Uncorrelated Sources Research Articles

METROID: an automated method for robust quantification of subcellular fluorescence events at low SNR

BackgroundIn cell biology, increasing focus has been directed to fast events at subcellular space with the advent of fluorescent probes. As an example, voltage sensitive dyes (VSD) have been used to measure membrane potentials. Yet, even the most recently developed genetically encoded voltage sensors have demanded exhausting signal averaging through repeated experiments to quantify action potentials (AP). This analysis may be further hampered in subcellular signals defined by small regions of interest (ROI), where signal-to-noise ratio (SNR) may fall substantially. Signal processing techniques like blind source separation (BSS) are designed to separate a multichannel mixture of signals into uncorrelated or independent sources, whose potential to separate ROI signal from noise has been poorly explored. Our aims are to develop a method capable of retrieving subcellular events with minimal a priori information from noisy cell fluorescence images and to provide it as a computational tool to be readily employed by the scientific community.ResultsIn this paper, we have developed METROID (Morphological Extraction of Transmembrane potential from Regions Of Interest Device), a new computational tool to filter fluorescence signals from multiple ROIs, whose code and graphical interface are freely available. In this tool, we developed a new ROI definition procedure to automatically generate similar-area ROIs that follow cell shape. In addition, simulations and real data analysis were performed to recover AP and electroporation signals contaminated by noise by means of four types of BSS: Principal Component Analysis (PCA), Independent Component Analysis (ICA), and two versions with discrete wavelet transform (DWT). All these strategies allowed for signal extraction at low SNR (− 10 dB) without apparent signal distortion.ConclusionsWe demonstrate the great capability of our method to filter subcellular signals from noisy fluorescence images in a single trial, avoiding repeated experiments. We provide this novel biomedical application with a graphical user interface at https://doi.org/10.6084/m9.figshare.11344046.v1, and its code and datasets are available in GitHub at https://github.com/zoccoler/metroid.

Localization of Swept Free-Tip Airfoil Noise Sources by Microphone Array Processing

A postprocessing methodology of microphone-array results for accurate source localization and separation is described. A method constrained iterative restoration algorithm with an assumption of uncorrelated sources is used to extract quantitative spectral results for multiple noise sources identified on a wall-mounted finite-span swept and cambered airfoil tested in an open-jet aeroacoustic facility. This allows understanding of the contribution of each source in the noise generation process. The total sound pressure level is reconstructed from the individual spectra of each noise source and extrapolated in the far field to be compared with a single-microphone spectrum. The Bayesian algorithm is used to improve the comparison between reconstructed and experimental spectra because it takes into account the coherent nature of the sources. The analytical models of the source mechanisms and of their spanwise correlation are proposed as a tool to define future improvements.

Optimum sparse array configuration for DOA estimation on moving platforms

Sparse array motion can efficiently expand the numbers of achievable degrees of freedom (DOFs) and consecutive lags, improving direction-of-arrival (DOA) estimation. Sparse arrays on a moving platform benefit from motion translation that introduces new sensor positions, which collectively with the original positions can increase the number of spatial autocorrelation lags and lead to full array augmentability. This property has been recently used for the case of environment-independent sparse array configurations, such as those defined by nested and co-prime arrays. In this paper, we consider environment-dependent sparse arrays (EDSAs) design using Cramer-Rao bound (CRB) as the metric of optimality for DOA estimation. The CRB is derived for a sparse array on a moving platform, where the number of identifiable uncorrelated sources exceeds the number of sensors. The CRB expression is used to solve for the sparse array configuration by applying the Genetic algorithm. Simulation results are provided to validate the effectiveness of the proposed EDSA design.

A spatial correlation model for broadband surface noise.

The spatial correlation function for broadband ocean surface noise is considered in horizontally stratified media. It is expressed as an integral over the correlation function of the sound field radiated by a single noise source in the waveguide, assuming spatially uncorrelated noise sources with the same intensity that are distributed on the sea surface uniformly. An equation for the spatial-temporal correlation coefficient of the surface noise in a certain frequency band can then be derived. Numerical simulations are carried out for band limited white noise and wind noise, which show that the fluctuation of the correlation coefficient decreases with increasing bandwidth.

Novel algorithms for analyzing the robustness of difference coarrays to sensor failures

Sparse arrays have drawn attention because they can identify O(N2) uncorrelated source directions using N physical sensors, whereas uniform linear arrays (ULA) find at most N−1 sources. The main reason is that the difference coarray, defined as the set of differences between sensor locations, has size of O(N2) for some sparse arrays. However, the performance of sparse arrays may degrade significantly under sensor failures. In the literature, the k-essentialness property characterizes the patterns of k sensor failures that change the difference coarray. Based on this concept, the k-essential family, the k-fragility, and the k-essential Sperner family provide insights into the robustness of arrays. This paper proposes novel algorithms for computing these attributes. The first algorithm computes the k-essential Sperner family without enumerating all possible k-essential subarrays. With this information, the second algorithm finds the k-essential family first and the k-fragility next. These algorithms are applicable to any 1-D array. However, for robust array design, fast computation for the k-fragility is preferred. For this reason, a simple expression associated with the k-essential Sperner family is proposed to be a tighter lower bound for the k-fragility than the previous result. Numerical examples validate the proposed algorithms and the presented lower bound.

Elastic-net regularization based multi-point vibration response prediction in situation of unknown uncorrelated multiple sources load

In order to reduce the influence of ill-posed inverse on response prediction in the situation of unknown uncorrelated multiple sources load, a response prediction method based on elastic-net regularization in the frequency domain was proposed. This method utilized the linear relationship between known responses and the unknown responses instead of the transfer function to predict the response. Moreover, the elastic-net regularization model has two regularization parameters combining l1, l2 regularization to reduce the influence of ill-posed inverse. The experiment results on the data of acoustic and vibration sources on cylindrical shells showed that the elastic-net regularization in predicting response could obtain higher accurate results compared with the method of transfer function and the method of ordinary least squares, and predict vibration response effectively and satisfy industrial requirements.

Sparse Array Design via Fractal Geometries

Sparse sensor arrays have attracted considerable attention in various fields such as radar, array processing, ultrasound imaging and communications. In the context of correlation-based processing, such arrays enable to resolve more uncorrelated sources than physical sensors. This property of sparse arrays stems from the size of their difference coarrays, defined as the differences of element locations. Thus, the design of sparse arrays with large difference coarrays is of great interest. In addition, other array properties such as symmetry, robustness and array economy are important in different applications. Numerous studies have proposed diverse sparse geometries, focusing on certain properties while lacking others. Incorporating multiple properties into the design task leads to combinatorial problems which are generally NP-hard. For small arrays these optimization problems can be solved by brute force, however, in large scale they become intractable. In this paper, we propose a scalable systematic way to design large sparse arrays considering multiple properties. To that end, we introduce a fractal array design in which a generator array is recursively expanded according to its difference coarray. Our main result states that for an appropriate choice of the generator such fractal arrays exhibit large difference coarrays. Furthermore, we show that the fractal arrays inherit their properties from their generators. Thus, a small generator can be optimized according to desired requirements and then expanded to create a fractal array which meets the same criteria. This approach paves the way to efficient design of large arrays of hundreds or thousands of elements with specific properties.

An adapted eigenvalue-based filter for ocean ambient noise processing

Accurate approximations of Green’s functions retrieved from the correlations of ambient noise require a homogeneous distribution of random and uncorrelated noise sources. In the real world, the existence of highly coherent, strong directional noise generated by ships, earthquakes, and other human activities can result in biases in the ambient-noise crosscorrelations (NCCs). We have developed an adapted eigenvalue-based filter to attenuate the interference of strong directional sources. The filter is based on the statistical model of the sample covariance matrix and can separate different components of the data covariance matrix in the eigenvalue spectrum. To improve the effectiveness and make it adaptable for different data sets, a weight is introduced to the filter. Then, the NCCs can be calculated directly from the filtered data covariance matrix. This approach is applied to a 1.02 h data set of ambient noise recorded by a permanent reservoir monitoring receiver array installed on the seabed. The power spectral density indicates that the noise recordings were contaminated by strong directional noise over nearly half of the whole observation period. Beamforming and crosscorrelation results indicate that the interference still exists even after applying traditional temporal and spectral normalization techniques, whereas the adapted eigenvalue-based filter can significantly attenuate it and help to obtain improved crosscorrelations. The approach makes it possible to retrieve reliable approximations of Green’s functions over a much shorter recording time.

Stochastic and Deterministic Framework for Modeling the Effect of Antennas Location Error on DOA Estimation

This article focuses on the estimation of the direction of Arrival based on the interpolation approaches of the sparse array. Such as the minimum redundancy array, co-prime array, and the nested array have attracted much attention, especially for a non-linear array antenna. We analyze the effect of antennas locations errors on overall estimation performance for deterministic and stochastic error models and to improve the estimator performance in the case of uncorrelated sources of signals in spatially-smoothed MUSIC scenarios. In two scenarios: we determine the Cramer-Rao bound in the case of the antennas locations are perfect, and in other cases, we take into account antennas locations errors. For the first scenario, the Cramer-Rao bound converges as the SNR increase. For the second scenario, the Signal-to-noise ratio increases to infinity, to achieve the same Cramer-Rao bound as in the first scenarios. There is a significant gap between the Cramer-Rao bound values in a situation where antennas locations errors are considered, and when other locations errors are not considered. This disparity shows that unknown antenna locations errors have a significant impact on the estimated achievable performance of the direction of Arriva of scattered linear matrices.

Accuracy of Green's function estimation from correlation of diffuse elastic waves on thin plates.

In a reverberant cavity, when a noise field is sufficiently diffuse, the correlation of the signal measured by two sensors provides an estimation of the Green's function (GF) between them. Here, the convergence of this passive estimation in the case of elastic waves on thin plates is studied. A statistical approach is proposed, which relates the similarity between the cross correlation and the GF to the structural properties of the plate and the number of uncorrelated sources. The analysis is sustained by experimental results obtained on an aluminum plate. This study allows us to evaluate the efficiency of passive structural health monitoring of plate-like structures based on noise correlation. Finally, a most interesting finding shows an absolute upper bound of the signal-to-noise ratio for GF quality reconstruction: 4Ns/5, independently of the plate properties.

An empirical noise model for III-V compound semiconductor based HBT

This paper presents a novel approach for the modeling of noise behavior of III-V compound semiconductor based HBT’s over a wide frequency range. The main advantage is that the proposed model is based on two individual un-correlated noise sources, and easy to be incorporated with commercial circuit simulation software. The model is verified by measurements of the four noise parameters of an InP HBT up to 20 GHz and a GaAs HBT up to 26 GHz. The good agreements have been obtained.

Improvements in closed-section wind-tunnel beamforming experiments of acoustic sources distributed along a line

Phased-array microphone techniques are widely used tools for the measurement and analysis of aeroacoustic noise sources. Nevertheless, beamforming results of sources distributed along a line, such as airfoil trailing-edge and slat, have not been entirely understood. This paper investigates the performance of beamforming methods in representing sources distributed along a line and estimating their spectral level. Conventional beamforming and the deconvolution techniques DAMAS and CLEAN-SC were employed for both synthetic and physical sources. The physical source is the slat of an MD30P30N high-lift model tested in a closed-section wind-tunnel with array microphones mounted flush to the tunnel wall. The synthetic source consisted of a large number of uncorrelated aligned monopole point sources. DAMAS was found to be the most accurate approach for both synthetic and physical test cases. The physical source results were not as accurate as the synthetic source ones, nevertheless, they were substantially improved by array shading and by an acoustic treatment (foam coating) on the working section walls. The most effective array shading methodology was based on the mean coherence level of each microphone, here referred to as CW (Coherence Weighting shading).

Robustness of Difference Coarrays of Sparse Arrays to Sensor Failures—Part I: A Theory Motivated by Coarray MUSIC

In array processing, sparse arrays are capable of resolving O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) uncorrelated sources with N sensors. Sparse arrays have this property because they possess uniform linear array (ULA) segments of size O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) in the difference coarray, defined as the differences between sensor locations. However, the coarray structure of sparse arrays is susceptible to sensor failures, and the reliability of sparse arrays remains a significant but challenging topic for investigation. Broadly speaking, ULAs whose difference coarrays only have O(N) elements are more robust than sparse arrays with O(N <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) coarray sizes. This paper advances a theory for quantifying such robustness by introducing the k-essentialness of sensors and the k-essential family of arrays. The proposed theory is motivated by the coarray MUltiple SIgnal Classification (MUSIC) algorithm, which estimates source directions based on difference coarrays. Furthermore, the concept of essentialness not only characterizes the patterns of k faulty sensors that shrink the difference coarray, but also leads to the notion of k-fragility, which assesses the robustness of array geometries quantitatively. However, the large size of the k-essential family usually complicates the theory. It will be shown that the k-essential family can be compactly represented by the so-called k-essential Sperner family. Finally, the proposed theory is used to provide insights into the probability of change of the difference coarray, as a function of the sensor failure probability and array geometry. In a companion paper, the k-essential Sperner family for several commonly used array geometries will be derived in closed form, resulting in a quantitative comparison of the robustness of these arrays.

Robustness of Difference Coarrays of Sparse Arrays to Sensor Failures—Part II: Array Geometries

In array processing, sparse arrays are capable of resolving O(N^2) uncorrelated sources with N sensors. Sparse arrays have this property because they possess uniform linear array (ULA) segments of size O(N^2) in the difference coarray, defined as the differences between sensor locations. However, the coarray structure of sparse arrays is susceptible to sensor failures and the reliability of sparse arrays remains a significant but challenging topic for investigation. In the companion paper, a theory of the k -essential family, the k -fragility, and the k -essential Sperner family were presented not only to characterize the patterns of k faulty sensors that shrink the difference coarray, but also to provide a number of insights into the robustness of arrays. This paper derives closed-form characterizations of the k -essential Sperner family for several commonly used array geometries, such as ULA, minimum redundancy arrays (MRA), minimum holes arrays (MHA), Cantor arrays, nested arrays, and coprime arrays. These results lead to many insights into the relative importance of each sensor, the robustness of these arrays, and the DOA estimation performance in the presence of sensor failure. Broadly speaking, ULAs are more robust than coprime arrays, while coprime arrays are more robust than maximally economic sparse arrays, such as MRA, MHA, Cantor arrays, and nested arrays.

Cross-correlation of shipping noise: Refraction and receiver-motion effects.

The spatial correlation of a diffuse isotropic noise field generated from a uniform distribution of uncorrelated noise sources contains information about the time-domain Green's function (TDGF) corresponding to propagation between the correlated locations. The distribution of noise in the ocean due to shipping-the prevailing origin of continuous low-frequency noise-is far from uniform. Besides the location of noise sources, the propagation conditions and the hydrophone locations have a significant influence on whether the TDGF can be reliably reconstructed through the cross-correlation procedure. A wave-theoretic scheme is implemented to simulate the cross-correlation function of a noise field in the time domain for arbitrary distributions of deterministic or random noise sources in refractive environments, and it is used to study the influence of propagation conditions and receiver motion on the efficiency of the cross-correlation procedure to obtain the TDGF from shipping noise.

Benchmark analytical solutions for steady state high frequency broadband sound fields in three rectangular enclosures.

Analytical solutions are presented for broadband sound fields in three rectangular enclosures with absorption applied on the floor and ceiling, rigid sidewalls, and a vertically oriented dipole source. The solutions are intended to serve as benchmarks that can be used to assess the performance of broadband techniques, particularly energy-based methods, in a relatively straightforward configuration with precisely specified boundary conditions. A broadband Helmholtz solution is developed using a frequency-by-frequency modal approach to determine the exact band averaged mean-square pressures along spatial trajectories within each enclosure. Due to the specific choice of enclosure configuration and absorption distribution, an approximate specular solution can be obtained through a summation of uncorrelated image sources. Comparisons between the band averaged Helmholtz solution and the uncorrelated image solution reveal excellent agreement for a wide range of absorption levels and improve the understanding of correlation effects in broadband sound fields. A boundary element solution with diffuse boundaries is also presented, which produces consistently higher mean-square pressures in comparison with the specular solution, emphasizing the careful attention that must be placed on correctly modeling reflecting boundary conditions and demonstrating the errors that can result from assuming a Lambertian surface.

Further Results on the Cramér–Rao Bound for Sparse Linear Arrays

Sparse linear arrays, such as co-prime and nested arrays, can identify up $O(M^2)$ uncorrelated sources with only $O(M)$ sensors by utilizing their difference coarray model. In our previous work, we derived closed-form asymptotic mean-squared error (MSE) expressions for two coarray based MUSIC algorithms and analyzed the Cramer-Rao bound (CRB) in high signal-to-noise ratio (SNR) regions, under the assumption of uncorrelated sources. In this paper, we provide further analysis of the CRB presented in our previous work. We first establish the connection between two CRBs, the CRB derived with the assumption that the sources are uncorrelated, and the classical stochastic CRB derived without this assumption. We show that they are asymptotically equal in high SNR regions for uncorrelated sources. Next, we analyze the behavior of the former CRB for co-prime and nested arrays with a large number of sensors. We investigate the effect of configuration parameters on this CRB. We show that, for co-prime and nested arrays, this CRB can decrease at a rate of $O(M^{-5})$ for large values of $M$ , while this rate is only $O(M^{-3})$ for an $M$ -sensor ULA. This finding analytically demonstrates that co-prime and nested arrays can achieve better asymptotic estimation performance when the number of sensors is a limiting factor. We also show that for a fixed aperture, co-prime and nested arrays require more snapshots to achieve the same performance as ULAs, showing the trade-off between the number of spatial samples and the number of temporal samples. Finally, we demonstrate our analytical results with numerical experiments.

Impaired Array Diagnosis and Mitigation With Khatri–Rao Processing

Impaired array may significantly deteriorate the beampattern and consequently degrade the system performance. In this letter, we propose a signal processing scheme for impaired array diagnosis and mitigation via Khatri–Rao processing, which requires uncorrelated far-field sources to evaluate the mutual correlation between the vector signal received by the impaired array and a failure-free array. The essence is to detect impaired elements by a difference operation and then reconstruct an unpaired array through the Khatri–Rao processing. Moreover, the correlation problem due to the Khatri–Rao processing is addressed by a compressive sensing reconstruction algorithm instead of a conventional spatial smoothing algorithm to achieve improved performance. Both diagnosis and mitigation approaches require no a priori knowledge of the failed elements, but the diagnosis method needs the failure-free beampattern.

Decoherence of two entangled spin qubits coupled to an interacting sparse nuclear spin bath: Application to nitrogen vacancy centers

We consider pure dephasing of Bell states of electron spin qubits interacting with a sparse bath of nuclear spins. Using the newly developed two-qubit generalization of cluster correlation expansion method, we calculate the spin echo decay of $|\Psi\rangle$ and $|\Phi\rangle$ states for various interqubit distances. Comparing the results with calculations in which dephasing of each qubit is treated independently, we identify signatures of influence of common part of the bath on the two qubits. At large interqubit distances, this common part consists of many nuclei weakly coupled to both qubits, so that decoherence caused by it can be modeled by considering multiple uncorrelated sources of noise (clusters of nuclei), each of them weakly affecting the qubits. Consequently, the resulting genuinely two-qubit contribution to decoherence can be described as being caused by classical Gaussian noise. On the other hand, for small interqubit distances the common part of the environment contains clusters of spins that are strongly coupled to both qubits, and their contribution to two-qubit dephasing has visibly non-Gaussian character. We show that one van easily obtain information about non-Gaussianity of environmental noise affecting the qubits from the comparison of dephasing of $|\Psi\rangle$ and $|\Phi\rangle$ Bell states. Numerical results are obtained for two nitrogen vacancy centers interacting with a bath of $^{13}$C nuclei of natural concentration, for which we obtain that Gaussian description of correlated part of environmental noise starts to hold for centers separated by about 3 nm.

Analysis of sound field isotropy based on directional energy decay curves

The analysis of the diffuseness of sound fields is of great interest in room acoustic applications ranging from the analysis of concert venues to reverberation room design and calibration. However, a standardized robust diffuseness estimation method is currently lacking. The fundamental definition of the diffuse sound field is that it is isotropic—requiring the sound field to be composed of infinitely many sound waves from uncorrelated sources with directions of arrival uniformly distributed over a sphere. Due to their symmetry, spherical microphone arrays are especially favorable for the analysis of the isotropy requirement. In this work, we propose the directional energy decay curve which we calculate from a directional room impulse response captured with a spherical microphone array. Further, we show how the analysis of the spatial variations of the directional energy decay curve enables examining the isotropy of sound fields in rooms. Finally, we present a simulation study of multiple room configurations with varying degrees of sound field diffuseness.