[Paper Review] High-Resolution CMB Lensing Reconstruction with Deep Learning

Peikai Li, Ipek Ilayda Onur+2 more|arXiv (Cornell University)|May 15, 2022

Radio Astronomy Observations and Technology4 citations

TL;DR

This paper proposes a deep learning-based super-resolution approach using a modified Pix2PixHD generative adversarial network (GAN) to reconstruct high-resolution cosmic microwave background (CMB) lensing convergence maps from noisy CMB Q and U polarization maps. The method outperforms the traditional quadratic estimator and ResUNet by better preserving small-scale power spectrum features, achieving near-perfect alignment with the true power spectrum even at 2 μK-arcmin noise levels, with only ~15% signal-to-noise degradation compared to the optimal case.

ABSTRACT

Next-generation cosmic microwave background (CMB) surveys are expected to provide valuable information about the primordial universe by creating maps of the mass along the line of sight. Traditional tools for creating these lensing convergence maps include the quadratic estimator and the maximum likelihood based iterative estimator. Here, we apply a generative adversarial network (GAN) to reconstruct the lensing convergence field. We compare our results with a previous deep learning approach -- Residual-UNet -- and discuss the pros and cons of each. In the process, we use training sets generated by a variety of power spectra, rather than the one used in testing the methods.

Motivation & Objective

• To develop a deep learning model that reconstructs high-resolution CMB lensing convergence maps from noisy CMB polarization data.
• To improve upon existing deep learning methods like ResUNet by focusing on accurate small-scale structure recovery.
• To test the robustness of the model across diverse convergence power spectra not seen during training.
• To evaluate the performance of the GAN-based approach against the quadratic estimator and ResUNet under varying detector noise levels.
• To explore the potential of GANs in cosmological signal reconstruction, particularly for future low-noise CMB surveys.

Proposed method

• A modified Pix2PixHD GAN architecture is used, where the input is the observed CMB Stokes parameters Q and U, rather than a low-resolution version of the target map.
• The conditional GAN assumption is removed, and a Fourier-space loss is added to the discriminator to improve high-frequency structure learning.
• The model is trained to predict the lensing convergence map κ from Q and U maps, using a dataset of simulated realizations with varied convergence power spectra.
• The training dataset includes 1,500 realizations per noise level, with power spectra scaled to 0.75, 1.0, and 1.25 times the reference spectrum.
• Performance is evaluated via signal-to-noise ratio and power spectrum reconstruction fidelity, comparing the GAN, ResUNet, and quadratic estimator.
• The model is evaluated on a generalized test set with unseen power spectra to assess generalization and robustness.

Experimental results

Research questions

• RQ1 Can a GAN-based super-resolution model outperform traditional quadratic estimators and ResUNet in reconstructing high-resolution CMB lensing convergence maps under realistic noise levels?
• RQ2 How well does the GAN model preserve small-scale power spectrum features when trained on a single power spectrum but tested on multiple unseen spectra?
• RQ3 What modifications to the Pix2PixHD architecture are necessary to effectively reconstruct lensing convergence from CMB polarization maps?
• RQ4 How does the signal-to-noise ratio of the GAN model compare to the quadratic estimator and ResUNet at 2 μK-arcmin detector noise?
• RQ5 Can the GAN model generalize to unseen convergence power spectra without fine-tuning, and how does its performance degrade with increasing noise?

Key findings

• The GAN-based model achieves near-perfect alignment between the reconstructed lensing power spectrum and the true power spectrum, even at 2 μK-arcmin detector noise.
• Despite a ~15% signal-to-noise degradation compared to the noiseless case, the GAN model maintains higher signal-to-noise than the vanilla quadratic estimator at the same noise level.
• The GAN model outperforms ResUNet in capturing small-scale power spectrum features, particularly in the presence of non-negligible detector noise.
• The model generalizes well across different convergence power spectra in the robustness test, correctly distinguishing between 0.75, 1.0, and 1.25 times the reference spectrum.
• The modified GAN architecture with Fourier-space loss and removal of conditional assumptions improves high-frequency structure recovery compared to standard super-resolution networks.
• The results suggest that GANs can be a viable alternative to iterative maximum-likelihood methods for high-resolution CMB lensing reconstruction in next-generation surveys.