A Quaternion Weighted Fourier Linear Combiner for Modeling Physiological Tremor

Adhikari, Kabita; Tatinati, Sivanagaraja; Ang, Wei Tech; Veluvolu, Kalyana C.; Nazarpour, Kianoush

doi:10.1109/tbme.2016.2530564

Cited by 43 publications

(13 citation statements)

References 41 publications

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“…where q n ∈ H M×1 is a random quaternion vector that is i.i.d, zero-mean and independent of s n . The expression in (14) is an approximation of a Markov model given by [45] w n = Aw n−1 + q n (15) where the coefficient matrix A is assumed to be close to I M in a number of practical applications. For example, in modelling Rayleigh fading channels in a wireless communications environment, (15) is a first-order approximation of the variation of fading coefficients, and A is usually close to I M [29].…”

Section: Quaternion Adaptive Filtersmentioning

confidence: 99%

“…Recent research mainly focuses on adaptive filtering, neural networks, independent component analysis, and spectral estimation [6]- [11]. Quaternions have subsequently found new applications in communications, motion tracking, and biomedical engineering [12]- [15]. Recently, there have been recent extensive works on theory and applications of quaternion filters [16]- [20].…”

Section: Introductionmentioning

confidence: 99%

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Performance Analysis of Quaternion-Valued Adaptive Filters in Nonstationary Environments

Xiang

Kanna

Mandic

2018

IEEE Trans. Signal Process.

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Quaternion adaptive filters have been widely used for the processing of 3D and 4D phenomena, but complete analysis of their performance is still lacking, partly due to the cumbersomeness of multivariate quaternion analysis. This causes difficulties in both understanding their behaviour and designing optimal filters. Based on a thorough exploration of the augmented statistics of quaternion random vectors, this paper extends an analysis framework for real-valued adaptive filters to the mean and mean square convergence analyses of general quaternion adaptive filters in non-stationary environments. The extension is non-trivial, considering the non-commutative quaternion algebra, only recently resolved issues with quaternion gradient, and the multidimensional augmented quaternion statistics. Also, for rigour, in order to model a non-stationary environment, the system weights are assumed to vary according to a first-order random-walk model. Transient and steady-state performance of a general class of quaternion adaptive filters is provided by exploiting the augmented quaternion statistics. An innovative quaternion decorrelation technique allows us to develop intuitive closed-form expressions for the performance of quaternion least mean square (QLMS) filters with Gaussian inputs, which provide new insights into the relationship between the filter behaviour and the complete second-order statistics of the input signal, that is, quaternion noncircularity. The closed-form expressions for the performance of strictly linear, semi-widely linear, and widely linear QLMS filters are investigated in detail, while numerical simulations for the three classes of QLMS filters with correlated Gaussian inputs support the theoretical analysis.

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Section: Quaternion Adaptive Filtersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Performance Analysis of Quaternion-Valued Adaptive Filters in Nonstationary Environments

Xiang

Kanna

Mandic

2018

IEEE Trans. Signal Process.

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“…The position was calulated by the reflected infra-red rays onto the detectors. For more details please refer to [10]- [12].…”

Section: E Experimental Setupmentioning

confidence: 99%

“…This will further validate the performance of RSSA across a wide range of subjects. Other two main areas of investigation would include: investigating prediction algorithms to reduce the current delay offered by RSSA and extending the RSSA algorithm to multidimensional and quaternion RSSA, as our previous work shows processing tremor signal in the quaternion domain yields better results due to xyz cross-axis temporal dependency [12], [13].…”

Section: Future Workmentioning

confidence: 99%

Real-time physiological tremor estimation using recursive singular spectrum analysis

Adhikari

Tatinati

Veluvolu

et al. 2017

2017 39th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC)

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Physiological hand tremor causes undesirable vibration of hand-held surgical instruments which results in imprecisions and poor surgical outcomes. Existing tremor cancellation algorithms are based on detection of the tremulous component from the whole motion; then adding an anti-phase tremor signal to the whole motion to cancel it out. These techniques are based on adaptive filtering algorithms which need a reference signal that is highly correlated with the actual tremor signal. Hence, such adaptive approaches use a non-linear phase filter to pre-filter the tremor signal either offline or in real-time. However, pre-filtering causes unnecessary delays and non-linear phase distortions as the filter has frequency selective delays. Consequently, the anti-phase tremor signal cannot be generated accurately which results in poor tremor cancellation. In this paper, we present a new technique based on singular spectrum analysis (SSA) and its recursive version, that is, recursive singular spectrum analysis (RSSA). These algorithms decompose the whole motion into dominant voluntary components corresponding to larger eigenvalues and oscillatory tremor components having smaller eigenvalues. By selecting a group of specific decomposed signals based on their eigenvalues and spectral range, both voluntary and tremor signals can be reconstructed accurately. We test the SSA and RSSA algorithms using recorded tremor data from five novice subjects. This new approach shows the tremor signal can be estimated from the whole motion with an accuracy of up to 85% offline. In real-time, tolerating a delay of ≈ 72ms, the tremor signal can be estimated with at least 70% accuracy. This delay is found to be one-tenth of the delay caused by a conventional linear-phase bandpass filter to achieve similar performance in real-time.

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“…Hence, to track the non-stationary tremor, they utilised an adaptive filtering approach called a weighted Fourier linear combiner (wFLC) [6]. In recent years, wFLC has been extended to autoregressive [27], bandlimited [28]- [30] and quaternion [31] versions. To function accurately, all of these adaptive techniques required a reference tremor signal, which was generated by pre-filtering the whole motion with an infinite impulse response (IIR) filter.…”

Section: Introductionmentioning

confidence: 99%

Physiological Tremor Filtering Without Phase Distortion for Robotic Microsurgery

Adhikari

Tatinati

Veluvolu

et al. 2022

IEEE Trans. Automat. Sci. Eng.

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All existing physiological tremor filtering algorithms, developed for robotic microsurgery, use non-linear phase pre-filters to isolate the tremor signal. Such filters cause phase distortion to the filtered tremor signal and limit the filtering accuracy. We revisited this long-standing problem to enable filtering of the physiological tremor without any phase distortion. We developed a combined estimation-prediction paradigm that offers zero-phase type filtering. The estimation is achieved with the mathematically modified recursive singular spectrum analysis algorithm and the prediction is delivered with the standard extreme learning machine. In addition, to limit the computational cost; we developed two moving window versions of this structure, appropriate for real-time implementation. The proposed paradigm preserved the natural phase of the filtered tremor. It achieved the key performance index of error limitation below 10µm, yielding the estimation accuracy larger than 70%, at a time delay of 36ms only. Both moving window versions of the proposed approach restricted the computational cost considerably; whilst offering the same performance. It is for the first time that effective estimation of the physiological tremor is achieved, without any pre-filtering and phase distortion. This proposed method is feasible for real-time implantation. Clinical translation of the proposed paradigm can significantly enhance the outcome in hand-held surgical robotics. Note to Practitioners-The imprecision caused by physiological hand tremor in microsurgeries has motivated researchers to innovate an efficient tremor compensating technique that can improve the surgical performance. Yet, all the existing tremor filtering algorithms, implemented in hand-held surgical instruments, use non-linear phase pre-filters to separate the tremor signal. The inherent phase distortion caused by such pre-filters restricts the filtering performance significantly and renders the existing methods inadequate for hand-held robotic surgery. Motivated by this, we proposed a novel estimator-predictor based framework, by adopting the modified recursive singular spectrum analysis estimator and the extreme learning machine predictor. The proposed framework filters the tremor signal accurately, without distorting it, but at a small fixed lag. In a set of rigorous testing performed by emulating a real-time processing, the proposed Manuscript received August 29, 2019.

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A Quaternion Weighted Fourier Linear Combiner for Modeling Physiological Tremor

Abstract: By taking into account interactions of the 3-D tremor and the force data, the tremor modeling performance enhances significantly.

Cited by 43 publications

References 41 publications

Performance Analysis of Quaternion-Valued Adaptive Filters in Nonstationary Environments

Performance Analysis of Quaternion-Valued Adaptive Filters in Nonstationary Environments

Real-time physiological tremor estimation using recursive singular spectrum analysis

Physiological Tremor Filtering Without Phase Distortion for Robotic Microsurgery

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