In many scientific disciplines, weak signals of interest are obscured by dominant nuisance signals that are several orders of magnitude stronger. Recovering these weak signals requires subtracting the dominant ones; however, this calibration process inherently distorts or partially suppresses the underlying signal of interest. To address this problem, we propose the use of normalizing flow models to reconstruct calibration-affected weak signals. By leveraging the statistical invariance of the target signals and assuming minimal initial suppression, our framework effectively recovers the lost signal components. We provide a comprehensive theoretical overview of this normalizing flow-based recovery method and demonstrate its efficacy using simulated data.
Figures & tables
Figure 1: A schematic of the signal flow. The nuisance signals are subtracted from the observed data x by calibration to get the residual y .
Figure 2: An example simulation where the observed data x , the residual data y and the ground truth weak signal μ are shown.
Figure 3: Estimated weak signal using 3000 samples compared with the ground truth (note the change in scale compared to Fig. 2 ). The averaged residual y gives a lower estimate of μ (suppressing the signal and losing power). The average prediction by the trained normalized flow model n gives a more accurate result.
Figure 4: Average images made using the test observation (all frequencies), covering about 8×8 square degrees in the sky, centered at the north celestial pole. Note that the beam pointing direction of this observation is elsewhere in the sky while the weak (diffuse) signal is simulated to be at the pole. The four columns from left to right show the images made using the observed data (prior to calibration), the ground truth (without noise), the residual (after calibration) and the prediction from the DNN, respectively. Note the difference in the color scale in the left column, where the dominant component is the nuisance signal and its artifacts. The four rows from top to bottom correspond to the Stokes I, Q, U and V polarizations. Note that the images made using the residual has significant suppression of the desired signal while the DNN prediction closely agrees with the ground truth. The ground truth images are without any noise while the DNN prediction contains the expected noise as well. This is evidenced by the Stokes V images in the last row, where the image made by uncalibrated data (leftmost column) and the DNN prediction (rightmost column) have more or less the same power level.
Appendix figures & tables2 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: A schematic of the DNN used in both examples discussed in section IV . The exact parameters for D , H , Mx , and T vary for each example.
Department of Mathematical and Statistical Sciences, Marquette University, USA · The University of Texas at Austin, USA · Cornell Ann S. Bowers College of Computing and Information Science, Cornell University, USA