Atomic Representation of Glitches - Preliminary Results

Glitches are transients of environmental or instrumental origin appearing in the data channel of existing large baseline interferometer based gravitational wave detectors. Their presence limits severely the performance of gravitational wave detection/estimation algorithms based on the customary Gaussian noise assumption, and requires adopting ad-hoc data laundering techniques. Modeling glitches is in important issue both for simulating the instruments' noise background and for designing gravitational wave detection algorithms with improved performance. We believe that glitches can be modeled as superpositions of very simple time-frequency atoms, and discuss the use of a Matching-Pursuit algorithm to decompose glitches into Sine-Gaussian and Ring-Down components. The method has been tested on the data-channel glitch database maintained by P. Saulson and co-Workers [1]. Preliminary results appear encouraging, and suggest that only a few atoms may be needed to represent most of the observed glitches. The Waves Group Implementation. Matching Pursuit We used a dictionary of (complex) Sine-Gaussian (Gabor) functions. These are minimum spread atoms, depending on 5 parameters only (amplitude, initial phase, location in time, location in frequency, and time spread). In order to decompose glitches into time-frequency atoms we implemented a modified Matching Pursuit (MP) algorithm [4]. MP was originally designed to decompose very complicated (e.g., musical) signals into thousands of time-frequency atoms. Hopefully, MP should be effective in decomposing much simpler signal into a much smaller number of atoms. Our preliminary findings suggest that this approach is generally successful, although special care is required in several stages of the algorithm, compared to standard implementations. The MP flow diagram is sketched below. 1 ( (4 ) ) t f π − Δ ⋅Δ =