Justin Lee, Air Force Institute of Technology; Stephen Cain, Air Force Institute of Technology
Keywords: blind deconvolution,long-exposure,separable, separability, atmosphere, turbulence, algorithm
Abstract:
Currently, astronomers utilize a two-dimensional blind deconvolution algorithm to deconvolve an unknown object from an unknown point spread function (PSF). This two-dimensional algorithm is highly demanding of the core processing unit (CPU) and is typically applied in post-processing. A faster algorithm could be obtained using a one-dimensional blind deconvolution algorithm on spatially separable objects and PSFs. While there has been research done on the application of one-dimensional algorithms on spatially separable objects, this research focuses on the spatial separability of a PSF. This would significantly decrease processing time by decreasing the number of Fourier transforms and through the elimination of all two-dimensional Fourier transforms.
In short exposure imaging scenarios, the two-dimensional PSF is rarely spatially separable, but when an imaging system produces a long exposure image, the PSF tends to take on a shape similar to that of a two-dimensional Gaussian or a two-dimensional Lorentzian function depending on the amount of atmospheric compensation utilized during the exposure. Atmospherically compensated long exposure images make a superior starting point for obtaining high-resolution images of objects in space over images gathered with short exposures for many reasons. The primary causes of this are that compensated images achieve higher spatial bandwidth of the raw data and a lower amount of readout noise injected into the observation. Other algorithms have been proposed for achieving blind deconvolution of images in two-dimensions and will be used for comparison purposes in this research.
To achieve spatially separable blind deconvolution, two conditions must be met. First, the image of the object under observation predicted by geometric optics must be able to be described as the outer product of a horizontal vector and a vertical vector. This is generally true if this image as a matrix has a rank of one. Although most satellite images are not spatially separable, when they are imaged from distances greater than approximately 35,000 km, or the distance between geosynchronous earth orbit (GEO) and earths surface, they appear as nearly point sources. Collections of these objects, therefore, would appear as collections of point sources, which will be shown in this paper to be spatially separable. The second condition is that the PSF as a matrix must also be able to be described as the outer product of a horizontal vector and a vertical vector. This will be shown in this paper to be generally true for astronomical telescopes with little to no optical aberrations taking long-exposure images through the turbulent atmosphere.
In this paper, a spatially separable blind deconvolution algorithm is demonstrated that achieves a significantly faster processing time and superior sensitivity when processing long-exposure image data of objects that are at geosynchronous orbit from a ground-based telescope. The proposed approach takes advantage of the structure of the long exposure PSFs radial symmetric characteristics to approximate it as a product of one-dimensional horizontal and vertical intensity distributions. Because objects at geosynchronous or geostationary orbit can be well approximated as being spatially separable as they are, in general, non-resolvable, they are optimal candidates for use with this algorithm.
The algorithm’s performance is measured by computing the mean-squared error compared with the true object as well as the processing time required to perform the blind deconvolution. It will be shown that images processed by the proposed technique will possess, on average, a lower mean-squared error than images that are processed through the traditional two-dimensional blind deconvolution approach. In addition, the one-dimensional algorithm will be shown to perform the deconvolution significantly faster. In both cases the seeing parameter is treated as an unknown variable in the image reconstruction problem.
Date of Conference: September 15-18, 2020
Track: Adaptive Optics & Imaging