Single-channel Problem Research Articles

A novel SSA-CCA framework for muscle artifact removal from ambulatory EEG

BackgroundElectroencephalography (EEG) has gained popularity in various types of biomedical applications as a signal source that can be easily acquired and conveniently analyzed. However, owing to a complex scalp electrical environment, EEG is often polluted by diverse artifacts, with electromyography artifacts being the most difficult to remove. In particular, for ambulatory EEG devices with a restricted number of channels, dealing with muscle artifacts is a challenge. MethodsIn this study, we propose a simple but effective novel scheme that combines singular spectrum analysis (SSA) and canonical correlation analysis (CCA) algorithms for single-channel problems and then extend it to a fewchannel case by adding additional combining and dividing operations to channels. ResultsWe evaluated our proposed framework on both semi-simulated and real-life data and compared it with some state-of-theart methods. The results demonstrate this novel framework's superior performance in both single-channel and few-channel cases. ConclusionsThis promising approach, based on its effectiveness and low time cost, is suitable for real-world biomedical signal processing applications.

Neural Cascade Architecture for Multi-Channel Acoustic Echo Suppression

Traditional acoustic echo cancellation (AEC) works by identifying an acoustic impulse response using adaptive algorithms. This paper proposes a neural cascade architecture for joint acoustic echo and noise suppression to address both single-channel and multi-channel AEC (MCAEC) problems. The proposed cascade architecture consists of two modules. A convolutional recurrent network (CRN) is employed in the first module for complex spectral mapping. Its output is fed as an additional input to the second module, where a long short-term memory network (LSTM) is utilized for magnitude mask estimation. The entire architecture is trained in an end-to-end manner with the two modules optimized jointly using a single loss function. The final output is generated using the enhanced phase and magnitude obtained from the first and the second module, respectively. The cascade architecture enables the proposed method to obtain robust magnitude estimation as well as phase enhancement. The proposed method is investigated under different AEC setups. We find that the deep learning based approach avoids the no-uniqueness problem in traditional MCAEC. For MCAEC setups with multiple microphones, combining deep MCAEC with supervised beamforming further improves the system performance. Evaluation results show that the proposed approach effectively suppresses acoustic echo and noise while preserving speech quality, and consistently outperforms related methods under different setups.

Optimal Control and Stabilization for Itô Systems with Input Delay

The paper considers the linear quadratic regulation (LQR) and stabilization problems for Ito stochastic systems with two input channels of which one has input delay. The underlying problem actually falls into the field of asymmetric information control because of the nonidentical measurability induced by the input delay. In contrast with single-channel single-delay problems, the challenge of the problems under study lies in the interaction between the two channels which are measurable with respect to different filtrations. The key techniques conquering such difficulty are the stochastic maximum principle and the orthogonal decomposition and reorganization technique proposed in a companion paper. The authors provide a way to solve the delayed forward backward stochastic differential equation (D-FBSDE) arising from the maximum principle. The necessary and sufficient solvability condition and the optimal controller for the LQR problem are given in terms of a new Riccati differential equation established herein. Further, the necessary and sufficient stabilization condition in the mean square sense is provided and the optimal controller is given. The idea proposed in the paper can be extended to solve related control problems for stochastic systems with multiple input channels and multiple delays.

Calculation of the Lowest Resonant States of H− and Li by the Complex Absorbing Potential Method

The analysis of the features of the method of complex absorbing potential (CAP) is carried out for a single-channel problem with an explicit parameterization of the scattering matrix. It is shown that there can be several types of CAP trajectories depending on the choice of the initial conditions. In any case, the estimation of the resonance parameters from the position of the optimal trajectory point can lead to a systematic error or an ambiguous result. In special cases, the search for the optimal point can be replaced by the averaging over a closed section of the trajectory. The CAP trajectories constructed in the H− and Li resonance calculations correlate well with the model trajectories, which have a curl around the resonance. The averaging over a closed area of the trajectory leads to better estimates of the energy and width of the resonance in comparison with the technique of searching for the optimal point.

Predicting impurity spectral functions using machine learning

The Anderson Impurity Model (AIM) is a canonical model of quantum many-body physics. Here we investigate whether machine learning models, both neural networks (NN) and kernel ridge regression (KRR), can accurately predict the AIM spectral function in all of its regimes, from empty orbital, to mixed valence, to Kondo. To tackle this question, we construct two large spectral databases containing approximately 410 000 and 600 000 spectral functions of the single-channel impurity problem. We show that the NN models can accurately predict the AIM spectral function in all of its regimes, with pointwise mean absolute errors down to 0.003 in normalized units. We find that the trained NN models outperform models based on KRR and enjoy a speedup on the order of ${10}^{5}$ over traditional AIM solvers. The required size of the training set of our model can be significantly reduced using farthest point sampling in the AIM parameter space, which is important for generalizing our method to more complicated multichannel impurity problems of relevance to predicting the properties of real materials.

LQR for Ito systems with input delays

Linear quadratic regulation (LQR) is very fundamental in modern control theory. The theory has been developing for several decades. However, the LQR problem for stochastic systems with input delays still remains outstanding. The paper focuses on the LQR problem for Ito stochastic systems with two control channels and a delay, which will pave a way to approach the corresponding H∞ control problem. In contrast with the single channel problem, this problem is more typical and involved since the two channels problem actually encounters interaction between channels besides the delay. The paper focuses on providing a necessary and sufficient solvability condition and optimal control. The sufficiency is proved by finding a suitable value functional and completing the square. The necessary condition is obtained by the variant of the calculus of variations. What’s more important, due to that the result is given based on coupling ordinary and partial differential equations, we present the analytic solution to these equations. The idea is also suitable for handling the LQR problem for Ito stochastic systems with multiple control channels and multiple delays.

Applicability of the Wong formula for fusion cross sections from light to heavy systems

We discuss the applicability of the Wong formula for fusion cross sections in a single-channel problem. To this end, we carry out a systematic study and compare the approximate fusion cross sections with the exact results in a wide mass region of reaction systems. We show that the deviation of the approximate results from the exact cross sections is large for light systems, even though the Wong formula provides a reasonable approximation for heavy systems. We also discuss the energy dependence of the deviation, and show that for a given projectile nucleus the critical energy, at which the deviation exceeds 5\% of the exact cross sections, increases as a function of the mass number of the target nucleus.

Recent developments in heavy-ion fusion reactions around the Coulomb barrier

The nuclear fusion is a reaction to form a compound nucleus. It plays an important role in several circumstances in nuclear physics as well as in nuclear astrophysics, such as synthesis of superheavy elements and nucleosynthesis in stars. Here we discuss two recent theoretical developments in heavy-ion fusion reactions at energies around the Coulomb barrier. The first topic is a generalization of the Wong formula for fusion cross sections in a single-channel problem. By introducing an energy dependence to the barrier parameters, we show that the generalized formula leads to results practically indistinguishable from a full quantal calculation, even for light symmetric systems such as $^{12}$C+$^{12}$C, for which fusion cross sections show an oscillatory behavior. We then discuss a semi-microscopic modeling of heavy-ion fusion reactions, which combine the coupled-channels approach to the state-of-the-art nuclear structure calculations for low-lying collective motions. We apply this method to subbarrier fusion reactions of $^{58}$Ni+$^{58}$Ni and $^{40}$Ca+$^{58}$Ni systems, and discuss the role of anharmonicity of the low-lying vibrational motions.

Research on Methods for Narrow-Band Interference Suppression in Synthetic Aperture Radar Data

Narrow-band interference (NBI) poses a hindrance to high-quality imaging for synthetic aperture radar (SAR). It is an under-determined single-channel separation problem. In this paper, we addressed the NBI suppression problem by introducing two advanced data-driven nonparametric techniques: 1) the eigen subspace filtering and 2) the independent component analysis (ICA). Both of these two methods utilize the statistical difference between the useful radar echoes and NBI. The interference-contaminated pulse is decomposed into a set of basis signals, from which the bases corresponding to NBI are selected out. Then, the contribution of NBI is excised by filtering out the corresponding interference components. The performances of these advanced methods are compared with the conventional notch filtering method. The experimental results on real datasets show the effectiveness of the proposed methods.

Degarbling Mode S replies received in single channel stations with a digital incremental improvement

Multilateration and automatic dependent surveillance-broadcast systems are used in air traffic control to detect, locate and identify cooperating aircraft using signals emitted by airborne transponders and received by dedicated ground stations. In areas with a high traffic density, these stations may receive simultaneously several superimposed signals. Present operational systems use only one receiving channel connected to a non-directional antenna. When the received replies are superimposed, that is, 'garbled', their detection and/or decoding are severely affected in nowadays equipment. The aim of this study is to transform the single channel problem into a multiple channels problem in order to solve it using specific knowledge about the Mode S signals. In fact, the multiple channels problem is a typical signals separation problem applied to Mode S mixture for which several algorithms already exist. The authors' algorithm, named projection algorithm (PA) single antenna, is based on the existing PA and can be easily implemented on existing receiving stations. The effectiveness of their method is demonstrated using real data collected from their experimental receiver.

Application of a coupled-channel complex scaling method with Feshbach projection to the K-pp system

Kaonic nuclei (nuclear system with anti-kaons) have been an interesting subject in hadron and strange nuclear physics, because the strong attraction between anti-kaon and nucleon might bring exotic properties to that system. In this article, we investigate $K^-pp$ as a prototype of kaonic nuclei. Here, $K^-pp$ is a three-body resonant state in the $\bar{K}NN$-$\pi YN$ coupled channels. ($Y$=$\Lambda$, $\Sigma$) To treat resonant states in a coupled-channel system properly, we propose newly a coupled-channel complex scaling method combined with the Feshbach projection (ccCSM+Feshbach method). In this method, the Feshbach projection is realized with help of so-called the extended closure relation held in the complex scaling method, and a complicated coupled-channel problem is reduced to a simple single-channel problem which one can treat easily. First, we confirm that the ccCSM+Feshbach method completely reproduces results of a full coupled-channel calculation in case of two-body $\bar{K}N$-$\pi Y$ system. We then proceed to study of three-body $\bar{K}NN$-$\pi YN$ system, and successfully find solutions of the $K^-pp$ resonance by imposing self-consistency for the complex $\bar{K}N$ energy. Obtained binding energy of $K^-pp$ is well converged around 27 MeV, with an energy-dependent $\bar{K}N$(-$\pi Y$) potential based on the chiral SU(3) theory, independently of ansatz for the self-consistency. This binding energy is small as ones reported in earlier studies based on chiral models. The decay width of $K^-pp$ strongly depends on the ansatz. We calculate also the correlation density of $NN$ and $\bar{K}N$ pairs by using the obtained complex-scaled wave function of the $K^-pp$ resonance. Effect of the repulsive core of $NN$ potential and survival of $\Lambda^*$ resonance are confirmed.

Investigation of K b a r N N resonances with a coupled-channel Complex Scaling Method + Feshbach projection

We have investigated a prototype of kaonic nuclei, "$K^-pp$", with a coupled-channel Complex Scaling Method (ccCSM). Combining the ccCSM with Feshbach projection method, we can handle a coupled-channel problem effectively as a single-channel problem. By using an energy-dependent chiral SU(3)-based $\bar{K}N$ potential, the $K^-pp$ ($J^\pi=0^-$ and $T=1/2$) is obtained to be shallowly bound with the binding energy of 20-30 MeV. The mesonic decay width depends on the interaction parameters and ansatz; the decay width is ranging from 20 to 65 MeV. In case of $J^\pi=1^-$ state, no three-body $\bar{K}NN$ resonant states are found.

Essential K̄ cluster "K−pp" studied with a coupled-channel Complex Scaling Method + Feshbach method

We have investigated an essential K̄ cluster "K−pp", which is the simplest system of kaonic nuclei, with a coupled-channel Complex Scaling Method (ccCSM). Combining the ccCSM with Feshbach method we can handle a coupled-channel problem effectively as a singlechannel problem. As a result of a study of the K−pp with the ccCSM+Feshbach method using an energy-dependent chiral-theory based potential, it is found that the K−pp is shallowly bound with the binding energy of around 20-35 MeV. The mesonic decay width is rather dependent on the interaction parameters and ansatz; the half decay width is ranging from 20 to 65 MeV.

Narrow-Band Interference Mitigation for SAR Using Independent Subspace Analysis

The mitigation of narrow-band interference (NBI) is an appealing topic in the synthetic aperture radar (SAR) community. It is an underdetermined single-channel separation problem. This paper proposes a method for NBI mitigation using the independent subspace analysis. First, each single pulse is transformed onto a manifold time-frequency distribution by the short-time Fourier transform (STFT). Then, the singular value analysis is carried out to extract the prominent features corresponding to the NBIs. Next, independent component analysis is employed to obtain statistically independent basis components. Furthermore, the independent subspaces corresponding to NBI are reconstructed and subtracted from the raw signal space. The signal with NBI mitigated is resynthesized by inverse STFT. Finally, after processing all the pulses, a well-focused SAR imagery is obtained by a conventional imaging algorithm. Experimental results of simulated and measured data have demonstrated the effectiveness of the proposed method.

Energy-Efficiency Optimization for MIMO-OFDM Mobile Multimedia Communication Systems With QoS Constraints

It is widely recognized that, in addition to the quality-of-service (QoS), energy efficiency is also a key parameter in designing and evaluating mobile multimedia communication systems, which has catalyzed great interest in recent literature. In this paper, an energy-efficiency model is first proposed for multiple-input-multiple-output orthogonal frequency-division multiplexing (MIMO-OFDM) mobile multimedia communication systems with statistical QoS constraints. Employing the channel-matrix singular value decomposition (SVD) method, all subchannels are classified by their channel characteristics. Furthermore, the multichannel joint optimization problem in conventional MIMO-OFDM communication systems is transformed into a multitarget single-channel optimization problem by grouping all subchannels. Therefore, a closed-form solution of the energy-efficiency optimization is derived for MIMO-OFDM mobile multimedia communication systems. As a consequence, an energy-efficiency optimized power allocation (EEOPA) algorithm is proposed to improve the energy efficiency of MIMO-OFDM mobile multimedia communication systems. Simulation comparisons validate that the proposed EEOPA algorithm can guarantee the required QoS with high energy efficiency in MIMO-OFDM mobile multimedia communication systems.

Examining potential shortcomings in using phase shifts as a link between experiment and QCD

Luscher has shown that in single channel problem (elastic region below first inelastic threshold) there exists a direct link between the discrete value of the energy in a finite QCD volume and the scattering phase shift at the same energy. However, when the extension of the theorem is made to the baryon resonance sector (multi-channel situation in the inelastic region above first inelastic threshold), eigenphases (diagonal multi-channel quantities) replace phase shifts (single channel quantities). It is necessary to stress that the renowned pi/2 resonance criterion is formulated for eigenphases and not for phase shifts, so the resonance extracting procedure has to be applied with utmost care. The potential instability of extracting eigenphases from experimental data which occurs if insufficient number of channels is used can be reduced if a trace function which explicitly takes multi-channel aspect of the problem into account is used instead of single-channel phase shifts.

Enhancement of Residual Echo for Robust Acoustic Echo Cancellation

This paper examines the technique of using a noise-suppressing nonlinearity in the adaptive filter error feedback-loop of an acoustic echo canceler (AEC) based on the least mean square (LMS) algorithm when there is an interference at the near end. The source of distortion may be linear, such as local speech or background noise, or nonlinear due to speech coding used in the telecommunication networks. Detailed derivation of the error recovery nonlinearity (ERN), which “enhances” the filter estimation error prior to the adaptation in order to assist the linear adaptation process, will be provided. Connections to other existing AEC and signal enhancement techniques will be revealed. In particular, the error enhancement technique is well-founded in the information-theoretic sense and has strong ties to independent component analysis (ICA), which is the basis for blind source separation (BSS) that permits unsupervised adaptation in the presence of multiple interfering signals. The single-channel AEC problem can be viewed as a special case of semi-blind source separation (SBSS) where one of the source signals is partially known, i.e., the far-end microphone signal that generates the near-end acoustic echo. The system approach to robust AEC will be motivated, where a proper integration of the LMS algorithm with the ERN into the AEC “system” allows for continuous and stable adaptation even during double talk without precise estimation of the signal statistics. The error enhancement paradigm encompasses many traditional signal enhancement techniques and opens up an entirely new avenue for solving the AEC problem in a real-world setting.

A Widely Linear Distortionless Filter for Single-Channel Noise Reduction

Traditionally in the single-channel noise-reduction problem, speech distortion is inevitable since the desired signal is also filtered while filtering the noise. In fact, the more the noise is reduced, the more the speech distortion is added into the desired signal, as proved in the literature. So, if we require no speech distortion, we either end up with no noise reduction at all or have to use multiple sensors. In this paper, we attempt to apply the widely linear (WL) estimation theory to noise reduction. Unlike the traditional approaches that only filter the short-time Fourier transform (STFT) of the noisy signal, the method developed in this paper applies the noise-reduction filter to both the STFT of the noisy signal and its conjugate. With the constraint of no speech distortion, a WL distortionless filter is derived. We show that this new optimal filter can fully take advantage of the noncircularity property of speech signals to achieve up to 3-dB signal-to-noise-ratio (SNR) improvement without introducing any speech distortion, which can only be obtained with the traditional approaches if two or more microphones are used.

Padé approximation of the S-matrix as a way of locating quantum resonances and bound states

It is shown that the spectral points (bound states and resonances) generated by a central potential of a single-channel problem, can be found using rational parametrization of the S-matrix. To achieve this, one only needs values of the S-matrix along the real positive energy axis. No calculations of the S-matrix at complex energies or a complex rotation are necessary. The proposed method is therefore universal in that it is applicable to any potential (local, non-local, discontinuous, etc) provided that there is a way of obtaining the S-matrix (or scattering phase shifts) at real collision energies. Besides this, combined with any method that extracts the phase shifts from the scattering data, the proposed rational parametrization technique would be able to do the spectral analysis using the experimental data.

Edge states and tunneling of non-Abelian quasiparticles in theν=5∕2quantum Hall state andp+ipsuperconductors

We study quasiparticle tunneling between the edges of a non-Abelian topological state. The simplest examples are a p+ip superconductor and the Moore-Read Pfaffian non-Abelian fractional quantum Hall state; the latter state may have been observed at Landau-level filling fraction nu=5/2. Formulating the problem is conceptually and technically non-trivial: edge quasiparticle correlation functions are elements of a vector space, and transform into each other as the quasiparticle coordinates are braided. We show in general how to resolve this difficulty and uniquely define the quasiparticle tunneling Hamiltonian. The tunneling operators in the simplest examples can then be rewritten in terms of a free boson. One key consequence of this bosonization is an emergent spin-1/2 degree of freedom. We show that vortex tunneling across a p+ip superconductor is equivalent to the single-channel Kondo problem, while quasiparticle tunneling across the Moore-Read state is analogous to the two-channel Kondo effect. Temperature and voltage dependences of the tunneling conductivity are given in the low- and high-temperature limits.