Application of higher order statistics/spectra in biomedical signals : a review

For many decades correlation and power spectrum have been primary tools for digital signal processing applications in the biomedical area. The information contained in the power spectrum is essentially that of the autocorrelation sequence; which is sufficient for complete statistical descriptions of Gaussian signals of known means. However, there are practical situations where one needs to look beyond autocorrelation of a signal to extract information regarding deviation from Gaussianity and the presence of phase relations. Higher order spectra, also known as polyspectra, are spectral representations of higher order statistics, i.e. moments and cumulants of third order and beyond. HOS (higher order statistics or higher order spectra) can detect deviations from linearity, stationarity or Gaussianity in the signal. Most of the biomedical signals are non-linear, non-stationary and non-Gaussian in nature and therefore it can be more advantageous to analyze them with HOS compared to the use of second order correlations and power spectra. In this paper we have discussed the application of HOS for different bio-signals. HOS methods of analysis are explained using a typical heart rate variability (HRV) signal and applications to other signals are reviewed.

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.

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

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

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

Extreme ultraviolet (EUV) degradation of poly(olefin sulfone)s : towards applications as EUV photoresists

Poly(olefin sulfone)s, formed by the reaction of sulfur dioxide (SO2) and an olefin, are known to be highly susceptible to degradation by radiation and thus have been identified as candidate materials for chain scission-based extreme ultraviolet lithography (EUVL) resist materials. In order to investigate this further, the synthesis and characterisation of two poly(olefin sulfone)s namely poly(1-pentene sulfone) (PPS) and poly(2-methyl-1-pentene sulfone) (PMPS), was achieved and the two materials were evaluated for possible chain scission EUVL resist applications. It was found that both materials possess high sensitivities to EUV photons; however; the rates of outgassing were extremely high. The only observed degradation products were found to be SO2 and the respective olefin suggesting that depolymerisation takes place under irradiation in a vacuum environment. In addition to depolymerisation, a concurrent conversion of SO2 moieties to a sulfide phase was observed using XPS.

Chain scission resists for extreme ultraviolet lithography based on high performance polysulfone-containing polymers

A series of polymers with a comb architecture were prepared where the poly(olefin sulfone) backbone was designed to be highly sensitive to extreme ultraviolet (EUV) radiation, while the well-defined poly(methyl methacrylate) (PMMA) arms were incorporated with the aim of increasing structural stability. It is hypothesized that upon EUV radiation rapid degradation of the polysulfone backbone will occur leaving behind the well-defined PMMA arms. The synthesized polymers were characterised and have had their performance as chain-scission EUV photoresists evaluated. It was found that all materials possess high sensitivity towards degradation by EUV radiation (E0 in the range 4–6 mJ cm−2). Selective degradation of the poly(1-pentene sulfone) backbone relative to the PMMA arms was demonstrated by mass spectrometry headspace analysis during EUV irradiation and by grazing-angle ATR-FTIR. EUV interference patterning has shown that materials are capable of resolving 30 nm 1:1 line:space features. The incorporation of PMMA was found to increase the structural integrity of the patterned features. Thus, it has been shown that terpolymer materials possessing a highly sensitive poly(olefin sulfone) backbone and PMMA arms are able to provide a tuneable materials platform for chain scission EUV resists. These materials have the potential to benefit applications that require nanopattering, such as computer chip manufacture and nano-MEMS.

Patterning of tailored polycarbonate based non-chemically amplified resists using extreme ultraviolet lithography

A series of high-performance polycarbonates have been prepared with glass-transition temperatures and decomposition temperatures that are tunable by varying the repeat-unit chemical structure. Patterning of the polymers with extreme UV lithography has been achieved by taking advantage of direct photoinduced chain scission of the polymer chains, which results in a molecular-weight based solubility switch. After selective development of the irradiated regions of the polymers, feature sizes as small as 28.6 nm have been printed and the importance of resist-developer interactions for maximizing image quality has been demonstrated.

Polycarbonate based nonchemically amplified photoresists for extreme ultraviolet lithography

Some initial EUVL patterning results for polycarbonate based non-chemically amplified resists are presented. Without full optimization the developer a resolution of 60 nm line spaces could be obtained. With slight overexposure (1.4 × E0) 43.5 nm lines at a half pitch of 50 nm could be printed. At 2x E0 a 28.6 nm lines at a half pitch of 50 nm could be obtained with a LER that was just above expected for mask roughness. Upon being irradiated with EUV photons, these polymers undergo chain scission with the loss of carbon dioxide and carbon monoxide. The remaining photoproducts appear to be non-volatile under standard EUV irradiation conditions, but do exhibit increased solubility in developer compared to the unirradiated polymer. The sensitivity of the polymers to EUV light is related to their oxygen content and ways to increase the sensitivity of the polymers to 10 mJ cm-2 is discussed.