Cone Kernel Research Articles

Portal dose image verification: formalism and application of the collapsed cone superposition method

A formalism tailored for portal dose image verification is proposed to facilitate the comparison of calculated and measured portal dose distributions. Each portal image is converted into a dose proportional image and normalized to the reference beam calibration dose per monitor unit. The calculated or measured dose to a detector phantom is accordingly normalized so as to enable direct comparison.The collapsed cone kernel superposition method is adapted and evaluated for calculation of portal dose distributions in a water-equivalent detector phantom through comparisons with Monte Carlo calculations and with measurements. The deviation compared with Monte Carlo calculations for 6 and 15 MV was between +0.9% (the 0.9 quantile) and −2.1% (the 0.1 quantile) for a range of investigated geometries. Collapsed cone calculations compared with measurements for clinical fields agreed within [−1.9%, +2.4%] for 15 MV and [−0.9%, +3.2%] for 6 MV for the 0.1 and 0.9 quantiles, respectively. Hence, the absolute portal dose to a detector phantom could be calculated and verified well within the present accuracy requirements for clinical dose calculations.

Adaptive short-time Fourier analysis

This article presents a method of adaptively adjusting the window length used in short-time Fourier analysis, related to our earlier work in which we developed a means of adaptively optimizing the performance of the cone kernel distribution (CKD). The optimal CKD cone length is, by definition, a measure of the interval over which the signal has constant or slowly changing frequency structure. The article shows that this length can also be used to compute a time-varying short-time Fourier transform (STFT). The resulting adaptive STFT shares many desirable properties with the adaptive CKD, such as the ability to adapt to transient as well as long-term signal components. The optimization requires O(N) operations per step, less than the fast Fourier transform (FFT) used in computing each time slice, making it competitive in complexity with nonadaptive time-frequency algorithms.

Analysis of myoelectric signals recorded during dynamic contractions

This article presents the theoretical considerations that justify the choice of specific time-frequency transforms for processing nonstationary myoelectric signals as a method of studying fatigue prior to the failure point. It shows some preliminary results obtained by applying these techniques to computer-synthesized realizations of stochastic processes, as well as to real signals detected during different types of dynamic contractions of healthy human volunteers. Five different time-frequency transforms were applied in this study (the Wigner-Ville, the smoothed Wigner-Ville, the Cone kernel, the reduced interference, and the Choi-Williams), but for the sake of brevity, this article reports only the results obtained by applying the Choi-Williams transform, because the authors found it to be the most suitable for processing these specific signals.

Kernel synthesis for generalized time-frequency distributions using the method of alternating projections onto convex sets

Cohen's generalized time-frequency distribution (GTFR) requires the choice of a two-dimensional kernel. The kernel directly affects many performance attributes of the GTFR such as time resolution, frequency resolution, realness, and conformity to time and frequency marginals. A number of different kernels may suffice for a given performance constraint (high-frequency resolution, for example). Interestingly, most sets of kernels satisfying commonly used performance constraints are convex. We describe a method whereby kernels can be designed that satisfy two or more of these constraints. If there exists a nonempty intersection among the constraint sets, then the theory of alternating projection onto convex sets (POCS) guarantees, convergence to a kernel that satisfies all of the constraints. If the constraints can be partitioned into two sets, each with a nonempty intersection, then POCS guarantees convergence to a kernel that satisfies the inconsistent constraints with minimum mean-square error. We apply kernels synthesized using POCS to the generation of some example GTFRs, and compare their performance to the spectrogram, Wigner distribution, and cone kernel GTFR.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A comparison of the stability of stationary and non-stationary magnetotelluric analysis methods

A Magnetotelluric (MT) sounding was carried out at a site in south‐east Queensland, in the Clarence‐Moreton Basin. The synoptic recordings were taken over a period of four months at sampling frequencies from 500 Hz to 5 × 10‐5 Hz. The resulting data was analysed by the stationary cross‐frequency and the Cone kernel time‐frequency distribution (TFD) methods of MT analysis. The results were compared as apparent resistivities on a daily basis for frequencies above 1 Hz, as well as over all the available data. The TFD MT apparent‐resistivity results were more stable and less noisy on an daily basis than the cross‐frequency results. Similarly the TFD analysis gave less noisy results than the cross‐frequency analysis when all available data was processed. Application of these new non‐stationary analysis techniques to MT processing should decrease the bias error problem of the MT methods and so increase reliability and repeatability of MT soundings.

Alternative procedures for spectral estimation

This paper compares four alternative procedures for estimating the acoustical characteristics of speech and other complex signals: the fast Fourier transform (FFT), two autoregressive techniques (the autocorrelation and modified covariance methods), and the Cone–Kernel method. All four techniques are now widely available to researchers in Version 4.0 of the CSRE (Canadian Speech Research Environment) software system. FFT spectral estimates are characterized by many known tradeoffs: good frequency resolution is obtained at the expense of good time resolution, and vice versa. Autoregressive methods overcome some of the inherent limitations of the FFT method, but still use a quasi-stationary approach to analyze nonstationary signals such as speech. The Cone–Kernel method offers the opportunity for both good frequency and good time resolution, and cancels many of the cross terms that have made it difficult to interpret previous approaches based on the Wigner distribution. Examples of applying the various analysis procedures to signals will be shown, including situations where the Cone–Kernel approach facilitates the interpretation of certain details of the speech signal.

Time-frequency analyses of coherent frequency fluctuations among spontaneous otoacoustic emissions

Previously it has been shown [e.g., Keefe etal., J. Acoust. Soc. Am. Suppl. 1 88, S17 (1990)] that in ears with multiple spontaneous otoacoustic emissions (SOAEs) there are often short-term amplitude fluctuations that are highly correlated (either positively or negatively) among SOAEs widely separated in frequency. In this report it is shown that in many such ears there are also coherent frequency fluctuations among widely spaced SOAEs. However, the demonstration of these small (a few tenths of a percent), short-term frequency fluctuations is difficult using the usual spectrogram-based analysis because of the inability of the spectrogram to accurately resolve frequency-modulated signals. To circumvent this drawback, advanced time-frequency representations (TFRs) have also been employed: e.g., the cone kernel TFR and the Wigner distribution. These time-frequency representations provide additional insights into the nature of the short-term frequency and amplitude fluctuations in SOAEs. [Work supported by NIDCD.]