Abstract: Since the first experimental evidence for the existence of gravitational waves in 2015, the amount of data in this scientific area has increased enormously. The interferometers, used to capture these waves, need to achieve a high level of instrumental sensitivity to be able to detect and analyse the weak signals emitted by sources of low intensity. 

High sensitivity is often accompanied by high levels of noise that difficult data analysis. In nowadays interferometers, large amounts of data are recorded with a high percentage of noise from which we attempt to extract the possible gravitational waves buried therein. In this dissertation we propose to use a denoising method based on the minimisation of the total variance of the time series that constitute the data. Known as the ROF method, it assumes that the largest contribution to the total variance of a function comes from noise. In this way, a minimisation of this variance should lead to a drastic reduction in the presence of noise. This denoising procedure should help to improve the detection and data quality of gravitational wave analysis.

We have implemented two ROF-based denoising algorithms in a commonly used gravitational-wave analysis software package. The analysis package is known as coherent WaveBurst (cWB) and uses the excess energy from the coherence between data from two or more interferometers to find gravitational waves. The denoising methods are the one-step regularised ROF (rROF), and the iterative rROF procedure (irROF). The latter is designed as an improvement of the former for those cases where the noise cleaning is excessive and extracts a portion of the signal in an unrecoverable way.

We have tested both methods using events from the gravitational-wave catalogue of the first three observing periods of the LIGO-Virgo-KAGRA scientific collaboration. These events, named GW1501914, GW151226, GW170817 and GW190521, comprise different wave morphologies of compact binary systems injected at different noise quality levels. We can see that the analysis of these wavelets with the rROF method is defective as it incorrectly extracts a portion of the signal at the high frequencies. However, the use of the irROF enhancement procedure effectively removes the noise while preserving nearly intact the wavelet function of the signals, providing a significant increase in the signal-to-noise ratio values.

One of our goals has been to use the irROF denoising method during a data collection period to support on-the-fly signal detection. To this end, we have extended our study by characterising the background noise of one week of data after the application of the irROF method. We have calculated and analysed the detection efficiencies of a selection of signals mimicking various types of gravitational waves. The results obtained so far do not support the effect found in the analysis of individual gravitational waves. However, we have found that further improvements and variations of the irROF denoising method could improve the detection efficiencies.

Our work demonstrates that, although the irROF method applied to a period of data does not improve the detection achieved using methods that treat individual wavelets, this improvement can be achieved by further developing and fine-tuning some of the strategies proposed here. The methodology presented here can be used in the implementation of other denoising methods currently in use or under development. The present work provides a set of suggestions and proposals that will allow to increase the detection of these gravitational waves.