Strong-Lensing Source Reconstruction with Denoising Diffusion Restoration Models

Konstantin Karchev, Noemi Anau Montel, Adam Coogan, Christoph Weniger

Submitted on 8 November 2022


Analysis of galaxy--galaxy strong lensing systems is strongly dependent on any prior assumptions made about the appearance of the source. Here we present a method of imposing a data-driven prior / regularisation for source galaxies based on denoising diffusion probabilistic models (DDPMs). We use a pre-trained model for galaxy images, AstroDDPM, and a chain of conditional reconstruction steps called denoising diffusion reconstruction model (DDRM) to obtain samples consistent both with the noisy observation and with the distribution of training data for AstroDDPM. We show that these samples have the qualitative properties associated with the posterior for the source model: in a low-to-medium noise scenario they closely resemble the observation, while reconstructions from uncertain data show greater variability, consistent with the distribution encoded in the generative model used as prior.


Comment: Accepted for the NeurIPS 2022 workshop Machine Learning and the Physical Sciences; 9 pages, 4 figures

Subjects: Astrophysics - Instrumentation and Methods for Astrophysics; Astrophysics - Cosmology and Nongalactic Astrophysics; Astrophysics - Astrophysics of Galaxies


Top: from left to right, the mock observation, $\y$ (with a medium noise level), the true source, $\x$ (an unconstrained sample from \AstroDDPM), the mean and standard deviation of \num{100} posterior samples from \gls*{ddrm}, $\x_{0, i} \sim \denoisep[](\x_0 \given \y)$, and the residual of the mean with respect to the true source and with respect to the observation in the image plane; finally, a histogram of the latter compared to a Gaussian. Bottom: each column is a random posterior sample (top row), which is then lensed to produce the respective noiseless image $\H\x_{0, i}$ (middle row). Shown (bottom row) are also the residuals between $\H\x_{0, i}$ and the observation. In residual plots, negative values in one channel are shown as positive values in the other two (red $\leftrightarrow$ cyan, green $\leftrightarrow$ magenta, blue $\leftrightarrow$ yellow), considering complementary colors as "negative".