approach is based on viewing the problem as one of separating overlapped texts and then reformulating it as a blind source separation problem, approached through independent component analysis techniques. These methods have the advantage that no models are required for the background. In addition, we use the spectral components of the image at different bands, so that there is no need for registration. Examples of bleed-through cancellation and recovery of underwriting from palimpsests are provided.

A Markov model for blind image separation by a mean-field EM algorithm

This paper deals with blind separation of images from noisy linear mixtures with unknown coefficients, formulated as a Bayesian estimation problem. This is a flexible framework, where any kind of prior knowledge about the source images and the mixing matrix can be accounted for. In particular, we describe local correlation within the individual images through the use of Markov random field (MRF) image models. These are naturally suited to express the joint pdf of the sources in a factorized form, so that the statistical independence requirements of most independent component analysis approaches to blind source separation are retained. Our model also includes edge variables to preserve intensity discontinuities. MRF models have been proved to be very efficient in many visual reconstruction problems, such as blind image restoration, and allow separation and edge detection to be performed simultaneously. We propose an expectation-maximization algorithm with the mean field approximation to derive a procedure for estimating the mixing matrix, the sources, and their edge maps. We tested this procedure on both synthetic and real images, in the fully blind case (i.e., no prior information on mixing is exploited) and found that a source model accounting for local autocorrelation is able to increase robustness against noise, even space variant. Furthermore, when the model closely fits the source characteristics, independence is no longer a strict requirement, and cross-correlated sources can be separated, as well.

Separation of correlated astrophysical sources using multiple-lag data covariance matrices

This paper proposes a new strategy to separate astrophysical sources that are mutually correlated. This strategy is based on second-order statistics and exploits prior information about the possible structure of the mixing matrix. Unlike ICA blind separation approaches, where the sources are assumed mutually independent and no prior knowledge is assumed about the mixing matrix, our strategy allows the independence assumption to be relaxed and performs the separation of even significantly correlated sources. Besides the mixing matrix, our strategy is also capable to evaluate the source covariance functions at several lags. Moreover, once the mixing parameters have been identified, a simple deconvolution can be used to estimate the probability density functions of the source processes. To benchmark our algorithm, we used a database that simulates the one expected from the instruments that will operate onboard ESAs Planck Surveyor Satellite to measure the CMB anisotropies all over the celestial sphere.

Estimating the spectral indices of correlated astrophysical foregrounds by a second‐order statistical approach

We present the first tests of a new method, the correlated component analysis (CCA) based on second-order statistics, to estimate the mixing matrix, a key ingredient to separate astrophysical foregrounds superimposed to the Cosmic Microwave Background (CMB). In the present application, the mixing matrix is parametrized in terms of the spectral indices of Galactic synchrotron and thermal dust emissions, while the free-free spectral index is prescribed by basic physics, and is thus assumed to be known. We consider simulated observations of the microwave sky with angular resolution and white stationary noise at the nominal levels for the Planck satellite, and realistic foreground emissions, with a position-dependent synchrotron spectral index. We work with two sets of Planck frequency channels: the low-frequency set, from 30 to 143 GHz, complemented with the Haslam 408 MHz map, and the high-frequency set, from 217 to 545 GHz. The concentration of intense free-free emission on the Galactic plane introduces a steep dependence of the spectral index of the global Galactic emission with Galactic latitude, close to the Galactic equator. This feature makes difficult for the CCA to recover the synchrotron spectral index in this region, given the limited angular resolution of Planck, especially at low frequencies. A cut of a narrow strip around the Galactic equator (|b| < 3°), however, allows us to overcome this problem. We show that, once this strip is removed, the CCA allows an effective foreground subtraction, with residual uncertainties inducing a minor contribution to errors on the recovered CMB power spectrum.

Blind spectral unmixing by local maximization of non-Gaussianity

We approach the estimation of material percentages per pixel (endmember fractional abundances) in hyperspectral remote-sensed images as a blind source separation problem. This task is commonly known as spectral unmixing. Classical techniques require the knowledge of the existing materials and their spectra, which is an unrealistic situation in most cases. In contrast to recently presented blind techniques based on independent component analysis, we implement here a dependent component analysis strategy, namely the MaxNG (maximum non-Gaussianity) algorithm, which is capable to separate even strongly dependent signals. We prove that, when the abundances verify a separability condition, they can be extracted by searching the local maxima of non-Gaussianity. We also provide enough theoretical as well as experimental facts that indicate that this condition holds true for endmember abundances. In addition, we discuss the implementation of MaxNG in a noisy scenario, we introduce a new technique for the removal of scale ambiguities of estimated sources, and a new fast algorithm for the calculation of a Parzen windows-based NG measure. We compare MaxNG to commonly used independent component analysis algorithms, such as FastICA and JADE. We analyze the efficiency of MaxNG in terms of the number of sensor channels, the number of available samples and other factors, by testing it on synthetically generated as well as real data. Finally, we present some examples of application of our technique to real images captured by the MIVIS airborne imaging spectrometer. Our results show that MaxNG is a good tool for spectral unmixing in a blind scenario.

Source separation in astrophysical maps using independent factor analysis

A microwave sky map results from a combination of signals from various astrophysical sources, such as cosmic microwave background radiation, synchrotron radiation and galactic dust radiation. To derive information about these sources, one needs to separate them from the measured maps on different frequency channels. Our insufficient knowledge of the weights to be given to the individual signals at different frequencies makes this a difficult task. Recent work on the problem led to only limited success due to ignoring the noise and to the lack of a suitable statistical model for the sources. In this paper, we derive the statistical distribution of some source realizations, and check the appropriateness of a Gaussian mixture model for them. A source separation technique, namely, independent factor analysis, has been suggested recently in the literature for Gaussian mixture sources in the presence of noise. This technique employs a three layered neural network architecture which allows a simple, hierarchical treatment of the problem. We modify the algorithm proposed in the literature to accommodate for space-varying noise and test its performance on simulated astrophysical maps. We also compare the performances of an expectation-maximization and a simulated annealing learning algorithm in estimating the mixture matrix and the source model parameters. The problem with expectation-maximization is that it does not ensure global optimization, and thus the choice of the starting point is a critical task. Indeed, we did not succeed to reach good solutions for random initializations of the algorithm. Conversely, our experiments with simulated annealing yielded initialization-independent results. The mixing matrix and the means and coefficients in the source model were estimated with a good accuracy while some of the variances of the components in the mixture model were not estimated satisfactorily.