A flexible Expectation-Maximization framework for fast, scalable and high-fidelity multi-frame astronomical image deconvolution

TL;DR

The paper tackles large-scale ground-based astronomical imaging by developing a flexible EM framework for fast, scalable multi-frame deconvolution and super-resolution. It models each exposure as the convolution of a common latent sky image with exposure-specific PSFs and uses a joint, multiplicative EM update across all frames to recover a non-parametric, non-negative sky image. A super-resolution extension optimizes higher-resolution PSFs and uses a down-sampling operator to produce Δ-fold higher resolution reconstructions, implemented in TensorFlow with GPU acceleration. On 33 Hyper Suprime-Cam exposures, the method achieves ~60 seconds per dataset with high-fidelity results, revealing fine structures such as galaxy spiral arms and enabling precise photometry; future work includes robust noise modeling and sky-background subtraction.

Abstract

We present a computationally efficient expectation-maximization framework for multi-frame image deconvolution and super-resolution. Our method is well adapted for processing large scale imaging data from modern astronomical surveys. Our Tensorflow implementation is flexible, benefits from advanced algorithmic solutions, and allows users to seamlessly leverage Graphical Processing Unit (GPU) acceleration, thus making it viable for use in modern astronomical software pipelines. The testbed for our method is a set of $4$K by $4$K Hyper Suprime-Cam exposures, which are closest in terms of quality to imaging data from the upcoming Rubin Observatory. The preliminary results are extremely promising: our method produces a high-fidelity non-parametric reconstruction of the night sky, from which we recover unprecedented details such as the shape of the spiral arms of galaxies, while also managing to deconvolve stars perfectly into essentially single pixels.

Figures (2)

• Figure 1: Hyper Suprime-Cam data. We are given a set of $n=33$ exposures $y\!\equiv\!\{y^{(1)}, \dots, y^{(n)}\}$, each of size $4$K by $4$K pixels (left), and corresponding PSFs $f\!\equiv\!\{f^{(1)}, \dots, f^{(n)}\}$ of size $43$ by $43$ pixels (right).
• Figure 2: Comparison: Selected cutouts from a "sample mean" co-add (left) vs. a restored image $\Hat{x}$ from our EM approach without super-resolution (middle), and with super-resolution using $\Delta = 2$ (right). Our method de-blurs a wide array of sources, such as spiral arm and elliptical galaxies, and stars of varying sizes and shapes (top row), as well as small, faint sources (bottom row). The reconstructions contain none of the usual unwanted artifacts (e.g ringing, speckles, noise in the sky background), producing high-fidelity images where e.g., the pixels are non-negative, the sky-background has zero pixel values, and the number and relative sizes, shapes and fluxes of the sources is preserved. Overall, the method produces a physically meaningful restored image of the night sky which is suitable for photometry, especially when super-resolution is used.