Fourier convolutional decoder: reconstructing solar flare images via deep learning

Reconstructing images from observational data is a complex and time-consuming process, particularly in astronomy, where traditional algorithms like CLEAN require extensive computational resources and expert interpretation to distinguish genuine features from artifacts, especially without ground truth data. To address these challenges, we developed the Fourier convolutional decoder (FCD), a custom-made overcomplete autoencoder trained on simulated data with available ground truth. This enables the network to generate outputs that closely approximate expected ground truth. The model's versatility was demonstrated on both simulated and observational datasets, with a specific application to data from the spectrometer/telescope for imaging X-rays (STIX) on the solar orbiter. In the simulated environment, FCD's performance was evaluated using multiple-image reconstruction metrics, demonstrating its ability to produce accurate images with minimal artifacts. For observational data, FCD was compared with benchmark algorithms, focusing on reconstruction metrics related to Fourier components. Our evaluation found that FCD is the fastest imaging method, with runtimes on the order of milliseconds. Its computational cost is comparable to the most efficient reconstruction algorithm and 280 $\times$ faster than the slowest imaging method for single-image reconstruction on a CPU. Additionally, its runtime can be reduced by an order of magnitude for multiple-image reconstruction on a GPU. FCD outperforms or matches state-of-the-art methods on simulated data, achieving a mean MS-SSIM of 0.97, LPIPS of 0.04, PSNR of 35.70 dB, a Dice coefficient of 0.83, and a Hausdorff distance of 5.08. Finally, on experimental STIX observations, FCD remains competitive with top methods despite reduced performance compared to simulated data.