Zhenghan Zhu

Emulating conventional disc electrode with the outer ring of the tripolar concentric ring electrode in phantom and human electroencephalogram data

Conventional electroencephalography (EEG) with disc electrodes has major drawbacks including poor spatial resolution, selectivity and low signal-to-noise ratio that critically limit its use. Concentric ring electrodes are a promising alternative with potential to improve all of the aforementioned aspects significantly. In our previous work, the tripolar concentric ring electrode (TCRE) was successfully used in a wide range of applications demonstrating its superiority to conventional disc electrodes, in particular, in accuracy of Laplacian estimation (tEEG). For applications that may benefit from simultaneous recording of EEG and tEEG in this paper we propose to use the signal from the outer ring of the TCRE as an emulation (eEEG) of EEG recorded using conventional disc electrodes. This will allow us to record EEG emulation from the exact same locations at the exact same time as the tEEG using a single recording system. Time domain neuronal signal synchrony was measured using cross-correlation in phantom and human experiments suggesting the potential of eEEG as an emulation of EEG.

Estimate the degree of noncircularity of complex-valued vectors via exponentially embedded family

Complex-valued signal processing is a fundamental task in many signal processing areas such as radar, sonar and communications. Modeling complex data as noncircular may provide better fitting of physical conditions. However, it requires more complicated signal processing algorithms and hence has more computations. Testing of noncircularity and estimating its degree are helpful in choosing a model. In this paper we focus on estimating the degree of noncircularity if the data is decided noncircular. It essentially a model order selection problem; therefore, we adopt the recently proposed exponentially embedded family (EEF) rule. Computer simulations are given to evaluate the EEFs performance and compare it with the minimum description length (MDL).

Information-Theoretic Optimal Radar Waveform Design

In this letter, we address the problem of designing the optimal radar waveform for the detection of an extended target in a colored noise environment. The locally most powerful detector and the corresponding optimal waveform based on maximizing the detectors performance under a small-signal assumption are derived. The performance is evaluated analytically, and numerically compared with that of the mutual information based method. The locally most powerful detection metric is shown to be the Kullback–Leibler divergence. The use of the latter measure leads to a substantial performance improvement. Moreover, a useful relationship among the three existing waveform design metrics, namely the output signal-to-noise ratio, the Kullback–Leibler divergence, and the mutual information, is provided. It explains the tradeoffs of the various metrics currently used for radar waveform design.

The Complex Parameter Rao Test

The Rao test is an important method in signal detection in the presence of unknown parameters. The traditional approach to the problem when the unknown parameters are complex valued is to form a corresponding real-valued parameter vector and then to use the real Rao test. Alternatively, we present a complex parameter Rao test by reformulating the calculations with respect to the complex-valued quantities directly. Two important examples of the application of the complex parameter Rao test are given to illustrate the procedure.

Feasibility of recording high frequency oscillations with tripolar concentric ring electrodes during pentylenetetrazole-induced seizures in rats

As epilepsy remains a refractory condition in about 30% of patients with complex partial seizures, electrical stimulation of the brain has recently shown potential for additive seizure control therapy. Previously, we applied noninvasive transcranial focal stimulation via novel tripolar concentric ring electrodes (TCREs) on the scalp of rats after inducing seizures with pentylenetetrazole (PTZ). We developed a close-loop system to detect seizures and automatically trigger the stimulation and evaluated its effect on the electrographic activity recorded by TCREs in rats. In our previous work the detectors of seizure onset were based on seizure-induced changes in signal power in the frequency range up to 100 Hz, while in this preliminary study we assess the feasibility of recording high frequency oscillations (HFOs) in the range up to 300 Hz noninvasively with scalp TCREs during PTZ-induced seizures. Grand average power spectral density estimate and generalized likelihood ratio tests were used to compare power of electrographic activity at different stages of seizure development in a group of rats (n= 8). The results suggest that TCREs have the ability to record HFOs from the scalp as well as that scalp-recorded HFOs can potentially be used as features for seizure onset detection.

The penalty term of Exponentially Embedded Family is estimated mutual information

The penalty term plays an important role in model order selection rules. The Exponentially Embedded Families (EEF) is consistent and effective in model order selection. In this paper we show that the EEF penalty term can be viewed as estimated mutual information (MI) between unknown parameters and received data from Bayesian viewpoints. The finding is a result of an important relationship between Kullback-Leibler Divergence (KLD), signal-to-noise ratio (SNR) and MI in estimation/detection of random signals, which is also introduced.

On detection of nonstationarity in radar signal processing

Space-time adaptive processing (STAP) has become a leading technique in airborne radar signal processing. The optimality of the STAP assumes the stationarity of the covariance matrices. In practice, however, the covariance matrices may be nonstationary. If such nonstationarity is not detected and not well treated, the STAP systems performance decreases substantially. In this paper, we present two detectors for detecting the covariance matrix nonstationarity. We form the first detector based on generalized likelihood ratio test, which inherits the property of asymptotically optimal detection performance. A second detector employs Rao test and requires significantly less computation than the first detector, which can be the favorable choice when computation load is of concern to the signal processing system.

Frequency domain synchrony between signals from the conventional disc electrode and the outer ring of the tripolar concentric ring electrode in human electroencephalogram data

For applications that may benefit from simultaneous recording of conventional electroencephalography (EEG) and tEEG, Laplacian EEG with tripolar concentric ring electrodes (TCREs), we proposed to use the signal from the outer ring of the TCRE as an emulation (eEEG) of EEG recorded using conventional disc electrodes. This allows recording EEG emulation from the exact same locations at the exact same time as the tEEG using a single recording system. In our previous work, time domain neuronal signal synchrony was assessed in phantom and human experiments suggesting the potential of eEEG as an emulation of EEG. In this paper, frequency domain neuronal signal synchrony was measured using coherence in human experiments further suggesting the potential of eEEG (C ≥ 0.98).

Equivalency Between Emulated Disc Electrodes and Conventional Disc Electrode Human Electroencephalography

We have previously shown that tripolar concentric ring electrode (TCRE) Laplacian electroencephalography (tEEG) has significantly better signal-to-noise ratio, spatial resolution, and mutual information than disc electrode electroencephalography (EEG). This paper compares the EEG signals acquired simultaneously from the outer ring of the TCRE (oTCRE), shorting all three elements of the TCRE (sTCRE) and disc electrode (disc) concurrently from nearly the same location on the human scalp. We calculated the average correlation for the time series between each pair of signals and average coherence over the pass-band frequencies between all pairs of signals as well. All the correlations and coherences were above 0.99. The results suggest that the oTCRE can be used to record EEG concurrently with tEEG from the same sensor at the same location.

The Rao test for testing handedness of complex-valued covariance matrix

Banding the inverse of covariance matrix has become a popular technique to estimate a high dimensional covariance matrix from limited number of samples. However, little work has been done in providing a criterion to determine when a matrix is bandable. In this paper, we present a detector to test the bandedness of a Cholesky factor matrix. The test statistic is formed based on the Rao test, which does not require the maximum likelihood estimates under the alternative hypothesis. In many fields, such as radar signal processing, the covariance matrix and its unknown parameters are often complex-valued. We focus on dealing with complex-valued cases by utilizing the complex parameter Rao test, instead of the traditional real Rao test. This leads to a more intuitive and efficient test statistic. Examples and computer simulations are given to investigate the derived detector performance.