TY - JOUR
T1 - Real-Time dynamics acquisition from irregular samples-With application to anesthesia evaluation
AU - Chui, Charles K.
AU - Lin, Yu Ting
AU - Wu, Hau Tieng
N1 - Publisher Copyright:
© 2016 World Scientific Publishing Company.
PY - 2016/7/1
Y1 - 2016/7/1
N2 - Although most digital representations of information sources are obtained by uniform sampling of some continuous function representations, there are many important events for which only irregular data samples are available, including trading data of the financial market and various clinical data, such as the respiration signals hidden in ECG measurements. For such digital information sources, the only available effective smooth function interpolation scheme for digital-To-Analog (D/A) conversion algorithms are mainly for offline applications. Hence, in order to adapt the powerful continuous-function mathematical approaches for real-Time applications, it is necessary to introduce an effective D/A conversion scheme as well as to modify the desired continuous-function mathematical method for online implementation. The powerful signal processing tool to be discussed in this paper is the synchrosqueezed continuous wavelet transform (SST), which requires computation of the continuous wavelet transform (CWT), as well as its derivative, of the analog signal of interest. An important application of this transform is to extract information, such as the underlying dynamics, hidden in the signal representation. The first objective of this paper is to introduce a unified approach to remove the two main obstacles for adapting the SST approach to irregular data samples in order to allow online computation. Firstly, for D/A conversion, a real-Time algorithm, based on spline functions of arbitrarily desired order, is proposed to interpolate the irregular data samples, while preserving all polynomials of the same spline order, with assured maximum order of approximation. Secondly, for real-Time dynamic information extraction from an oscillatory signal via SST, a family of vanishing-moment and minimum-supported spline-wavelets (to be called VM wavelets) are introduced for online computation of the CWT and its derivative. The second objective of this paper is to apply the proposed real-Time algorithm and VM wavelets to clinical applications, particularly to the study of the "anesthetic depth" of a patient during surgery, with emphasis on analyzing two dynamic quantities: The "instantaneous frequencies" and the "non-rhythmic to rhythmic ratios" of the patient's respiration, based on a one-lead electrocardiogram (ECG) signal. Indeed, the "R-peaks" of the ECG signal, which constitute a waveform landmark for clinical evaluation, are non-uniform samples of the respiratory signal. It is envisioned that the proposed algorithm and VM wavelets should enable real-Time monitoring of "anesthetic depth", during surgery, from the respiration signal via ECG measurement.
AB - Although most digital representations of information sources are obtained by uniform sampling of some continuous function representations, there are many important events for which only irregular data samples are available, including trading data of the financial market and various clinical data, such as the respiration signals hidden in ECG measurements. For such digital information sources, the only available effective smooth function interpolation scheme for digital-To-Analog (D/A) conversion algorithms are mainly for offline applications. Hence, in order to adapt the powerful continuous-function mathematical approaches for real-Time applications, it is necessary to introduce an effective D/A conversion scheme as well as to modify the desired continuous-function mathematical method for online implementation. The powerful signal processing tool to be discussed in this paper is the synchrosqueezed continuous wavelet transform (SST), which requires computation of the continuous wavelet transform (CWT), as well as its derivative, of the analog signal of interest. An important application of this transform is to extract information, such as the underlying dynamics, hidden in the signal representation. The first objective of this paper is to introduce a unified approach to remove the two main obstacles for adapting the SST approach to irregular data samples in order to allow online computation. Firstly, for D/A conversion, a real-Time algorithm, based on spline functions of arbitrarily desired order, is proposed to interpolate the irregular data samples, while preserving all polynomials of the same spline order, with assured maximum order of approximation. Secondly, for real-Time dynamic information extraction from an oscillatory signal via SST, a family of vanishing-moment and minimum-supported spline-wavelets (to be called VM wavelets) are introduced for online computation of the CWT and its derivative. The second objective of this paper is to apply the proposed real-Time algorithm and VM wavelets to clinical applications, particularly to the study of the "anesthetic depth" of a patient during surgery, with emphasis on analyzing two dynamic quantities: The "instantaneous frequencies" and the "non-rhythmic to rhythmic ratios" of the patient's respiration, based on a one-lead electrocardiogram (ECG) signal. Indeed, the "R-peaks" of the ECG signal, which constitute a waveform landmark for clinical evaluation, are non-uniform samples of the respiratory signal. It is envisioned that the proposed algorithm and VM wavelets should enable real-Time monitoring of "anesthetic depth", during surgery, from the respiration signal via ECG measurement.
KW - anesthesia depth
KW - Blending operator
KW - real-Time EDR algorithm
KW - real-Time time frequency analysis
KW - synchrosqueezing transform
KW - VM wavelet
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U2 - 10.1142/S0219530515500165
DO - 10.1142/S0219530515500165
M3 - Article
AN - SCOPUS:84948401909
SN - 0219-5305
VL - 14
SP - 537
EP - 590
JO - Analysis and Applications
JF - Analysis and Applications
IS - 4
ER -