Sparsity and adaptivity for the blind separation of partially correlated sources

Blind source separation (BSS) is a very popular technique to analyze multichannel data. In this context, the data are modeled as the linear combination of sources to be retrieved. For that purpose, standard BSS methods all rely on some discrimination principle, whether it is statistical independence or morphological diversity, to distinguish between the sources. However, dealing with real-world data reveals that such assumptions are rarely valid in practice: the signals of interest are more likely partially correlated, which generally hampers the performances of standard BSS methods. In this article, we introduce a novel sparsity-enforcing BSS method coined Adaptive Morphological Component Analysis (AMCA), which is designed to retrieve sparse and partially correlated sources. More precisely, it makes profit of an adaptive re-weighting scheme to favor/penalize samples based on their level of correlation. Extensive numerical experiments have been carried out which show that the proposed method is robust to the partial correlation of sources while standard BSS techniques fail. The AMCA algorithm is evaluated in the field of astrophysics for the separation of physical components from microwave data.Comment: submitted to IEEE Transactions on signal processin

Semi-Sparsity for Smoothing Filters

In this paper, we propose an interesting semi-sparsity smoothing algorithm based on a novel sparsity-inducing optimization framework. This method is derived from the multiple observations, that is, semi-sparsity prior knowledge is more universally applicable, especially in areas where sparsity is not fully admitted, such as polynomial-smoothing surfaces. We illustrate that this semi-sparsity can be identified into a generalized $L_0$-norm minimization in higher-order gradient domains, thereby giving rise to a new "feature-aware" filtering method with a powerful simultaneous-fitting ability in both sparse features (singularities and sharpening edges) and non-sparse regions (polynomial-smoothing surfaces). Notice that a direct solver is always unavailable due to the non-convexity and combinatorial nature of $L_0$-norm minimization. Instead, we solve the model based on an efficient half-quadratic splitting minimization with fast Fourier transforms (FFTs) for acceleration. We finally demonstrate its versatility and many benefits to a series of signal/image processing and computer vision applications

Automated Source Extraction for the Next Generation of Neutral Hydrogen Surveys

This thesis is a first step to develop the necessary tools to automatically extract and parameterize sources from future HI surveys with ASKAP, WSRT/Apertif, and SKA. The current approach to large-scale HI surveys, that is, automated source finding followed by manual classification and parametrization, is no longer feasible in light of the data volumes expected for future surveys. We use data from EBHIS to develop and test a completely automated source extraction pipeline for extragalactic HI surveys. We apply a 2D-1D wavelet de-noising technique to HI data and show that it is well adapted to the typical shapes of sources encountered in HI surveys. This technique allows to reliably extract sources even from data containing defects commonly encountered in single-dish HI surveys. Automating the task of false-positive rejection requires reliable parameters for all source candidates generated by the source-finding step. For this purpose, we develop a reliable, automated parametrization pipeline that combines time-tested algorithms with new approaches to baseline estimation, spectral filtering, and mask optimization. The accuracy of the algorithms is tested by performing extensive simulations. By comparison with the uncertainty estimates from HIPASS we show that our automated pipeline gives equal or better accuracy than manual parametrization. We implement the task of source classification using artificial neural networks using the automatically determined parameters of the source candidates as inputs. The viability of this approach is verified on a training data set comprised of parameters measured from simulated sources and false positives extracted from real EBHIS data. Since the number of true positives from real data is small compared to the number of false positives, we explore various methods of training artificial neural networks from imbalanced data sets. We show that the artificial neural networks trained in this way do not achieve sufficient completeness and reliability when applied to the source candidates detected from the extragalactic EBHIS survey. We use the trained artificial neural networks in a semi-supervised manner to compile the first extragalactic EBHIS source catalog. The use of artificial neural networks reduces the number of source candidates that require manual inspection by more than an order of magnitude. We compare the results from EBHIS to HIPASS and show that the number of sources in the compiled catalog is approximately half of the sources expected. The main reason for this detection inefficiency is identified to be mis-classification by the artificial neural networks. This is traced back to the limited training data set, which does not cover the parameter space of real detections sufficiently, and the similarity of true and false positives in the parameter space spanned by the measured parameters. We conclude that, while our automated source finding and parametrization algorithms perform satisfactorily, the classification of sources is the most challenging task for future HI surveys. Classification based on the measured source parameters does not provide sufficient discriminatory power and we propose to explore methods based on machine vision which learns features of real sources from the data directly