TRUFAS, a wavelet based algorithm for the rapid detection of planetary transits

Aims: We describe a fast, robust and automatic detection algorithm, TRUFAS, and apply it to data that are being expected from the CoRoT mission. Methods: The procedure proposed for the detection of planetary transits in light curves works in two steps: 1) a continuous wavelet transformation of the detrended light curve with posterior selection of the optimum scale for transit detection, and 2) a period search in that selected wavelet transformation. The detrending of the light curves are based on Fourier filtering or a discrete wavelet transformation. TRUFAS requires the presence of at least 3 transit events in the data. Results: The proposed algorithm is shown to identify reliably and quickly the transits that had been included in a standard set of 999 light curves that simulate CoRoT data. Variations in the pre-processing of the light curves and in the selection of the scale of the wavelet transform have only little effect on TRUFAS' results. Conclusions: TRUFAS is a robust and quick transit detection algorithm, especially well suited for the analysis of very large volumes of data from space or ground-based experiments, with long enough durations for the target-planets to produce multiple transit events.Comment: 9 pages, 10 figures, accepted by A&

Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering

This study introduces a new method for detecting and sorting spikes from multiunit recordings. The method combines the wavelet transform, which localizes distinctive spike features, with superparamagnetic clustering, which allows automatic classification of the data without assumptions such as low variance or gaussian distributions. Moreover, an improved method for setting amplitude thresholds for spike detection is proposed. We describe several criteria for implementation that render the algorithm unsupervised and fast. The algorithm is compared to other conventional methods using several simulated data sets whose characteristics closely resemble those of in vivo recordings. For these data sets, we found that the proposed algorithm outperformed conventional methods

Wavelet Lifting over Information-Based EEG Graphs for Motor Imagery Data Classification

The imagination of limb movements offers an intuitive paradigm for the control of electronic devices via brain computer interfacing (BCI). The analysis of electroencephalographic (EEG) data related to motor imagery potentials has proved to be a difficult task. EEG readings are noisy, and the elicited patterns occur in different parts of the scalp, at different instants and at different frequencies. Wavelet transform has been widely used in the BCI field as it offers temporal and spectral capabilities, although it lacks spatial information. In this study we propose a tailored second generation wavelet to extract features from these three domains. This transform is applied over a graph representation of motor imaginary trials, which encodes temporal and spatial information. This graph is enhanced using per-subject knowledge in order to optimise the spatial relationships among the electrodes, and to improve the filter design. This method improves the performance of classifying different imaginary limb movements maintaining the low computational resources required by the lifting transform over graphs. By using an online dataset we were able to positively assess the feasibility of using the novel method in an online BCI context

Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, 'shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by 'trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the 'Haar' wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI