From EEG dependency multichannel matching pursuit to sparse topographic EEG decomposition

In this work, we present a multichannel EEG decomposition model based on an adaptive topographic time-frequency approximation technique. It is an extension of the Matching Pursuit algorithm and called dependency multichannel matching pursuit (DMMP). It takes the physiologically explainable and statistically observable topographic dependencies between the channels into account, namely the spatial smoothness of neighboring electrodes that is implied by the electric leadfield. DMMP decomposes a multichannel signal as a weighted sum of atoms from a given dictionary where the single channels are represented from exactly the same subset of a complete dictionary. The decomposition is illustrated on topographical EEG data during different physiological conditions using a complete Gabor dictionary. Further the extension of the single-channel time-frequency distribution to a multichannel time-frequency distribution is given. This can be used for the visualization of the decomposition structure of multichannel EEG. A clustering procedure applied to the topographies, the vectors of the corresponding contribution of an atom to the signal in each channel produced by DMMP, leads to an extremely sparse topographic decomposition of the EEG.

Electrical neuroimaging in the time domain

A publication entitled “A default mode of brain function” initiated a new way of looking at functional imaging data. In this PET study the authors discussed the often-observed consistent decrease of brain activation in a variety of tasks as compared with the baseline. They suggested that this deactivation is due to a task-induced suspension of a default mode of brain function that is active during rest, i.e. that there exists intrinsic well-organized brain activity during rest in several distinct brain regions. This suggestion led to a large number of imaging studies on the resting state of the brain and to the conclusion that the study of this intrinsic activity is crucial for understanding how the brain works. The fact that the brain is active during rest has been well known from a variety of EEG recordings for a very long time. Different states of the brain in the sleep–wake continuum are characterized by typical patterns of spontaneous oscillations in different frequency ranges and in different brain regions. Best studied are the evolving states during the different sleep stages, but characteristic EEG oscillation patterns have also been well described during awake periods (see Chapter 1 for details). A highly recommended comprehensive review on the brain's default state defined by oscillatory electrical brain activities is provided in the recent book by György Buzsaki, showing how these states can be measured by electrophysiological procedures at the global brain level as well as at the local cellular level.

Frequency of Sobolev and quasiconformal dimension distortion

We study Hausdorff and Minkowski dimension distortion for images of generic affine subspaces of Euclidean space under Sobolev and quasiconformal maps. For a supercritical Sobolev map f defined on a domain in RnRn, we estimate from above the Hausdorff dimension of the set of affine subspaces parallel to a fixed m-dimensional linear subspace, whose image under f has positive HαHα measure for some fixed α>mα>m. As a consequence, we obtain new dimension distortion and absolute continuity statements valid for almost every affine subspace. Our results hold for mappings taking values in arbitrary metric spaces, yet are new even for quasiconformal maps of the plane. We illustrate our results with numerous examples.

Critical Issues of Centralized and Cloudified LTE-FDD Radio Access Networks

Cloudification of the Centralized-Radio Access Network (C-RAN) in which signal processing runs on general purpose processors inside virtual machines has lately received significant attention. Due to short deadlines in the LTE Frequency Division Duplex access method, processing time fluctuations introduced by the virtualization process have a deep impact on C-RAN performance. This paper evaluates bottlenecks of the OpenAirInterface (OAI is an open-source software-based implementation of LTE) cloud performance, provides feasibility studies on C-RAN execution, and introduces a cloud architecture that significantly reduces the encountered execution problems. In typical cloud environments, the OAI processing time deadlines cannot be guaranteed. Our proposed cloud architecture shows good characteristics for the OAI cloud execution. As an example, in our setup more than 99.5% processed LTE subframes reach reasonable processing deadlines close to performance of a dedicated machine.

Gradient-domain Path Tracing

We introduce gradient-domain rendering for Monte Carlo image synthesis.While previous gradient-domain Metropolis Light Transport sought to distribute more samples in areas of high gradients, we show, in contrast, that estimating image gradients is also possible using standard (non-Metropolis) Monte Carlo algorithms, and furthermore, that even without changing the sample distribution, this often leads to significant error reduction. This broadens the applicability of gradient rendering considerably. To gain insight into the conditions under which gradient-domain sampling is beneficial, we present a frequency analysis that compares Monte Carlo sampling of gradients followed by Poisson reconstruction to traditional Monte Carlo sampling. Finally, we describe Gradient-Domain Path Tracing (G-PT), a relatively simple modification of the standard path tracing algorithm that can yield far superior results.