Autoregressive Extrapolation Research Articles

Spatially resolved free-induction decay spectroscopy using a 3D ultra-short echo time multi-echo imaging sequence with systematic echo shifting and compensation of B0 field drifts.

Biologically interesting signals can exhibit fast transverse relaxation and frequency shifts compared to free water. For spectral assignment, a ultra-short echo time (UTE) imaging sequence was modified to provide pixel-wise free-induction decay (FID) acquisition. The UTE-FID approach presented relies on a multi-echo 3D spiral UTE sequence with six echoes per radiofrequency (RF) excitation (TEmin 0.05ms, echo spacing 3ms). A complex pixel-wise raw data set for FID spectroscopy is obtained by several multi-echo UTE measurements with systematic shifting of the readout by 0.25 or 0.5ms, until the time domain is filled for 18 or 45ms. B0 drifts are compensated by mapping and according phase correction. Autoregressive extrapolation of the signal is performed before Gaussian filtering. This method was applied to a phantom containing collagen-water solutions of different concentrations. To calculate the collagen content, a 19-peak collagen model was extracted from a non-selective FID spectrum (50% collagen solution). Proton-density-collagen-fraction (PDCF) was calculated for 10 collagen solutions (2%-50%). Furthermore, an in vivo UTE-FID spectrum of adipose tissue was recorded. UTE-FID signal patterns agreed well with the non-spatially selective pulse-acquire FID spectrum from a sphere filled with 50% collagen. Differentiation of collagen solution from distilled water in the PDCF map was possible from 4% collagen concentration for a UTE-FID sequence with 128 × 128 × 64 matrix (voxel size 1 × 1 × 2.85mm3 ). The mean values of the PDCF correlate linearly with collagen concentration. The presented UTE-FID approach allows pixel-wise raw data acquisition similar to non-spatially selective pulse-acquire spectroscopy. Spatially resolved applications for assessment of spectra of rapidly decaying signals seem feasible.

Digital filters for low-latency quantification of brain rhythms in real time

Objective. The rapidly developing paradigm of closed-loop neuroscience has extensively employed brain rhythms as the signal forming real-time neurofeedback, triggering brain stimulation, or governing stimulus selection. However, the efficacy of brain rhythm contingent paradigms suffers from significant delays related to the process of extraction of oscillatory parameters from broad-band neural signals with conventional methods. To this end, real-time algorithms are needed that would shorten the delay while maintaining an acceptable speed-accuracy trade-off. Approach. Here we evaluated a family of techniques based on the application of the least-squares complex-valued filter (LSCF) design to real-time quantification of brain rhythms. These techniques allow for explicit optimization of the speed-accuracy trade-off when quantifying oscillatory patterns. We used EEG data collected from 10 human participants to systematically compare LSCF approach to the other commonly used algorithms. Each method being evaluated was optimized by scanning through the grid of its hyperparameters using independent data samples. Main results. When applied to the task of estimating oscillatory envelope and phase, the LSCF techniques outperformed in speed and accuracy both conventional Fourier transform and rectification based methods as well as more advanced techniques such as those that exploit autoregressive extrapolation of narrow-band filtered signals. When operating at zero latency, the weighted LSCF approach yielded 75% accuracy when detecting alpha-activity episodes, as defined by the amplitude crossing of the 95th-percentile threshold. Significance. The LSCF approaches are easily applicable to low-delay quantification of brain rhythms. As such, these methods are useful in a variety of neurofeedback, brain-computer-interface and other experimental paradigms that require rapid monitoring of brain rhythms.

Nondestructive measurement of mill-scale thickness on steel by terahertz time-of-flight tomography

We measure in a nondestructive and noncontact fashion the thicknesses of three scale films with thicknesses 28.5 ± 1.4 μm, 13.4± 0.9 μm, and 5.1 ± 0.3 μm on steel substrates employing terahertz time-of-flight tomography combined with advanced signal-processing techniques. Wüstite is the dominant phase in the scale films, though magnetite and hematite are also present. Because wüstite is electrically insulating, the incident terahertz electromagnetic pulses largely penetrate into the scale film; however, the pulses are entirely reflected by the underlying electrically conductive steel substrate. Because the film layers are thin, in some cases optically thin, the distinct pulses reflected at the air/scale and scale/steel interfaces overlap in time and thus are not visually evident in the reflected terahertz signal, necessitating the use of deconvolution techniques to recover the sample structure. We compare the merits of three deconvolution techniques, one unsuccessful (frequency-wavelet domain deconvolution) and two successful (sparse deconvolution and autoregressive extrapolation), to characterize the thicknesses of these scale films.

An application of the autoregressive extrapolation technique to enhance deconvolution results: a 2D marine data example

Interpreting a post-stack seismic section is difficult due to the band-limited nature of the seismic data even post deconvolution. Deconvolution is a process that is universally applied to extend the bandwidth of seismic data. However, deconvolution falls short of this task as low and high frequencies of the deconvolved data are either still missing or contaminated by noise. In this paper we use the autoregressive extrapolation technique to recover these missing frequencies, using the high signal-to-noise ratio (S/N) portions of the spectrum of deconvolved data. I introduce here an algorithm to extend the bandwidth of deconvolved data. This is achieved via an autoregressive extrapolation technique, which has been widely used to replace missing or corrupted samples of data in signal processing. This method is performed in the spectral domain. The spectral band to be extrapolated using autoregressive prediction filters is first selected from the part of the spectrum that has a high signal-to-noise ratio (S/N) and is then extended. As there can be more than one zone of good S/N in the spectrum, the results of prediction filter design and extrapolation from three different bands are averaged. When the spectrum of deconvolved data is extended in this way, the results show higher vertical resolution to a degree that the final seismic data closely resemble what is considered to be a reflectivity sequence of the layered medium. This helps to obtain acoustic impedance with inversion by stable integration. The results show that autoregressive spectral extrapolation highly increases vertical resolution and improves horizon tracking to determine continuities and faults. This increase in coherence ultimately yields a more interpretable seismic section.

Frequency extrapolation to enhance the deconvolution of transmitted seismic waves

We investigate the enhanced deconvolution of transmitted seismic waves from distant natural sources using autoregressive extrapolation (AR) and extended time-domain deconvolution. The amplitude spectrum of deconvolved seismograms is often restricted to a reduced frequency range from the use of a water table for the deconvolution. The attenuation effects on the teleseismic seismic waves also reduce the frequency content of the data. We compare the deconvolved spectra obtained from an AR-extended deconvolution (EARD) and an extended time-domain deconvolution (ETDD) technique for teleseismic waves. For EARD, we analyse the spectral content for the deconvolved spectra to differentiate between the domains of known and unknown spectral values. A prediction error filter is used to perform the autoregressive extrapolation to estimate the unknown spectral values. This procedure is applied on 1D and 2D synthetic data to test the approach. The EARD approach is then compared with the ETDD approach which applies an extended high-pass filter to the time-domain deconvolution approach. Both the EARD and ETDD approaches for extending the effective frequency range of the deconvolution results are then compared using observed teleseismic data recorded in southern India.

Application of autoregressive extrapolation to the cross-borehole tomography

Autoregressive (AR) extrapolation of travel-time data is tested using several synthetic tomography examples using a cross-borehole geometry. Earlier studies have shown crossborehole tomography using travel-times can have reduced resolution because of the limitations on ray coverage. We apply AR extrapolation to partial travel-time data and then compare the tomographic inversions using the full data and the extrapolated data. Both the overall patterns of the extended data and the tomographic reconstructions with the extended data show that AR extrapolation can effectively extend the synthetic crossborehole tomographic data to a broader coverage and can improve the cross-hole reconstruction images.

Application of Autoregressive Extrapolation to Seismic Tomography

Seismic tomography used in the laboratory, as well as in the field, is strongly affected by limited and nonuniform ray coverage. A two-stage autoregres- sive extrapolation technique is proposed that can be used to extend the observed data and provide better tomographic images. The algorithm is based on the principle that the extrapolated data add minimal information to the existing data. The first stage of the extrapolation is to find the optimal prediction-error (PE) filter. The second stage is to use the PE filter to find the values of the missing data. The missing data are estimated to have the same spectrum as the observed data and are similar to maxi- mizing an entropy criterion. To test the method, synthetic tomography experiments for laboratory rock samples are used in which full ray coverage can be obtained. Autoregressive methods are then used to extrapolate the partial ray coverage and the tomographic results are compared with the full ray coverage case. The synthetic tests show that the autoregressive method can extrapolate known data to find missing data and can provide improved tomographic images. The autoregressive extrapolation is also tolerant to noise. Although the method was applied to a laboratory geometry where the ray coverage can be controlled, autoregressive methods may have impor- tant applications to tomography experiments in the field where complete ray coverage often cannot be easily realized. regressive methods to seismic tomography problems. We propose and implement a data extrapolation method based on Claerbout's approach for performing seismic data pre- diction beyond the measurement range. The idea of our al- gorithm is that the useful information in the known data is relevant and can be used to estimate the missing values by autoregressive extrapolation methods, and the estimated data only add minimum information to the known data. We apply this algorithm to synthetic arrival time data, with and without random noise added, and also to real laboratory experimental data. The results show that the proposed technique can ex- trapolate seismic travel-time data for seismic tomography, and the method is tolerant to random noise in the data.

European ionospheric forecast and mapping

A new technique is developed for forecasting and instantaneous mapping of the ionospheric parameters over Europe, based on analytical presentation of the mapped quantities. The diurnal and seasonal variations of the ionospheric foF2 and M(3000)F2 parameters are represented by a modified version of the regional model ISIRM adjusted to the past measured data. An autoregressive extrapolation of the data from the past month enables the 15-day-ahead forecast of the quiet ionospheric distribution to be performed. In addition, the short-term variations due to geomagnetic activity are defined as a plane surface superimposed on the quiet distribution. This correction is obtained by two plane characteristics as functions of the geomagnetic three-hour Kp index. In this way the 24-hour forecast can be obtain during quiet as well as disturbed ionospheric conditions. The corresponding EIFM software provides a variety of options to perform the short-term forecast depending on availability of the measured ionospheric data and predicted Kp values.

An instrument for real-time spectral estimation of heart rate variability signals

A Digital Signal Processor (DSP)-based instrument is proposed for estimating and displaying the Heart Rate Variability (HRV) spectrum in real-time. It consists of an intelligent module which is properly interfaced to an IBM PC and whose operations are independent from the computer's other tasks. In this way, the simultaneous recording of the ECG sequence, needed for the more complete off-line analysis, can be performed by the same host. The employed hybrid spectral estimator (in which a classical FFT analysis follows the autoregressive extrapolation of data) appears to be the most apt for the present fixed point arithmetics implementation. The reliability of the instrument and its accuracy are checked both with suitable test signals and by comparison with the results obtained through off-line analysis of the same ECG tracks. The instrument is presently used for cardiovascular investigations, in particular for quickly picking patients with cardiac autonomic neuropathy (CAN) out of a population of diabetic subjects.

FM com: Has this ? Scuti-star variable frequency spectra?

Component frequencies of FM Com were analysed using 43 hrV band photoelectric observations. Both the usual Fourier and the autoregressive extrapolation techniques applied to the closely spaced nights of observation yielded variable frequency patterns. Comparison of the observed and synthetic light curves calculated by the two frequencies obtained by analysing a previously obtained compact data segment supports the suggestion of this star's nonstationary light variation.