Covariance-domain Dictionary Learning for Overcomplete EEG Source Identification

We propose an algorithm targeting the identification of more sources than channels for electroencephalography (EEG). Our overcomplete source identification algorithm, Cov-DL, leverages dictionary learning methods applied in the covariance-domain. Assuming that EEG sources are uncorrelated within moving time-windows and the scalp mixing is linear, the forward problem can be transferred to the covariance domain which has higher dimensionality than the original EEG channel domain. This allows for learning the overcomplete mixing matrix that generates the scalp EEG even when there may be more sources than sensors active at any time segment, i.e. when there are non-sparse sources. This is contrary to straight-forward dictionary learning methods that are based on the assumption of sparsity, which is not a satisfied condition in the case of low-density EEG systems. We present two different learning strategies for Cov-DL, determined by the size of the target mixing matrix. We demonstrate that Cov-DL outperforms existing overcomplete ICA algorithms under various scenarios of EEG simulations and real EEG experiments

On Probability of Support Recovery for Orthogonal Matching Pursuit Using Mutual Coherence

In this paper we present a new coherence-based performance guarantee for the Orthogonal Matching Pursuit (OMP) algorithm. A lower bound for the probability of correctly identifying the support of a sparse signal with additive white Gaussian noise is derived. Compared to previous work, the new bound takes into account the signal parameters such as dynamic range, noise variance, and sparsity. Numerical simulations show significant improvements over previous work and a closer match to empirically obtained results of the OMP algorithm.Comment: Submitted to IEEE Signal Processing Letters. arXiv admin note: substantial text overlap with arXiv:1608.0038

Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)

The implicit objective of the biennial "international - Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST) is to foster collaboration between international scientific teams by disseminating ideas through both specific oral/poster presentations and free discussions. For its second edition, the iTWIST workshop took place in the medieval and picturesque town of Namur in Belgium, from Wednesday August 27th till Friday August 29th, 2014. The workshop was conveniently located in "The Arsenal" building within walking distance of both hotels and town center. iTWIST'14 has gathered about 70 international participants and has featured 9 invited talks, 10 oral presentations, and 14 posters on the following themes, all related to the theory, application and generalization of the "sparsity paradigm": Sparsity-driven data sensing and processing; Union of low dimensional subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph sensing/processing; Blind inverse problems and dictionary learning; Sparsity and computational neuroscience; Information theory, geometry and randomness; Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?; Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website: http://sites.google.com/site/itwist1

Designing Gabor windows using convex optimization

Redundant Gabor frames admit an infinite number of dual frames, yet only the canonical dual Gabor system, constructed from the minimal l2-norm dual window, is widely used. This window function however, might lack desirable properties, e.g. good time-frequency concentration, small support or smoothness. We employ convex optimization methods to design dual windows satisfying the Wexler-Raz equations and optimizing various constraints. Numerical experiments suggest that alternate dual windows with considerably improved features can be found

A sparsity-based framework for resolution enhancement in optical fault analysis of integrated circuits

The increasing density and smaller length scales in integrated circuits (ICs) create resolution challenges for optical failure analysis techniques. Due to flip-chip bonding and dense metal layers on the front side, optical analysis of ICs is restricted to backside imaging through the silicon substrate, which limits the spatial resolution due to the minimum wavelength of transmission and refraction at the planar interface. The state-of-the-art backside analysis approach is to use aplanatic solid immersion lenses in order to achieve the highest possible numerical aperture of the imaging system. Signal processing algorithms are essential to complement the optical microscopy efforts to increase resolution through hardware modifications in order to meet the resolution requirements of new IC technologies. The focus of this thesis is the development of sparsity-based image reconstruction techniques to improve resolution of static IC images and dynamic optical measurements of device activity. A physics-based observation model is exploited in order to take advantage of polarization diversity in high numerical aperture systems. Multiple-polarization observation data are combined to produce a single enhanced image with higher resolution. In the static IC image case, two sparsity paradigms are considered. The first approach, referred to as analysis-based sparsity, creates enhanced resolution imagery by solving a linear inverse problem while enforcing sparsity through non-quadratic regularization functionals appropriate to IC features. The second approach, termed synthesis-based sparsity, is based on sparse representations with respect to overcomplete dictionaries. The domain of IC imaging is particularly suitable for the application of overcomplete dictionaries because the images are highly structured; they contain predictable building blocks derivable from the corresponding computer-aided design layouts. This structure provides a strong and natural a-priori dictionary for image reconstruction. In the dynamic case, an extension of the synthesis-based sparsity paradigm is formulated. Spatial regions of active areas with the same behavior over time or over frequency are coupled by an overcomplete dictionary consisting of space-time or space-frequency blocks. This extended dictionary enables resolution improvement through sparse representation of dynamic measurements. Additionally, extensions to darkfield subsurface microscopy of ICs and focus determination based on image stacks are provided. The resolution improvement ability of the proposed methods has been validated on both simulated and experimental data