Analysis of cardiac and epileptic signals using higher order spectra

The theory of nonlinear dyamic systems provides some new methods to handle complex systems. Chaos theory offers new concepts, algorithms and methods for processing, enhancing and analyzing the measured signals. In recent years, researchers are applying the concepts from this theory to bio-signal analysis. In this work, the complex dynamics of the bio-signals such as electrocardiogram (ECG) and electroencephalogram (EEG) are analyzed using the tools of nonlinear systems theory. In the modern industrialized countries every year several hundred thousands of people die due to sudden cardiac death. The Electrocardiogram (ECG) is an important biosignal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computerbased intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and four classes of arrhythmia. This thesis presents some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. Several features were extracted from the HOS and subjected an Analysis of Variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, seven features were extracted from the heart rate signals using HOS and fed to a support vector machine (SVM) for classification. The performance evaluation protocol in this thesis uses 330 subjects consisting of five different kinds of cardiac disease conditions. The classifier achieved a sensitivity of 90% and a specificity of 89%. This system is ready to run on larger data sets. In EEG analysis, the search for hidden information for identification of seizures has a long history. Epilepsy is a pathological condition characterized by spontaneous and unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic early detection of the seizure onsets would help the patients and observers to take appropriate precautions. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, these features are used to train both a Gaussian mixture model (GMM) classifier and a Support Vector Machine (SVM) classifier. Results show that the classifiers were able to achieve 93.11% and 92.67% classification accuracy, respectively, with selected HOS based features. About 2 hours of EEG recordings from 10 patients were used in this study. This thesis introduces unique bispectrum and bicoherence plots for various cardiac conditions and for normal, background and epileptic EEG signals. These plots reveal distinct patterns. The patterns are useful for visual interpretation by those without a deep understanding of spectral analysis such as medical practitioners. It includes original contributions in extracting features from HRV and EEG signals using HOS and entropy, in analyzing the statistical properties of such features on real data and in automated classification using these features with GMM and SVM classifiers.

Cardiac state diagnosis using higher order spectra of heart rate variability

Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart, by the sympathetic and parasympathetic branches of the autonomic nervous system. Heart rate variability analysis is an important tool to observe the heart's ability to respond to normal regulatory impulses that affect its rhythm. A computer-based intelligent system for analysis of cardiac states is very useful in diagnostics and disease management. Like many bio-signals, HRV signals are nonlinear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of nonlinear systems and provides good noise immunity. In this work, we studied the HOS of the HRV signals of normal heartbeat and seven classes of arrhythmia. We present some general characteristics for each of these classes of HRV signals in the bispectrum and bicoherence plots. We also extracted features from the HOS and performed an analysis of variance (ANOVA) test. The results are very promising for cardiac arrhythmia classification with a number of features yielding a p-value < 0.02 in the ANOVA test.

Cardiac health diagnosis using higher order spectra and support vector machine

The Electrocardiogram (ECG) is an important bio-signal representing the sum total of millions of cardiac cell depolarization potentials. It contains important insight into the state of health and nature of the disease afflicting the heart. Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. The HRV signal can be used as a base signal to observe the heart's functioning. These signals are non-linear and non-stationary in nature. So, higher order spectral (HOS) analysis, which is more suitable for non-linear systems and is robust to noise, was used. An automated intelligent system for the identification of cardiac health is very useful in healthcare technology. In this work, we have extracted seven features from the heart rate signals using HOS and fed them to a support vector machine (SVM) for classification. Our performance evaluation protocol uses 330 subjects consisting of five different kinds of cardiac disease conditions. We demonstrate a sensitivity of 90% for the classifier with a specificity of 87.93%. Our system is ready to run on larger data sets.

Application of higher order spectra to identify epileptic EEG

Epilepsy is characterized by the spontaneous and seemingly unforeseeable occurrence of seizures, during which the perception or behavior of patients is disturbed. An automatic system that detects seizure onsets would allow patients or the people near them to take appropriate precautions, and could provide more insight into this phenomenon. Various methods have been proposed to predict the onset of seizures based on EEG recordings. The use of nonlinear features motivated by the higher order spectra (HOS) has been reported to be a promising approach to differentiate between normal, background (pre-ictal) and epileptic EEG signals. In this work, we made a comparative study of the performance of Gaussian mixture model (GMM) and Support Vector Machine (SVM) classifiers using the features derived from HOS and from the power spectrum. Results show that the selected HOS based features achieve 93.11% classification accuracy compared to 88.78% with features derived from the power spectrum for a GMM classifier. The SVM classifier achieves an improvement from 86.89% with features based on the power spectrum to 92.56% with features based on the bispectrum.

Higher order spectra based support vector machine for arrhythmia classification

Heart rate variability (HRV) refers to the regulation of the sinoatrial node, the natural pacemaker of the heart by the sympathetic and parasympathetic branches of the autonomic nervous system. HRV analysis is an important tool to observe the heart’s ability to respond to normal regulatory impulses that affect its rhythm. Like many bio-signals, HRV signals are non-linear in nature. Higher order spectral analysis (HOS) is known to be a good tool for the analysis of non-linear systems and provides good noise immunity. A computer-based arrhythmia detection system of cardiac states is very useful in diagnostics and disease management. In this work, we studied the identification of the HRV signals using features derived from HOS. These features were fed to the support vector machine (SVM) for classification. Our proposed system can classify the normal and other four classes of arrhythmia with an average accuracy of more than 85%.

Shape discrimination using invariants defined from higher-order spectra

An approach to pattern recognition using invariant parameters based on higher-order spectra is presented. In particular, bispectral invariants are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale- and amplification-invariant. A minimal set of these invariants is selected as the feature vector for pattern classification. Pattern recognition using higher-order spectral invariants is fast, suited for parallel implementation, and works for signals corrupted by Gaussian noise. The classification technique is shown to distinguish two similar but different bolts given their one-dimensional profiles

Pattern recognition using invariants defined from higher order spectra : 2-D image inputs

A new algorithm for extracting features from images for object recognition is described. The algorithm uses higher order spectra to provide desirable invariance properties, to provide noise immunity, and to incorporate nonlinearity into the feature extraction procedure thereby allowing the use of simple classifiers. An image can be reduced to a set of 1D functions via the Radon transform, or alternatively, the Fourier transform of each 1D projection can be obtained from a radial slice of the 2D Fourier transform of the image according to the Fourier slice theorem. A triple product of Fourier coefficients, referred to as the deterministic bispectrum, is computed for each 1D function and is integrated along radial lines in bifrequency space. Phases of the integrated bispectra are shown to be translation- and scale-invariant. Rotation invariance is achieved by a regrouping of these invariants at a constant radius followed by a second stage of invariant extraction. Rotation invariance is thus converted to translation invariance in the second step. Results using synthetic and actual images show that isolated, compact clusters are formed in feature space. These clusters are linearly separable, indicating that the nonlinearity required in the mapping from the input space to the classification space is incorporated well into the feature extraction stage. The use of higher order spectra results in good noise immunity, as verified with synthetic and real images. Classification of images using the higher order spectra-based algorithm compares favorably to classification using the method of moment invariants

A general procedure for the derivation of principal domains of higher-order spectra

A general procedure to determine the principal domain (i.e., nonredundant region of computation) of any higher-order spectrum is presented, using the bispectrum as an example. The procedure is then applied to derive the principal domain of the trispectrum of a real-valued, stationary time series. These results are easily extended to compute the principal domains of other higher-order spectra

Position, rotation, and scale invariant recognition of images using higher-order spectra

A new approach to recognition of images using invariant features based on higher-order spectra is presented. Higher-order spectra are translation invariant because translation produces linear phase shifts which cancel. Scale and amplification invariance are satisfied by the phase of the integral of a higher-order spectrum along a radial line in higher-order frequency space because the contour of integration maps onto itself and both the real and imaginary parts are affected equally by the transformation. Rotation invariance is introduced by deriving invariants from the Radon transform of the image and using the cyclic-shift invariance property of the discrete Fourier transform magnitude. Results on synthetic and actual images show isolated, compact clusters in feature space and high classification accuracies

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Robust image hash functions using higher order spectra

Robust hashing is an emerging field that can be used to hash certain data types in applications unsuitable for traditional cryptographic hashing methods. Traditional hashing functions have been used extensively for data/message integrity, data/message authentication, efficient file identification and password verification. These applications are possible because the hashing process is compressive, allowing for efficient comparisons in the hash domain but non-invertible meaning hashes can be used without revealing the original data. These techniques were developed with deterministic (non-changing) inputs such as files and passwords. For such data types a 1-bit or one character change can be significant, as a result the hashing process is sensitive to any change in the input. Unfortunately, there are certain applications where input data are not perfectly deterministic and minor changes cannot be avoided. Digital images and biometric features are two types of data where such changes exist but do not alter the meaning or appearance of the input. For such data types cryptographic hash functions cannot be usefully applied. In light of this, robust hashing has been developed as an alternative to cryptographic hashing and is designed to be robust to minor changes in the input. Although similar in name, robust hashing is fundamentally different from cryptographic hashing. Current robust hashing techniques are not based on cryptographic methods, but instead on pattern recognition techniques. Modern robust hashing algorithms consist of feature extraction followed by a randomization stage that introduces non-invertibility and compression, followed by quantization and binary encoding to produce a binary hash output. In order to preserve robustness of the extracted features, most randomization methods are linear and this is detrimental to the security aspects required of hash functions. Furthermore, the quantization and encoding stages used to binarize real-valued features requires the learning of appropriate quantization thresholds. How these thresholds are learnt has an important effect on hashing accuracy and the mere presence of such thresholds are a source of information leakage that can reduce hashing security. This dissertation outlines a systematic investigation of the quantization and encoding stages of robust hash functions. While existing literature has focused on the importance of quantization scheme, this research is the first to emphasise the importance of the quantizer training on both hashing accuracy and hashing security. The quantizer training process is presented in a statistical framework which allows a theoretical analysis of the effects of quantizer training on hashing performance. This is experimentally verified using a number of baseline robust image hashing algorithms over a large database of real world images. This dissertation also proposes a new randomization method for robust image hashing based on Higher Order Spectra (HOS) and Radon projections. The method is non-linear and this is an essential requirement for non-invertibility. The method is also designed to produce features more suited for quantization and encoding. The system can operate without the need for quantizer training, is more easily encoded and displays improved hashing performance when compared to existing robust image hashing algorithms. The dissertation also shows how the HOS method can be adapted to work with biometric features obtained from 2D and 3D face images.

Application of higher-order spectra for automated grading of diabetic maculopathy

Diabetic macular edema (DME) is one of the most common causes of visual loss among diabetes mellitus patients. Early detection and successive treatment may improve the visual acuity. DME is mainly graded into non-clinically significant macular edema (NCSME) and clinically significant macular edema according to the location of hard exudates in the macula region. DME can be identified by manual examination of fundus images. It is laborious and resource intensive. Hence, in this work, automated grading of DME is proposed using higher-order spectra (HOS) of Radon transform projections of the fundus images. We have used third-order cumulants and bispectrum magnitude, in this work, as features, and compared their performance. They can capture subtle changes in the fundus image. Spectral regression discriminant analysis (SRDA) reduces feature dimension, and minimum redundancy maximum relevance method is used to rank the significant SRDA components. Ranked features are fed to various supervised classifiers, viz. Naive Bayes, AdaBoost and support vector machine, to discriminate No DME, NCSME and clinically significant macular edema classes. The performance of our system is evaluated using the publicly available MESSIDOR dataset (300 images) and also verified with a local dataset (300 images). Our results show that HOS cumulants and bispectrum magnitude obtained an average accuracy of 95.56 and 94.39 % for MESSIDOR dataset and 95.93 and 93.33 % for local dataset, respectively.