Online DOA estimation using real eigenbeam ESPRIT with propagation vector matching

International audienceThe Eigenbeam estimation of signal parameters via rotational invariance technique (EB-ESPRIT) [1] is a method to estimate multiple directions-of-arrival (DOAs) of sound sources from a spherical microphone array recording in the spherical harmonics domain (SHD). The method, first, constructs a signal subspace from the SHD signal and then makes use of the fact that, for plane-wave sources, the signal subspace is spanned by the (complex conjugate) spherical harmonic vectors at the source directions. The DOAs are then estimated from the signal subspace using recurrence relations of spherical harmonics.In recent publications, the singularity and ambiguity problems of the original EB-ESPRIT have been solved by jointly combining several types of recurrence relations. The state-of-the-art EB-ESPRIT, denoted as DOA-vector EB-ESPRIT, is based on three recurrence relations [2,3]. This EB-ESPRIT variant can estimate the source DOAs with significantly higher accuracy compared to the other EB-ESPRIT variants [3]. However, a permutation problem arises, which can be solved by using, for example, a joint diagonalization method [3].For parametric spatial audio signal processing purposes in the short-time Fourier transform (STFT) domain, DOA estimates are usually needed per time-frame and frequency bin. In principle, one can use the DOA-vector EB-ESPRIT method to estimate the source DOAs per time-frequency bin in an online manner. However, due to the eigendecompostion of the PSD matrix and the joint diagonalization procedure, the computational cost might be too large for many real-time applications.In this work, we propose a computationally more efficient version of the DOA-vector EB-ESPRIT based on real spherical harmonics recurrence relations. First, we separate the real and imaginary parts of the real SHD signal in the STFT domain and then construct a real signal subspace thereof, which can be recursively estimated using the deflated projection approximation subspace tracking (PASTd) [4] method. For the case of one source per time-frequency bin, the joint diagonalization is not necessary and we can simplify the EB-ESPRIT equations. For the case of two sources, the plane-wave propagation vectors can directly be estimated from the signal subspace eigenvectors by employing properties of the propagation vectors. This method can be seen as a higher order ambisonics extension of the robust B-format DOA estimation in [5]. The proposed method for estimating two DOAs can be summarized as follows:1. Separate real and imaginary parts of the real SHD signal in the STFT domain.2. Recursively estimate the signal subspace eigenvectors using PASTd.3. Estimate the two plane-wave propagation vectors from the signal subspace eigenvectors by using that they span the same subspace and by using properties of the propagation vectors (subspace-propagation vector matching).4. Estimate the DOAs by using three types of real spherical harmonics recurrence relations.Alternatively, one can estimate the DOAs analogously to the complex DOA-vector EB-ESPRIT using the joint diagonalization method proposed in [3].For the evaluation, we simulate SHD signals up to third order with one and two speech sources in reverberant and noisy environments. For the one-source scenarios, we compare the real DOA-vector EB-ESPRIT with subspace estimation based on singular value decomposition (SVD) against PASTd. For the two-source scenarios, we compare the real DOA-vector EB-ESPRIT with joint diagonalization against subspace-propagation vector matching and the robust B-format DOA estimation method.We analyze the angular distributions of the DOA estimates and find, that the DOA estimation using PASTd for the signal subspace estimation is slightly less accurate than the SVD based method but computationally much more efficient. For the estimation of two DOAs, the EB-ESPRIT based methods outperform the robust B-format estimation method when higher SHD orders are considered. The joint diagonalization method is more accurate than the subspace-propagation vector matching method. However, the latter is computationally more efficient.References:[1] H. Teutsch and W. Kellermann, “Detection and localization of multiple wideband acoustic sources based on wavefield decomposition using spherical apertures,” in Proc. IEEE Intl. Conf. Acoust., Speech Signal Proc. (ICASSP), Mar. 2008, pp. 5276–5279.[2] B. Jo and J. W. Choi, “Nonsingular EB-ESPRIT for the localization of early reflections in a room,” J. Acoust. Soc. Am., vol. 144, no. 3, p. 1882, Sep. 2018.[3] A. Herzog and E. A. P. Habets, “Eigenbeam-ESPRIT for DOA-vector estimation,” IEEE Signal Process. Lett., vol. 26, no. 4, pp. 572-576, April 2019.[4] B. Yang – “Projection Approximation Subspace Tracking, IEEE Trans. Sig. Proc.,” vol. 43, no. 1, Jan. 1995.[5] O. Thiergart and E.A.P. Habets, “Robust direction-of-arrival estimation of two simultaneous plane waves from a B-format signal,” IEEE 27th Conv. of Electrical and Electronics Engineers in Israel, Nov. 2012

Gauge invariant variables for cosmological perturbation theory using geometrical clocks

Using the extended ADM-phase space formulation in the canonical framework we analyze the relationship between various gauge choices made in cosmological perturbation theory and the choice of geometrical clocks in the relational formalism. We show that various gauge invariant variables obtained in the conventional analysis of cosmological perturbation theory correspond to Dirac observables tied to a specific choice of geometrical clocks. As examples, we show that the Bardeen potentials and the Mukhanov-Sasaki variable emerge naturally in our analysis as observables when gauge fixing conditions are determined via clocks in the Hamiltonian framework. Similarly other gauge invariant variables for various gauges can be systematically obtained. We demonstrate this by analyzing five common gauge choices: longitudinal, spatially flat, uniform field, synchronous and comoving gauge. For all these, we apply the observable map in the context of the relational formalism and obtain the corresponding Dirac observables associated with these choices of clocks. At the linear order, our analysis generalizes the existing results in canonical cosmological perturbation theory twofold. On the one hand we can include also gauges that can only be analyzed in the context of the extended ADM-phase space and furthermore, we obtain a set of natural gauge invariant variables, namely the Dirac observables, for each considered choice of gauge conditions. Our analysis provides insights on which clocks should be used to extract the relevant natural physical observables both at the classical and quantum level. We also discuss how to generalize our analysis in a straightforward way to higher orders in the perturbation theory to understand gauge conditions and the construction of gauge invariant quantities beyond linear order.Comment: Discussion expanded, references added. To appear in Classical and Quantum Gravit

Hard Criteria for Empirical Theories of Consciousness

Consciousness is now a well-established field of empirical research. A large body of experimental results has been accumulated and is steadily growing. In parallel, many Theories of Consciousness (ToCs) have been proposed. These theories are diverse in nature, ranging from computational to neurophysiological and quantum theoretical approaches. This contrasts with other fields of natural science, which host a smaller number of competing theories. We suggest that one reason for this abundance of extremely different theories may be the lack of stringent criteria specifying how empirical data constrains ToCs. First, we argue that consciousness is a well-defined topic from an empirical point of view and motivate a purely empirical stance on the quest for consciousness. Second, we present a checklist of criteria that, we propose, empirical ToCs need to cope with. Third, we review 13 of the most influential ToCs and subject them to the criteria. Our analysis helps to situate these different ToCs in the theoretical landscape and sheds light on their strengths and weaknesses from a strictly empirical point of view

First-Person Experience Cannot Rescue Causal Structure Theories from the Unfolding Argument

We recently put forward an argument, the Unfolding Argument (UA), that integrated information theory (IIT) and other causal structure theories are either already falsified or unfalsifiable, which provoked significant criticism. It seems that we and the critics agree that the main question in this debate is whether first-person experience, independent of third-person data, is a sufficient foundation for theories of consciousness. Here, we argue that pure first-person experience cannot be a scientific foundation for IIT because science relies on taking measurements, and pure first-person experience is not measurable except through reports, brain activity, and the relationship between them. We also argue that pure first-person experience cannot be taken as ground truth because science is about backing up theories with data, not about asserting that we have ground truth independent of data. Lastly, we explain why no experiment based on third-person data can test IIT as a theory of consciousness. IIT may be a good theory of something, but not of consciousness. We conclude by exposing a deeper reason for the above conclusions: IIT’s consciousness is by construction fully dissociated from any measurable thing and, for this reason, IIT implies that both the level and content of consciousness are epiphenomenal, with no causal power. IIT and other causal structure theories end up in a form of dissociative epiphenomenalism, in which we cannot even trust reports about first-person experiences. But reports about first-person experiences are taken as ground truth and the foundation for IIT’s axioms. Therefore, accepting IIT leads to rejecting its own axioms. We also respond to several other criticisms against the UA

The Unfolding Argument: Why IIT and Other Causal Structure Theories Cannot Explain Consciousness

How can we explain consciousness? This question has become a vibrant topic of neuroscience research in recent decades. A large body of empirical results has been accumulated, and many theories have been proposed. Certain theories suggest that consciousness should be explained in terms of brain functions, such as accessing information in a global workspace, applying higher order to lower order representations, or predictive coding. These functions could be realized by a variety of patterns of brain connectivity. Other theories, such as Information Integration Theory (IIT) and Recurrent Processing Theory (RPT), identify causal structure with consciousness. For example, according to these theories, feedforward systems are never conscious, and feedback systems always are. Here, using theorems from the theory of computation, we show that causal structure theories are either false or outside the realm of science

Dimensionality Reduction in spatio-temporal MaxEnt models and analysis of Retinal Ganglion Cell Spiking Activity in experiments

International audienceRetinal spike response to stimuli is constrained, on one hand by short range correlations (receptive field overlap) and on the other hand by lateral connectivity (cells connectivity). This last effect is difficult to handle fromstatistics because it requires to consider spatio-temporal correlations with a time delay long enough to take into account the time of propagation along synapses. Although MaxEnt model are useful to fit optimal model(maximizing entropy) under the constraints of reproducing observed correlations, they do address spatio-temporal correlations in their classical form (Ising or higher order interactions but without time delay). Binning insuch models somewhat integrates propagation effects, but in an implicit form, and increasing binning severely bias data [1]. To resolve this issue we have considered spatio-temporal MaxEnt model formerly developed e.g.by Vasquez et al. [2]. The price to pay, however is a huge set of parameters that must be fitted to experimental data to explain the observed spiking patterns statistics. There is no a priori knowledge of which parameters arerelevant and which ones are contributing to overfitting. We propose here a method of dimension reduction, i.e. a projection on a relevant subset of parameters, relying on the so-called Susceptibility matrix closely related tothe Fisher information. In contrast to standard methods in information geometry though, this matrix handle space and time correlations.We have applied this method for retina data obtained in a diurnal rodent (Octodon degus, having 30% of cones photoreceptors) and a 252-MEA system. Three types of stimuli were used: spatio-temporal uniform light, whitenoise and a natural movie. We show the role played by time-delayed pairwise interactions in the neural response to stimuli both for close and distant cells. Our conclusion is that, to explain the population spiking statisticswe need both short-distance interactions as well as long-distance interactions, meaning that the relevant functional correlations are mediated not only by common input (i.e. receptive field overlap, electrical coupling;spillover) but also by long range connections

Dimensionality Reduction on Maximum Entropy Models on Spiking Networks

Maximum entropy models (MEM) have been widely used in the last 10 years formodelling, explaining and predicting the statistics of networks of spiking neurons.However, as the network size increases, the number of model parameters increasesrapidily, hindering its interpretation and fast computation. However, these parametersare not necessarily independent from each other; when some of them are related byhidden dependencies, their number can be reduced, allowing to map the MEM into alower dimensional space. Here, we present a novel framework for MEM dimensionalityreduction that uses the geometrical properties of MEM to find the subset of dimensionsthat best captures the network high-order statistics, without fitting the model to data.This allows us define a parameter somehow representing the degree of compressibility ofthe code. The method was tested on synthetic data where the underlying statistics isknown and on retinal ganglion cells (RGC) data recorded using multi-electrode arrays(MEA) under different stimuli. We found that MEM dimensionality reduction dependson the interdependences between the network activity, the density of the raster and thenumber of observed events. For RGC data we found that the activity is highlyinterdependent, with a dimensionality reduction of almost 50%, compared to a randomraster, showing that the network activity is highly compressible, possibly due to thenetwork redundancies. This dimensionality reduction depends on the stimuli statistics,supporting the idea that sensory networks adapts to stimuli statistics, modifying thelevel of redundancy, i.e. the coding strategy

Multispectral Optoacoustic Tomography of Matrix Metalloproteinase Activity in Vulnerable Human Carotid Plaques

Elevated expression of cathepsins, integrins and matrix metalloproteinases (MMPs) is typically associated with atherosclerotic plaque instability. While fluorescent tagging of such molecules has been amply demonstrated, no imaging method was so far shown capable of resolving these inflammation-associated tags with high fidelity and resolution beyond microscopic depths. This study is aimed at demonstrating a new method with high potential for noninvasive clinical cardiovascular diagnostics of vulnerable plaques using high-resolution deep-tissue multispectral optoacoustic tomography (MSOT) technology. MMP-sensitive activatable fluorescent probe (MMPSense (TM) 680) was applied to human carotid plaques from symptomatic patients. Atherosclerotic activity was detected by tuning MSOT wavelengths to activation-dependent absorption changes of the molecules, structurally modified in the presence of enzymes. MSOT analysis simultaneously provided morphology along with heterogeneous MMP activity with better than 200 micron resolution throughout the intact plaque tissue. The results corresponded well with epi-fluorescence images made from thin cryosections. Elevated MMP activity was further confirmed by zymography, accompanied by increased macrophage influx. We demonstrated, for the first time to our knowledge, the ability of MSOT to provide volumetric images of activatable molecular probe distribution deep within optically diffuse tissues. High-resolution mapping of MMP activity was achieved deep in the vulnerable plaque of intact human carotid specimens. This performance directly relates to pre-clinical screening applications in animal models and to clinical decision potential as it might eventually allow for highly specific visualization and staging of plaque vulnerability thus impacting therapeutic clinical decision making

Menthol Cigarette Smoking and Obesity in Young Adult Daily Smokers in Hawaii

This study investigates 1) the relationship between menthol cigarette smoking and obesity and 2) the association of body mass index with the nicotine metabolite ratio among menthol and non-menthol daily smokers aged 18–35 (n = 175). A brief survey on smoking and measures of height and weight, carbon monoxide, and saliva samples were collected from participants from May to December 2013 in Honolulu, Hawaii. Multiple regression was used to estimate differences in body mass index among menthol and non-menthol smokers and the association of menthol smoking with obesity. We calculated the log of the nicotine metabolite ratio to examine differences in the nicotine metabolite ratio among normal, overweight, and obese smokers. Sixty-eight percent of smokers used menthol cigarettes. Results showed that 62% of normal, 54% of overweight, and 91% of obese smokers used menthol cigarettes (p = .000). The mean body mass index was significantly higher among menthol compared with non-menthol smokers (29.4 versus 24.5, p = .000). After controlling for gender, marital status, educational attainment, employment status, and race/ethnicity, menthol smokers were more than 3 times as likely as non-menthol smokers to be obese (p = .04). The nicotine metabolite ratio was significantly lower for overweight menthol smokers compared with non-menthol smokers (.16 versus .26, p = .02) in the unadjusted model, but was not significant after adjusting for the covariates. Consistent with prior studies, our data show that menthol smokers are more likely to be obese compared with non-menthol smokers. Future studies are needed to determine how flavored tobacco products influence obesity among smokers