Single Image Super-Resolution using Denoising Auto-Encoder

Hello everyone! As we wrap up Google Summer of Code 2024, I’m thrilled to share the completion of my project with ML4Sci, focusing on Single-Image Super-Resolution (SISR) for gravitational lensing images. In this blog post, I’ll introduce our novel approach: using an Iterative Denoising Auto-Encoder to map low-resolution image space to high-resolution image space.

Project Overview

Strong gravitational lensing is a critical observational tool for studying the distribution of dark matter, particularly through the identification of substructures within galaxy halos. The bending of light caused by massive objects distorts the images of background galaxies, producing features such as arcs and Einstein rings. However, analyzing these structures in detail requires high-resolution (HR) images, which are often unavailable due to the limitations of current observational equipment.

https://earthsky.org/space/what-is-gravitational-lensing-einstein-ring/

Our project aimed to develop a super-resolution technique to enhance the quality of low-resolution (LR) gravitational lensing images, enabling more precise analysis of lensing systems and, consequently, better insights into dark matter distribution.

Data

We worked with a dataset compiled from various strong gravitational lens candidates found in the literature. By cross-matching this list with the Hyper Suprime-Cam (HSC) PDR2 Wide-field survey and archival data from the Hubble Space Telescope (HST), we obtained 173 objects observed with both instruments. We extracted HSC cutouts in the i band as low-resolution examples (0.168"/pix) and HST images in the F814W filter as the high-resolution counterparts (0.05"/pix).

Methodology: Denoising Auto-Encoder

Our approach, the Iterative Auto-Encoder, is a novel modification of the Conditional Guided Diffusion Probabilistic Model (CG-DPM). It maintains the same forward process as traditional diffusion models but significantly alters the backward process.

Forward and Backward Process of Iterative Auto Encoder

Iterative Unet Encoder

Results & Discussions

We evaluated our Iterative Auto-Encoder against several baseline models, including SRCNN, RCAN, SRGAN, and a Variational Autoencoder (VAE). The performance was measured using Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM).

Our Iterative Auto-Encoder achieved the highest PSNR score of 33.56, surpassing RCAN (32.60) and SRCNN (31.76) by 0.96 and 1.80, respectively. This improvement, while numerically small, represents a significant enhancement in image clarity, particularly important for retaining the fine details characteristic of gravitational lensing structures.

In terms of SSIM, our model remained competitive with a score of 0.855, close to RCAN’s leading score of 0.890. This indicates that our approach maintains good structural fidelity while achieving superior perceptual quality.

Conclusion

The Iterative Auto-Encoder has shown promising results in enhancing low-resolution gravitational lensing images. Its ability to outperform existing models in terms of PSNR while maintaining competitive SSIM scores makes it a valuable tool for astrophysical applications, particularly in the context of upcoming large-scale astronomical surveys like Euclid and LSST.

Acknowledgements

I would like to thank my mentors at ML4Sci, the entire Google Summer of Code team, and the astrophysics community for their support and valuable datasets. This project wouldn’t have been possible without their guidance and resources.

Code

The code for this project is available at the link.