Solar multi-object multi-frame blind deconvolution with a spatially variant convolution neural emulator

TL;DR

This work tackles atmospheric blur in ground-based solar imaging by introducing a neural spatially variant convolution emulator (SVCE) that learns per-pixel PSFs and generalizes from invariant PSFs via Karhunen–Loève wavefront representations. The SVCE is embedded as a forward model in a multi-object multi-frame blind deconvolution (SV-MOMFBD) framework, enabling full-field deconvolution without patch-based mosaicking and delivering orders-of-magnitude speedups. Key contributions include a high-capacity conditional U-Net with instrument-conditioned encoding, a training regime that leverages synthetic PSFs and per-pixel KL coefficients, and a regularized optimization scheme that jointly recovers multiple solar objects and frame-wise wavefront modes. The approach yields reconstructions with performance comparable to conventional MOMFBD while dramatically reducing computational requirements, enabling scalable processing of large solar datasets and potentially informing future adaptive optics and imaging pipelines.

Abstract

The study of astronomical phenomena through ground-based observations is always challenged by the distorting effects of Earth's atmosphere. Traditional methods of post-facto image correction, essential for correcting these distortions, often rely on simplifying assumptions that limit their effectiveness, particularly in the presence of spatially variant atmospheric turbulence. Such cases are often solved by partitioning the field-of-view into small patches, deconvolving each patch independently, and merging all patches together. This approach is often inefficient and can produce artifacts. Recent advancements in computational techniques and the advent of deep learning offer new pathways to address these limitations. This paper introduces a novel framework leveraging a deep neural network to emulate spatially variant convolutions, offering a breakthrough in the efficiency and accuracy of astronomical image deconvolution. By training on a dataset of images convolved with spatially invariant point spread functions and validating its generalizability to spatially variant conditions, this approach presents a significant advancement over traditional methods. The convolution emulator is used as a forward model in a multi-object multi-frame blind deconvolution algorithm for solar images. The emulator enables the deconvolution of solar observations across large fields of view without resorting to patch-wise mosaicking, thus avoiding artifacts associated with such techniques. This method represents a significant computational advantage, reducing processing times by orders of magnitude.

Figures (14)

• Figure 1: Training and validation losses evolution for all the epochs. The neural network does not show overtraining, although a saturation occurs after epoch $\sim$50.
• Figure 2: Samples from the training set, showing the capabilities of our model. The upper row displays 12 original images from Stable ImageNet-1K and synthetic image of point-like objects. The second row displays the target convolved image, with a PSF that is compatible with Kolmogorov turbulence. The third rows shows the output of our model, with the fourth row displaying the residuals.
• Figure 3: Spatially variant convolution with a defocus obtained with the SVCE. The defocus PSF is shifted along the diagonal of the image.
• Figure 4: Original image from the stein12_a simulation (first panel), together with the image after diffraction when observed with SST/CRISP at 8542 Å (second panel). The third panel displays the spatially variant convolution with a region of defocus computed using per-pixel convolution, with the fourth panel showing the results obtained with the neural SVCE. The last panel displays the residuals, with an NMSE of 1.6$\times$10$^{-4}$.
• Figure 5: Computing time per convolution as a function of the size of the image and the batch size for the SVCE, both in CPU and GPU. As comparison, we show results obtained for the classical method of computing the convolution of the image with a PSF for every pixel.