Total-variation-based methods for gravitational wave denoising

We describe new methods for denoising and detection of gravitational waves embedded in additive Gaussian noise. The methods are based on total variation denoising algorithms. These algorithms, which do not need any a priori information about the signals, have been originally developed and fully tested in the context of image processing. To illustrate the capabilities of our methods we apply them to two different types of numerically-simulated gravitational wave signals, namely bursts produced from the core collapse of rotating stars and waveforms from binary black hole mergers. We explore the parameter space of the methods to find the set of values best suited for denoising gravitational wave signals under different conditions such as waveform type and signal-to-noise ratio. Our results show that noise from gravitational wave signals can be successfully removed with our techniques, irrespective of the signal morphology or astrophysical origin. We also combine our methods with spectrograms and show how those can be used simultaneously with other common techniques in gravitational wave data analysis to improve the chances of detection.

Figure 1

Gravitational waveforms of three representative signals from the core collapse catalog of [32] with different values of the degree of differential rotation. The equation of state and the progenitor mass are fixed for all represented signals. Signal “s20a1o05_shen” (a) is show in the upper panel, signal “s20a2o09_shen” (b) is shown in the middle panel, and signal “s20a3o15_shen” (c) in the bottom panel. $t_{\mathrm{b}}$ indicates the time of bounce.

Figure 2

Gravitational waveform of a representative signal from the BBH catalog of [40], signal “0001,” used for our test purposes.

Figure 3

Frequency distribution of noise weight coefficients obtained from the advanced LIGO sensitivity curve.

Figure 4

Histograms of the values of ${\mu }_{\text{opt}}$ for 500 noise generations for the three representative core collapse signals. The upper panels show the values of ${\mu }_{\text{opt}}$ for the rROF method in the time domain while the corresponding results for the SB method applied in the frequency domain are shown in the bottom panel. A $\mathrm{SNR}=15$ is assumed.

Figure 5

Dependence of the PSNR for different signal-to-noise ratios for the three representative core collapse signals. The upper panels show the values of PSNR for the rROF method in the time domain while the corresponding results for the SB method applied in the frequency domain are shown in the bottom panel. The insets in the top panels magnify the areas where the variations in the curves are larger.

Figure 6

Histograms of ${\mu }_{\text{opt}}$ for all signals of the core collapse catalog with $\mathrm{SNR}=15$. The left panel shows the span of values of ${\mu }_{\text{opt}}$ for the rROF method while the right panel displays the corresponding values for the SB method.

Figure 7

Denoising of the core collapse waveform signal C with $\mathrm{SNR}=20$. Top panel: original signal (red dashed line) and nonwhite Gaussian noise (black solid line). Middle panel: Original and denoised (black solid line) signals for the SB method in the frequency domain with $\mu =2.0$. Bottom panel: Original and denoised signals for the rROF method in the time domain with $\mu =0.09$.

Figure 8

Denoising of the core collapse waveform signal C for the rROF method with $\mu =0.09$ for three values of the SNR, 20 (top), 10 (middle), and 5 (bottom).

Figure 9

Denoising of the core collapse waveform signal C with $\mathrm{SNR}=20$ after applying both algorithms sequentially, rROF first with $\mu =0.05$ followed by SB with $\mu =8$.

Figure 10

Denoising of the BBH waveform signal “0001” with $\mathrm{SNR}=20$. Top panel: original signal (red dashed line) and nonwhite Gaussian noise (black solid line). Middle panel: Original and denoised (black solid line) signals for the SB method in the frequency domain with $\mu =1.6$. Bottom panel: Original and denoised signals for the rROF method in the time domain with $\mu =0.0026$.

Figure 11

Spectrograms of the original noisy signal (top panel) and denoised signal (bottom panel) for the core collapse signal C and $\mathrm{SNR}=10$. The higher values of the spectral power density are shown in red, while the lower power is represented in blue.

Figure 12

Spectrogram of the core collapse signal C for $\mathrm{SNR}=5$. The excess power around 0.5 s is supposed to be produced by the gravitational wave signal.