1,721,001 research outputs found
Parametric estimation of sample entropy in heart rate variability analysis
No full textIn this paper, a detailed study on the possibility and significance of performing a parametric estimation of sample entropy (SampEn) is proposed. SampEn is a non-linear metric, meant to quantify regularity of a time series. It is widely employed on biomedical signals, especially on heart rate variability. Results relevant to approximate entropy, a related index, are also reported. An analytical expression for SampEn of an autoregressive (AR) model is derived first. Then we study the feasibility of a parametric estimation of SampEn through AR models, both on synthetic and real series. RR series of different lengths are fitted to an AR model and then expected values of SampEn (SampEnμ) are estimated. Values of SampEn, computed from real beat-to-beat interval time series (obtained from 72 normal subjects and 29 congestive heart failure patients), with m = 1 and r = 0.2, are within the standard range of SampEnμ more than 83% (for series length N = 75) and 28% (for N = 1500) of the cases. Surrogate data have been employed to verify if departures from Gaussianity are to account for the mismatch. The work supports the finding that when numerical and parametric estimates of SampEn agree, SampEn is mainly influenced by linear properties of the series. A disagreement, on the contrary, might point those cases where SampEn is truly offering new information, not readily available with traditional temporal and spectral parameters
Sample entropy parametric estimation for heart rate variability analysis
Full text linkAims: Sample Entropy (SampEn) is a powerful approach for characterizing heart rate variability regularity. On the other hand, autoregressive (AR) models have been employed for maximum-entropy spectral estimation for more than 40 years. The aim of this study is to explore the feasibility of a parametric approach for SampEn estimation through AR models. We re-analyze the Physionet paroxysmal Atrial Fibrillation (AF) database, where RR series are provided before and after an AF episode, for 25 patients. In particular, we selected short RR series, close to AF episodes, to fit an AR model. Then, theoretical values of SampEn, based on each AR model, were analytically derived (SE th) and also estimated numerically (SEsyn). The value of SampEn (SErr), computed on the 50 RR series with r=0.2×STD, m=1 and N=120, were within the standard range of SEsyn in 30 cases (39 for SEth). This figure increased to 82% of cases, if shorter series were selected (N=75), and if RR series were replaced by surrogates with Gaussian amplitude distribution. Interestingly, without removing ectopic beats, every estimate of SampEn considered was significantly different between pre- and post- AF (SErr: p=0.02; SEsyn: p=0.0024; SEth: p=0.023). When an AR model is appropriate and theoretical estimates differ from numerical ones, a parametric approach might enlighten additional information brought by SampEn
FEATURE EXTRACTION AND CLASSIFICATION THROUGH ENTROPY MEASURES
Full text linkEntropy is a universal concept that represents the uncertainty of a series of random
events. The notion “entropy" is differently understood in different disciplines. In physics,
it represents the thermodynamical state variable; in statistics it measures the degree of
disorder. On the other hand, in computer science, it is used as a powerful tool for measuring
the regularity (or complexity) in signals or time series. In this work, we have
studied entropy based features in the context of signal processing.
The purpose of feature extraction is to select the relevant features from an entity. The
type of features depends on the signal characteristics and classification purpose. Many
real world signals are nonlinear and nonstationary and they contain information that
cannot be described by time and frequency domain parameters, instead they might be
described well by entropy.
However, in practice, estimation of entropy suffers from some limitations and is
highly dependent on series length. To reduce this dependence, we have proposed parametric
estimation of various entropy indices and have derived analytical expressions
(when possible) as well. Then we have studied the feasibility of parametric estimations
of entropy measures on both synthetic and real signals. The entropy based features
have been finally employed for classification problems related to clinical applications,
activity recognition, and handwritten character recognition. Thus, from a methodological
point of view our study deals with feature extraction, machine learning, and classification
methods.
The different versions of entropy measures are found in the literature for signals analysis.
Among them, approximate entropy (ApEn), sample entropy (SampEn) followed
by corrected conditional entropy (CcEn) are mostly used for physiological signals analysis.
Recently, entropy features are used also for image segmentation. A related measure
of entropy is Lempel-Ziv complexity (LZC), which measures the complexity of a
time-series, signal, or sequences. The estimation of LZC also relies on the series length.
In particular, in this study, analytical expressions have been derived for ApEn, SampEn,
and CcEn of an auto-regressive (AR) models. It should be mentioned that AR
models have been employed for maximum entropy spectral estimation since many
years. The feasibility of parametric estimates of these entropy measures have been
studied on both synthetic series and real data. In feasibility study, the agreement between
numeral estimates of entropy and estimates obtained through a certain number
of realizations of the AR model using Montecarlo simulations has been observed. This
agreement or disagreement provides information about nonlinearity, nonstationarity,
or nonGaussinaity presents in the series. In some classification problems, the probability
of agreement or disagreement have been proved as one of the most relevant
features.
VII
After feasibility study of the parametric entropy estimates, the entropy and related
measures have been applied in heart rate and arterial blood pressure variability analysis.
The use of entropy and related features have been proved more relevant in developing
sleep classification, handwritten character recognition, and physical activity
recognition systems.
The novel methods for feature extraction researched in this thesis give a good classification
or recognition accuracy, in many cases superior to the features reported in the
literature of concerned application domains, even with less computational costs
Bubble entropy : an entropy almost free of parameters
No full textObjective: A critical point in any definition of entropy is the selection of the parameters employed to obtain an estimate in practice. We propose a new definition of entropy aiming to reduce the significance of this selection. Methods: We call the new definition Bubble Entropy. Bubble Entropy is based on Permutation Entropy, where the vectors in the embedding space are ranked. We use the bubble sort algorithm for the ordering procedure and count instead the number of swaps performed for each vector. Doing so, we create a more coarse-grained distribution and then compute the entropy of this distribution. Results: Experimental results with both real and synthetic HRV signals showed that Bubble Entropy presents remarkable stability and exhibits increased descriptive and discriminating power compared to all other definitions, including the most popular ones. Conclusion: The definition proposed is almost free of parameters. The most common ones are the scale factor r and the embedding dimension m . In our definition, the scale factor is totally eliminated and the importance of m is significantly reduced. The proposed method presents increased stability and discriminating power. Significance: After the extensive use of some entropy measures in physiological signals, typical values for their parameters have been suggested, or at least, widely used. However, the parameters are still there, application and dataset dependent, influencing the computed value and affecting the descriptive power. Reducing their significance or eliminating them alleviates the problem, decoupling the method from the data and the application, and eliminating subjective factors
A new technique for segmentation of handwritten numerical strings of bangla language
No full textSegmentation of handwritten input into individual characters is a crucial step in connected handwriting recognition systems. In this paper we propose a robust scheme to segment handwritten Bangla numbers (numerical strings) against the variability involved in the writing style of different individuals. The segmentation of digits from a number is usually very tricky, as the digits in a Bangla number are seldom vertically separable. We have introduced the concept of Degenerated Lower Chain (DLC) for this purpose. The DLC method was proved efficient in case of segmenting handwriting digits in our experiments. Ten pages of handwritten Bangla numerical strings containing 2000 individual digits that construct 700 numbers written by five different writers of variable ages were segmented by the developed system. The system achieves more than 90% segmentation accuracy on average
Handwritten Character Recognition System for Bangla Text Containing Modifiers and Overlapped Characters
No full textThis paper deals with the design and development of a Bangla offline Handwritten Character Segmentation system.
Special focus of this work was on skewed text containing modifier and overlapped characters. The text pages were scanned using flatbed scanner and saved as 256 gray-level image in bmp file format. This image file was used as the input to the developed system. In order to segment the skewed lines, the text was divided into a number of vertical stripes called frame. Each frame was segmented by horizontal pixel scanning method and concatenated in proper order to form the original text line. Based on vertical pixel scanning method lines were segmented into words. In character segmentation, isolated characters were segmented by vertical scanning method but connected and overlapped characters are segmented using degenerated lower chain. The system was tested for handwritten text pages of five individual writers. The average segmentation accuracy rate of the system was about 94%
Low Computational Cost for Sample Entropy
Full text linkSample Entropy is the most popular definition of entropy and is widely used as a measure of the regularity/complexity of a time series. On the other hand, it is a computationally expensive method which may require a large amount of time when used in long series or with a large number of signals. The computationally intensive part is the similarity check between points in m dimensional space. In this paper, we propose new algorithms or extend already proposed ones, aiming to compute Sample Entropy quickly. All algorithms return exactly the same value for Sample Entropy, and no approximation techniques are used. We compare and evaluate them using cardiac inter-beat (RR) time series. We investigate three algorithms. The first one is an extension of the k d -trees algorithm, customized for Sample Entropy. The second one is an extension of an algorithm initially proposed for Approximate Entropy, again customized for Sample Entropy, but also improved to present even faster results. The last one is a completely new algorithm, presenting the fastest execution times for specific values of m, r, time series length, and signal characteristics. These algorithms are compared with the straightforward implementation, directly resulting from the definition of Sample Entropy, in order to give a clear image of the speedups achieved. All algorithms assume the classical approach to the metric, in which the maximum norm is used. The key idea of the two last suggested algorithms is to avoid unnecessary comparisons by detecting them early. We use the term unnecessary to refer to those comparisons for which we know a priori that they will fail at the similarity check. The number of avoided comparisons is proved to be very large, resulting in an analogous large reduction of execution time, making them the fastest algorithms available today for the computation of Sample Entropy
Implementation of radon transformation for electrical impedence tomography (EIT)
No full textRadon Transformation is generally used to construct optical image (like CT image) from the projection data in biomedical imaging. In this paper, the concept of Radon Transformation is implemented to reconstruct Electrical Impedance Topographic Image (conductivity or resistivity distribution) of a circular subject. A parallel resistance model of a subject is proposed for Electrical Impedance Topography(EIT) or Magnetic Induction Tomography(MIT). A circular subject with embedded circular objects is segmented into equal width slices from different angles. For each angle, Conductance and Conductivity of each slice is calculated and stored in an array. A back projection method is used to generate a two-dimensional image from one-dimensional projections. As a back projection method, Inverse Radon Transformation is applied on the calculated conductance and conductivity to reconstruct two dimensional images. These images are compared to the target image. In the time of image reconstruction, different filters are used and these images are compared with each other and target image
Effects of the series length on Lempel-Ziv complexity during sleep
No full textLempel-Ziv Complexity (LZC) has been demonstrated to be a powerful complexity measure in several biomedical applications. During sleep, it is still not clear how many samples are required to ensure robustness of its estimate when computed on beat-to-beat interval series (RR). The aims of this study were: i) evaluation of the number of necessary samples in different sleep stages for a reliable estimation of LZC; ii) evaluation of the LZC when considering inter-subject variability; and iii) comparison between LZC and Sample Entropy (SampEn). Both synthetic and real data were employed. In particular, synthetic RR signals were generated by means of AR models fitted on real data. The minimum number of samples required by LZC for having no changes in its average value, for both NREM and REM sleep periods, was 104 (p1000 when a tolerance of 5% is considered satisfying. The influence of the inter-subject variability on the LZC was first assessed on model generated data confirming what found (>104; p<;0.01) for both NREM and REM stage. However, on real data, without differentiate between sleep stages, the minimum number of samples required was 1.8×104. The linear correlation between LZC and SampEn was computed on a synthetic dataset. We obtained a correlation higher than 0.75 (p<;0.01) when considering sleep stages separately, and higher than 0.90 (p<;0.01) when stages were not differentiated. Summarizing, we suggest to use LZC with the binary quantization and at least 1000 samples when a variation smaller than 5% is considered satisfying, or at least 104 for maximal accuracy. The use of more than 2 levels of quantization is not recommended
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