Denoising weak lensing mass maps with diffusion model: systematic comparison with generative adversarial network

TL;DR

Though the training of DM is more computationally demanding compared with GAN, there are several advantages: numerically stable training, higher performance in the reconstruction of cosmological statistics, and sampling multiple realisations once the model is trained.

Abstract

Removing the shape noise from the observed weak lensing field, i.e., denoising, enhances the potential of WL by accessing information at small scales where the shape noise dominates without denoising. We utilise two machine learning (ML) models for denosing: generative adversarial network (GAN) and diffusion model (DM). We evaluate the performance of denosing with GAN and DM utilising the large suite of mock WL observations, which serve as the training and test data sets. We apply denoising to 1,000 noisy mass maps with GAN and DM models trained with 39,000 mock observations. Both models can fairly well reproduce the true convergence map on large scales. Then, we measure cosmological statistics: power spectrum, bispectrum, one-point probability distribution function, peak and minima counts, and scattering transform coefficients. We find that DM outperforms GAN in almost all considered statistics and recovers the correct statistics down to small scales. For example, the angular power spectrum can be recovered with DM up to multipoles $\ell \lesssim 6000$ while the noise power spectrum dominates from $\ell \simeq 2000$. We also conduct stress tests on the trained model; denoising the maps with different characteristics, e.g., different source redshifts, from the training data. The performance degrades at small scales, but the statistics can still be recovered at large scales. Though the training of DM is more computationally demanding compared with GAN, there are several advantages: numerically stable training, higher performance in the reconstruction of cosmological statistics, and sampling multiple realisations once the model is trained. It has been known that DM can generate higher-quality images in real-world problems than GAN, the superiority has been confirmed as well in the WL denoising problem.

Figures (19)

• Figure 1: Upper row: Comparison between the denoised convergence maps with GAN and DM and the ground truth map. These maps are pixellated with $256 \times 256$ grids with the area of $2.5 \times 2.5 \deg^2$, which corresponds to the pixel size of $0.586\,\mathrm{arcmin}$. Lower row: Zoom-in maps around the peak with the highest significance in the true noiseless map. The red squares in the maps in the upper row indicate the corresponding zoom-in regions displayed in the lower row. Note that each map is not normalised.
• Figure 2: Comparison of the denoised maps generated by five networks of GAN and five samples of DM from a single noisy map.
• Figure 3: Comparison between the true noiseless map and the mean and median of five denoising realisations with GAN and DM in Figure \ref{['fig:maps_sample']}.
• Figure 4: Pixel-level comparisons of SNR between the ground truth map and the denoised maps with GAN (left panel) and DM (right panel). The red (green) points with error bars correspond to the mean and standard deviation binned with pixel SNRs in 5000 denoised maps with GAN (DM). The black dashed line represents the case where the generated values perfectly match the ground-truth.
• Figure 5: The angular power spectra of the normalised ground-truth maps (dashed line) and denoised maps (solid lines) with GAN and DM. The five blue (orange) thin lines correspond to the five networks (samples) from GAN (DM). The thick blue (orange) line shows the average power spectrum for GAN (DM). The dotted line corresponds to the noise power spectrum. For normalisation of the noise power spectrum, the harmonic average of the variance of true maps is used. The bottom panel shows the error between the power spectra of the denoised and the true maps.