Real-time calculation of a limiting form of the Renyi entropy applied to detection of subtle changes in scattering architecture.

Previously a new method for ultrasound signal characterization using entropy H(f) was reported, and it was demonstrated that in certain settings, further improvements in signal characterization could be obtained by generalizing to Renyi entropy-based signal characterization I(f)(r) with values of r near 2 (specifically r=1.99) [M. S. Hughes et al., J. Acoust. Soc. Am. 125, 3141-3145 (2009)]. It was speculated that further improvements in sensitivity might be realized at the limit r-->2. At that time, such investigation was not feasible due to excessive computational time required to calculate I(f)(r) near this limit. In this paper, an asymptotic expression for the limiting behavior of I(f)(r) as r-->2 is derived and used to present results analogous to those obtained with I(f)(1.99). Moreover, the limiting form I(f,infinity) is computable directly from the experimentally measured waveform f(t) by an algorithm that is suitable for real-time calculation and implementation.

A comparison of Monte Carlo dose calculation denoising techniques.

Recent studies have demonstrated that Monte Carlo (MC) denoising techniques can reduce MC radiotherapy dose computation time significantly by preferentially eliminating statistical fluctuations ('noise') through smoothing. In this study, we compare new and previously published approaches to MC denoising, including 3D wavelet threshold denoising with sub-band adaptive thresholding, content adaptive mean-median-hybrid (CAMH) filtering, locally adaptive Savitzky-Golay curve-fitting (LASG), anisotropic diffusion (AD) and an iterative reduction of noise (IRON) method formulated as an optimization problem. Several challenging phantom and computed-tomography-based MC dose distributions with varying levels of noise formed the test set. Denoising effectiveness was measured in three ways: by improvements in the mean-square-error (MSE) with respect to a reference (low noise) dose distribution; by the maximum difference from the reference distribution and by the 'Van Dyk' pass/fail criteria of either adequate agreement with the reference image in low-gradient regions (within 2% in our case) or, in high-gradient regions, a distance-to-agreement-within-2% of less than 2 mm. Results varied significantly based on the dose test case: greater reductions in MSE were observed for the relatively smoother phantom-based dose distribution (up to a factor of 16 for the LASG algorithm); smaller reductions were seen for an intensity modulated radiation therapy (IMRT) head and neck case (typically, factors of 2-4). Although several algorithms reduced statistical noise for all test geometries, the LASG method had the best MSE reduction for three of the four test geometries, and performed the best for the Van Dyk criteria. However, the wavelet thresholding method performed better for the head and neck IMRT geometry and also decreased the maximum error more effectively than LASG. In almost all cases, the evaluated methods provided acceleration of MC results towards statistically more accurate results.

Wavelets, adapted waveforms and de-noising.

This is a short summary of a talk given at the Frontier Science in EEG Symposium, Continuous Waveform Analysis, held on 9 October 1993 in New Orleans. We describe some new libraries of waveforms well-adapted to various numerical analysis and signal processing tasks. The main point is that by expanding a signal in a library of waveforms which are well-localized in both time and frequency, one can achieve both understanding of structure and efficiency in computation. We briefly cover the properties of the new "wavelet packet" and "localized trigonometric" libraries. The main focus will be applications of such libraries to the analysis of complicated transient signals: a feature extraction and data compression algorithm for speech signals which uses best-adapted time and frequency decompositions, and an adapted waveform analysis algorithm for removing fish noises from hydrophone recordings. These signals share many of the same properties as EEG traces, but with distinct features that are easier to characterize and detect.