Topological attention for denoising astronomical images

Astronomical observations often involve capturing faint signals from celestial objects, such as distant galaxies or dim stars. These signals can be easily overwhelmed by noise, which includes electronic noise, atmospheric interference, and other artifacts. It is then clear that using an effective denoising algorithm is crucial to improve the accuracy of data interpretation by extracting the actual astronomical signals from the noisy background. In this work, we introduce a novel denoising approach based on deep neural networks with pixel attention derived from the topological structure extracted by 0-dimensional Persistent Homology (PH). Our network architecture combines an AutoEncoder (AE) with a Topological Module (TM) that assigns weights to pixels based on PH, providing nuanced attention to the relevant image regions. Our methodology is evaluated against widely used denoising methods, showcasing its potential for enhancing the quality of astronomical images.