Speaker
Description
Intermittent fluctuations with large amplitudes compared to the background level can arise in far-from equilibrium and turbulent systems as well as due to sudden, large-amplitude forcing [1, 2]. Conditional averaging has been a much-used tool for finding amplitudes of intermittent events and the waiting time between them [2]. However, conditional averaging requires both significant amplitude thresholding and a large minimal distance between events, significantly limiting the number of found events. This reduces the accuracy of reconstructing intermittent data time series and the statistical analyses that can be derived.
In this contribution, we study a variant of the Richardson-Lucy deconvolution algorithm [3, 4, 5]. This is an iterative method converging to a least squares solution which can be used to recover event amplitudes and arrival times from an intermittent time series for a known typical event shape. The method was applied to synthetically generated data time series consisting of a superposition of one-sided exponential pulses. Signal reconstruction and recovery of pulse amplitudes and arrivals is excellent for low to moderate overlap between events. As event overlap increases, signal recovery remains excellent, but an empirical threshold for reconstruction of amplitudes and arrival times is found. The sampling time must be 10 times lower than the average waiting time or less.
For uncorrelated noise, the method requires no event thresholding and events separated by as little as two sampling times may be distinguished. In the presence of noise with the same correlation function as the signal, spurious events are observed, and some thresholding or filtering must be used to separate the noise from the data time series.
Lastly, we demonstrate that the same method may be employed in recovering the typical event shape for known event amplitudes and arrival times. The event shape is reconstructed with good accuracy in the presence of noise and utilising different duration time distributions.
References
[1] R. Narasimha et. al., Phil. Trans. R. Soc. A (2007) 365, 841–858.
[2] A. Theodorsen et. al., Plasma Phys. Contr. F. (2016) 58, 044006.
[3] W. H. Richardson, J. Opt. Soc. Am. (1972) 62, 55-59.
[4] L. B. Lucy, Astron. J. (1974) 79, 745.
[5] F. Benvenuto et. al. Inverse Probl. (2009) 26, 025004.
