Semi-classical signal analysis
01 Mar 2013-Mathematics of Control, Signals, and Systems (Springer-Verlag)-Vol. 25, Iss: 1, pp 37-61
TL;DR: In this paper, a semi-classical approach based on the potential of a Schrodinger operator was proposed for signal analysis of arterial blood pressure waveforms, and the first results obtained with this method on the analysis of the waveform were presented.
Abstract: This study introduces a new signal analysis method, based on a semi-classical approach. The main idea in this method is to interpret a pulse-shaped signal as a potential of a Schrodinger operator and then to use the discrete spectrum of this operator for the analysis of the signal. We present some numerical examples and the first results obtained with this method on the analysis of arterial blood pressure waveforms.
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TL;DR: A reduced-order model algorithm, called ALP, is proposed to solve nonlinear evolution partial differential equations, based on approximations of generalized Lax pairs, which is well-suited to solving problems with progressive front or wave propagation.
66 citations
TL;DR: Machine learning of action potential recordings in patients revealed novel phenotypes for long-term outcomes in ischemic cardiomyopathy, which may reveal cellular mechanisms for clinical outcomes and could be applied to other conditions.
Abstract: Rationale: Susceptibility to VT/VF (ventricular tachycardia/fibrillation) is difficult to predict in patients with ischemic cardiomyopathy either by clinical tools or by attempting to translate cel...
33 citations
TL;DR: A new post‐processing technique called semi‐classical signal analysis (SCSA) for MRS data de‐noising that decomposes the input real positive MR spectrum into set of linear combinations of squared eigenfunctions equivalently represented by localized functions with shape derived from the potential function of the Schrödinger operator.
Abstract: In this paper, we propose a new post-processing technique called semi-classical signal analysis (SCSA) for MRS data de-noising. Similar to Fourier transformation, SCSA decomposes the input real positive MR spectrum into a set of linear combinations of squared eigenfunctions equivalently represented by localized functions with shape derived from the potential function of the Schrodinger operator. In this manner, the MRS spectral peaks represented as a sum of these 'shaped like' functions are efficiently separated from noise and accurately analyzed. The performance of the method is tested by analyzing simulated and real MRS data. The results obtained demonstrate that the SCSA method is highly efficient in localized MRS data de-noising and allows for an accurate data quantification.
27 citations
TL;DR: Wang et al. as mentioned in this paper developed and tested two frameworks for arterial blood pressure (ABP) estimation at the central arteries using photoplethysmography and electrocardiogram.
Abstract: Background and objective: Blood pressure (BP) is one of the crucial indicators that contains valuable medical information about cardiovascular activities. Developing photoplethysmography (PPG)-based cuffless BP estimation algorithms with enough robustness and accuracy is clinically useful in practice, due to its simplicity and noninvasiveness. In this paper, we have developed and tested two frameworks for arterial blood pressure (ABP) estimation at the central arteries using photoplethysmography and electrocardiogram. Methods: Supervised learning, as adapted by most studies regarding this topic, is introduced by comparing three machine learning algorithms. Features are extracted using semi-classical signal analysis (SCSA) tools. To further increase the accuracy of estimation, another BP estimation algorithm is presented. A single feed-forward neural network (FFNN) is utilized for BP regression with PPG features, which are extracted by SCSA and later used by FFNN as the network input. Both BP estimation algorithms perform robustly against MIMIC II database to guarantee statistical reliability. Results: We evaluated the performance against the Advancement of Medical Instrumentation (AAMI) and British Hypertension Society (BHS) standards, and we have compared the standard deviation (STD) of estimation error with current state of the arts. With the AAMI standard, the first method yields comparable performance against existing literature in the estimation of BP values. Regarding the BHS protocol, the second method achieves grade A in the estimation of BP values. Conclusion: We conclude that by using the PPG signal in combination with informative features from the Schrodinger’s spectrum, the BP can be non-invasively estimated in a reliable and accurate way. Furthermore, the proposed frameworks could potentially enable applications of cuffless estimation of the BP and development of mobile healthcare device.
26 citations
TL;DR: An algorithm based on the tensor product approach when writing the eigenfunctions of the semi-classical Schrodinger operator is proposed and the effect of some parameters on the convergence of this method are numerically studied.
18 citations
References
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Book•
01 Jan 1965
TL;DR: The basic concepts of quantum mechanics Energy and momentum Schrodinger's equation Angular momentum Perturbation theory Spin The identity of particles The atom The theory of symmetry Polyatomic molecules Motion in a magnetic field Nuclear structure Elastic collisions Mathematical appendices.
Abstract: The basic concepts of quantum mechanics Energy and momentum Schrodinger's equation Angular momentum Perturbation theory Spin The identity of particles The atom The theory of symmetry Polyatomic molecules Motion in a magnetic field Nuclear structure Elastic collisions Mathematical appendices.
5,955 citations
Book•
01 Jan 2000TL;DR: This paper presents a meta-analyses of Chebyshev differentiation matrices using the DFT and FFT as a guide to solving fourth-order grid problems.
Abstract: Preface 1 Differentiation matrices 2 Unbounded grids: the semidiscrete Fourier transform 3 Periodic grids: the DFT and FFT 4 Smoothness and spectral accuracy 5 Polynomial interpolation and clustered grids 6 Chebyshev differentiation matrices 7 Boundary value problems 8 Chebyshev series and the FFT 9 Eigenvalues and pseudospectra 10 Time-stepping and stability regions 11 Polar coordinates 12 Integrals and quadrature formulas 13 More about boundary conditions 14 Fourth-order problems Afterword Bibliography Index
3,696 citations