Blind Deconvolution for Astronomical and Space-Object Imaging

The angular resolution of an optical telescope under ideal circumstances is determined by the ratio of the light's wavelength to the telescope's diameter. A 1.6 meter ground-based telescope sensing green light, for example, should resolve features on the order of 10 inches when observing the Hubble Space Telescope in its 600 km orbit. Time-varying changes in the refractive index of Earth's atmosphere can, however, swell this resolution by a factor of 15 making meaningful inference about the satellite from ground-based pictures nearly impossible. This "seeing" problem has plagued astronomers for years.

In the figure shown above, a short exposure image of the Hubble Space Telescope as acquired by a 1.6 m telescope at Air Force Maui Optical Station clearly illustrates the distortions induced by atmospheric turbulence.

Adaptive compensation of the atmospheric wavefront-aberrations can be accomplished through the use of wavefront sensors and deformable mirrors. This adaptive-optics approach, however, requires high light-levels or artificial guide stars, and its cost can be prohibitive if full compensation is required for large-diameter telescopes. An alternative method, and one that can be used in conjunction with a partially-compensated adaptive-optics system, is to record a sequence of blurred, short-exposure images and then perform the deblurring through post-detection signal processing. Because the precise manner in which these images are blurred by the atmosphere is not known in advance or easily predicted, conventional approaches to image deblurring cannot be applied and the problem is one of blind deblurring.

In our research group, a maximum-likelihood estimation method has been considered for recovering fine-resolution imagery from a sequence of noisy, blurred images, and a numerical technique based on the expectation-maximization (EM) procedure has been developed for solving this multiframe blind deblurring problem. A parallel implementation of this algorithm on an IBM SP2 computer at the Maui High Performance Computing Center has been used to restore the resolution of ground-based telescope imagery of the Hubble Space Telescope. An example of a restored image is shown below, and an MPEG movie (1.3 M) can also be viewed to compare both the raw telescope data with the restored imagery.

Restored Image of the Hubble Space Telescope

Timothy J. Schulz