On the computation and interpretation of auto- and cross-trispectra

This paper discusses the principal domains of auto- and cross-trispectra. It is shown that the cumulant and moment based trispectra are identical except on certain planes in trifrequency space. If these planes are avoided, their principal domains can be derived by considering the regions of symmetry of the fourth order spectral moment. The fourth order averaged periodogram will then serve as an estimate for both cumulant and moment trispectra. Statistics of estimates of normalised trispectra or tricoherence are also discussed.

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

Digit recognition using trispectral features

Features derived from the trispectra of DFT magnitude slices are used for multi-font digit recognition. These features are insensitive to translation, rotation, or scaling of the input. They are also robust to noise. Classification accuracy tests were conducted on a common data base of 256× 256 pixel bilevel images of digits in 9 fonts. Randomly rotated and translated noisy versions were used for training and testing. The results indicate that the trispectral features are better than moment invariants and affine moment invariants. They achieve a classification accuracy of 95% compared to about 81% for Hu's (1962) moment invariants and 39% for the Flusser and Suk (1994) affine moment invariants on the same data in the presence of 1% impulse noise using a 1-NN classifier. For comparison, a multilayer perceptron with no normalization for rotations and translations yields 34% accuracy on 16× 16 pixel low-pass filtered and decimated versions of the same data.

Higher order spectral analysis of Chua's circuit

Higher order spectral analysis is used to investigate nonlinearities in time series of voltages measured from a realization of Chua's circuit. For period-doubled limit cycles, quadratic and cubic nonlinear interactions result in phase coupling and energy exchange between increasing numbers of triads and quartets of Fourier components as the nonlinearity of the system is increased. For circuit parameters that result in a chaotic Rossler-type attractor, bicoherence and tricoherence spectra indicate that both quadratic and cubic nonlinear interactions are important to the dynamics. When the circuit exhibits a double-scroll chaotic attractor the bispectrum is zero, but the tricoherences are high, consistent with the importance of higher-than-second order nonlinear interactions during chaos associated with the double scroll.

Higher-order spectral analysis of nonlinear ocean surface gravity waves

Higher-order spectral analysis is used to detect the presence of secondary and tertiary forced waves associated with the nonlinearity of energetic swell observed in 8- and 13-m water depths. Higher-order spectral analysis techniques are first described and then applied to the field data, followed by a summary of the results.

On the behaviour of higher-order spectral features for object recognition in the presence of various types of noise

This paper presents results on the robustness of higher-order spectral features to Gaussian, Rayleigh, and uniform distributed noise. Based on cluster plots and accuracy results for various signal to noise conditions, the higher-order spectral features are shown to be better than moment invariant features.

Effects of wearing a pressure redistribution belt while lying in a hospital bed

Bedsores (ulcers) are caused by multiple factors which include, but are not limited to; pressure, shear force, friction, temperature, age and medication. Specialised support services, such as specialised mattresses, sheepskin coverings etc., are thought to decrease or relieve pressure, resulting in a lowering of pressure ulcer incidence [3]. The primary aim of this study was to compare the upper/central body pressure distribution between normal lying in a hospital bed versus the use of a pressure redistribution belt. The study involved 16 healthy voluntary subjects lying on a hospital bed with and without wearing the belt. Results showed that the use of a pressure redistribution belt results in reduced pressure peaks and prevents the pressure from increasing over time.

Diurnal Variation of Retinal Thickness with Spectral Domain OCT

Purpose. To investigate whether diurnal variation occurs in retinal thickness measures derived from spectral domain optical coherence tomography (SD-OCT). Methods. Twelve healthy adult subjects had retinal thickness measured with SD-OCT every 2 h over a 10 h period. At each measurement session, three average B-scan images were derived from a series of multiple B-scans (each from a 5 mm horizontal raster scan along the fovea, containing 1500 A-scans/B-scan) and analyzed to determine the thickness of the total retina, as well as the thickness of the outer retinal layers. Average thickness values were calculated at the foveal center, at the 0.5 mm diameter foveal region, and for the temporal parafovea (1.5 mm from foveal center) and nasal parafovea (1.5 mm from foveal center). Results. Total retinal thickness did not exhibit significant diurnal variation in any of the considered retinal regions (p > 0.05). Evidence of significant diurnal variation was found in the thickness of the outer retinal layers (p < 0.05), with the most prominent changes observed in the photoreceptor layers at the foveal center. The photoreceptor inner and outer segment layer thickness exhibited mean amplitude (peak to trough) of daily change of 7 ± 3 μm at the foveal center. The peak in thickness was typically observed at the third measurement session (mean measurement time, 13:06). Conclusions. The total retinal thickness measured with SD-OCT does not exhibit evidence of significant variation over the course of the day. However, small but significant diurnal variation occurs in the thickness of the foveal outer retinal layers.

Gene duplication is an evolutionary mechanism for expanding spectral diversity in the long-wavelength photopigments of butterflies

Butterfly long-wavelength (L) photopigments are interesting for comparative studies of adaptive evolution because of the tremendous phenotypic variation that exists in their wavelength of peak absorbance (lambda(max) value). Here we present a comprehensive survey of L photopigment variation by measuring lambda(max) in 12 nymphalid and 1 riodinid species using epi-microspectrophotometry. Together with previous data, we find that L photopigment lambda(max) varies from 510-565 nm in 22 nymphalids, with an even broader 505- to 600-nm range in riodinids. We then surveyed the L opsin genes for which lambda(max) values are available as well as from related taxa and found 2 instances of L opsin gene duplication within nymphalids, in Hermeuptychia hermes and Amathusia phidippus, and 1 instance within riodinids, in the metalmark butterfly Apodemia mormo. Using maximum parsimony and maximum likelihood ancestral state reconstructions to map the evolution of spectral shifts within the L photopigments of nymphalids, we estimate the ancestral pigment had a lambda(max) = 540 nm +/- 10 nm standard error and that blueshifts in wavelength have occurred at least 4 times within the family. We used ancestral state reconstructions to investigate the importance of several amino acid substitutions (Ile17Met, Ala64Ser, Asn70Ser, and Ser137Ala) previously shown to have evolved under positive selection that are correlated with blue spectral shifts. These reconstructions suggest that the Ala64Ser substitution has indeed occurred along the newly identified blueshifted L photopigment lineages. Substitutions at the other 3 sites may also be involved in the functional diversification of L photopigments. Our data strongly suggest that there are limits to the evolution of L photopigment spectral shifts among species with only one L opsin gene and that opsin gene duplication broadens the potential range of lambda(max) values.

Electron paramagnetic resonance, optical absorption and Raman spectral studies on a pyrite/chalcopyrite mineral

Pyrite and chalcopyrite mineral samples from Mangampet barite mine, Kadapa, Andhra Pradesh, India are used in the present study. XRD data indicate that the pyrite mineral has a face centered cubic lattice structure with lattice constant 5.4179 Å. Also it possesses an average particle size of 91.9 nm. An EPR study on the powdered samples confirms the presence of iron in pyrite and iron and Mn(II) in chalcopyrite. The optical absorption spectrum of chalcopyrite indicates presence of copper which is in a distorted octahedral environment. NIR results confirm the presence of water fundamentals and Raman spectrum reveals the presence of water and sulfate ions.