Deconvolution and AI
Deconvolution is a mathematical inversion process where the goal is to reverse the convolution that occurs when an image is created through an optical system. This convolution typically reveals itself as blur due to imperfections in the optics, motion, atmospheric movement, or other distortions. The traditional approach to deconvolution involves using a Point Spread Function (PSF) to model these distortions and mathematically reverse them. AI-based deconvolution adheres to the same principles of reversing image blur, but with enhanced adaptability and precision through the use of specialized neural networks.
The core principle of deconvolution is to estimate the original image 𝑓 from the observed image 𝑔, given by:
𝑔 = (𝑓 ∗ ℎ) + 𝑛
where ℎ is the PSF, ∗ denotes convolution, and 𝑛 represents noise. The challenge is to solve this equation for 𝑓 when 𝑔 and ℎ are known, attempting to minimize the effect of 𝑛. AI-based deconvolution extends this concept by using large amounts of training data to learn to predict 𝑓. In the case of “Adaptive PSF” for Theia, this means it needs to inherently learn to estimate ℎ, as well as 𝑛 to be able to effectively ignore it. For Theia’s manual mode or after ℎ has been estimated adaptively, the model has learned how to use the given/predicted PSF to determine what 𝑔 would look like based on that.
Theia is capable of taking in a user-defined FWHM value to tell the model to deconvolve with a circular PSF with that FWHM value. It is also capable of dynamically inferring an optimal PSF from the image tiles themselves. This is particularly useful when the PSF varies across different areas of the same image. Moreover, this is actually one of the natural benefits of neural networks. It is unrealistic to use full, high-resolution images as model input, so they are split up into tiles. The PSF can be determined uniquely for each tile, whereas traditional deconvolution algorithms assume the same PSF across the entire image. Finally, Theia has been trained in such a way that the noise is not amplified in the deconvolution process, but instead ignored while sharpening the underlying stellar and nonstellar detail.
Theia User Interface Overview
Adaptive PSF: Traditional deconvolution methods require a predefined PSF, which is often not representative of the actual blurring effects of an entire image in astrophotography. Theia dynamically generates a PSF for each tile it processes, accounting for variations across the image due to atmospheric turbulence, optical aberrations, or sensor idiosyncrasies. This mode is currently experimental and is subject to further updating. Below is an example of Adaptive PSF’s current capabilities:
Manual Mode: Theia permits the manual specification of the Full Width Half Maximum (FWHM). This value dictates the assumed shape and size of a circular PSF with the provided FWHM, enabling the model to perform restoration based on this parameter. Below is an example of Manual PSF’s current capabilities:
Correction Model: Theia extends beyond simple circular PSF deconvolution to address specific aberrations like limited trailing and coma. It employs a specialized algorithm that adjusts these distortions. This functionality is in its early stages and is subject to further updates and improvement. Below are the current capabilities of the correction model:
Processing Options:
Luminance Only: This mode isolates the luminance of an RGB image for deconvolution, leaving the color balance unaltered.
Circularize Only: This mode attempts to transform elongated or distorted stars into more symmetrical, circular shapes, without altering their size.