Pixon reconstruction:

Getting the most out of space telescope images

By Eliot F. Young, ScD     image of PDF button


Dr. Eliot F. Young is a senior research scientist at SwRI's Boulder, Colo. Office and principal investigator of several grant-funded projects studying the applications of Pixon image enhancement in planetary science and astronomy.


High-resolution imaging--important to fields as diverse as the military, medicine and law enforcement--is one of the primary drivers in observational astronomy. The quest for sharper images has led to larger telescopes for increased light gathering and resolving power. Recent developments have been extraordinarily successful, such as the Hubble Space Telescope and adaptive optics technology, which uses deformable mirrors to compensate for distortions in the Earth's atmosphere. The Hubble telescope can resolve details on the scale that is roughly equivalent to detecting a dime from a distance of 25 miles. The 10-meter Keck Observatory telescope in Mauna Kea, Hawaii, competes with Hubble, seeing in infrared wavelengths using adaptive optics.

As remarkable as these achievements are, they can usually be improved upon by post-processing the images. Under a NASA Applied Information Systems research grant, Southwest Research Institute (SwRI) is leading a team of scientists from the Institute, NASA and Pixon LLC in development of a Pixon pipeline for image enhancement at the agency's Infrared Telescope Facility (IRTF), also at Mauna Kea. This unique "pipeline," a set of programs designed to apply autonomously the Pixon reconstruction method to space images obtained by NASA's telescope, is still a work in progress. Its goal is to provide observers with improved spatial resolution with minimal interaction or image-processing expertise required from the observer.

Background

SwRI scientists and Pixon LLC have used an image enhancement technique called the Pixon method on various data sets from Hubble and ground-based telescopes to improve the angular resolution by factors of 2 or 3. In addition to providing higher acuity, the Pixon method also improves dynamic range and the detection of faint objects in the sky.

The classic post-processing technique is deconvolution. Deconvolution assumes that the telescope consistently transforms an impulse response--a point source, like a star--to a characteristic blurry shape. The blur is called a point spread function (PSF), a term that describes how a point of light is spread out by the imaging system.

If one knew the PSF of the imaging system, one could, in theory, deconvolve the blurry image and undo the damage done by the imaging system. One popular method, Lucy-Richardson deconvolution, attempts to find the most likely true image given the presence of noise in the observations. Another scheme, the maximum entropy method, tries to minimize the difference between the "true" image and the raw data subject to the constraint that the entropy (the informational disorder in the pixels) is maximized. Both of these methods attempt to estimate the undegraded image in the presence of noise, but only the Pixon method explicitly compares the estimated noise levels to the residuals between the model and observations as a criterion for keeping or discarding parts of the model image. The Pixon method does a good job of "de-noising" images, and, as the figure shows, outperforms the Lucy-Richardson and maximum entropy methods.

The Pixon method--"Pix-" meaning "pixel" and "-on" representing a fundamental element, as in "photon"--decomposes an image into Pixon kernels, which are essentially small dots of various diameters and brightnesses. The Pixon method uses the fewest number of Pixon kernels possible to reconstruct an image.

The rationale for choosing the "minimum complexity" set of Pixon kernels is to de-noise the data and provide artifact-free enhanced images. If a particular Pixon kernel does not reduce the local residuals below the noise level, then it is omitted from the solution. Any unjustified kernels would potentially add artifacts to the solution, even if they made the solution look sharper.


The Case 1 image (top row) is an example of noise-free image deconvolution. The original image (far left) is convolved by an instrument's point spread function, a Gaussian function (in this hypothetical case) with a width of 10 pixels. The result is a blurred rendition of the true image. If the convolved image is divided by the point spread function in the frequency domain, the original image can be recovered. The addition of even a small amount of noise to the blurred image (Case 2, bottom row) renders a deconvolved image completely dominated by noise.


Using the fewest number of kernels is important, but difficult to realize in practice. Determining the set that uses the fewest number of kernels is an exhaustive process. The Pixon code SwRI scientists use is distributed by Pixon LLC and uses proprietary algorithms to find the least complex solution in a reasonable amount of time.

It is essential to accurately estimate the noise present in the collected image. If the actual noise is higher than the estimated noise, the Pixon algorithm will add superfluous kernels to fit the noise. If the estimated noise is too high, then the Pixon method will rest after fitting only the most obvious features, since fainter features would be considered insignificant pixels--or basically just more noise. In practice an accurate noise estimate is more important than an accurate PSF.

The pipeline now under development at SwRI will assess automatically the pixel-by-pixel noise level in an image, extract or estimate a PSF, then iteratively apply Pixon reconstruction techniques to sharpen the image. At each iteration the residuals between the observations and the enhanced model will be analyzed. The residuals (which are supposed to be pattern-free white noise) will guide subsequent Pixon iterations.

Test case: mapping Titan's atmosphere

In 1981 the Voyager spacecraft flew by Titan, Saturn's largest moon. Titan's nitrogen atmosphere is an excellent Earth-analogue, complete with photochemically produced smog from the ultraviolet photolysis of hydrocarbons. Unlike the Earth, however, Titan's hazes seem to migrate from the northern hemisphere to the southern hemisphere and back on a 30-year cycle. Voyager close-ups revealed a polar hood of haze over the North Pole and a detached haze layer around the rest of the planet. This detached haze layer resides 300 km above Titan's surface. Subsequent Hubble telescope imaging of Titan has shown that the polar hood has moved from north to south in the intervening 16 years, but even Hubble images could not resolve the optically thin detached haze layer.

SwRI scientists applied the Pixon method to the Hubble images with PSFs generated from an optical model of the telescope. Scientists found that not only is Titan's extended haze visible in the processed images, it seems to be moving back to Titan's north pole. The high-altitude migration of haze--now that observers can see it--is one of the best constraints on the winds and photochemical processes that take place in Titan's upper stratosphere

SwRI scientists have used the Hubble telescope in 1996, 1998 and 2000 to image Titan in several wavelengths. The various wavelengths probe different depths into Titan's thick atmosphere. A combination of enhanced images in the various wavelengths shows how Titan's haze migrates at different altitudes.

Bear in mind that Titan is a single-pixel object when viewed from most conventional ground-based telescopes. The roughly 750 pixels covering Titan's disk in the Pixon-processed Hubble images represent a major improvement in spacial resolution.


In this example of Pixon processing on a 512 by 512 subframe of a Spacewatch telescope image, all the sources have higher counts in the processed frame. This is a result of each source's broad "halo" being more concentrated into the central pixel. For some faint sources, this improvement is the difference between detection and non-detection.


Test case: searching for asteroids

Under a subcontract with the University of Arizona, SwRI scientists have collaborated with university astronomers to examine Spacewatch telescope images for faint moving objects. The basic strategy behind the Spacewatch program is to observe a patch of the sky three separate times over the course of a night. Stars will occupy the same positions in each frame, but moving objects, such as asteroids and Kuiper Belt objects, will appear as a linear set of three dots in the overlaid frames.

The Spacewatch Project has been operating for more than 15 years and has detected more than 50,000 asteroids to date. Nevertheless, the blur inherent in the Spacewatch telescope is broad enough that the Strehl ratio--the ratio of the brightest central pixel over the sum of all the pixels in the entire object--is only about 10 percent. This makes Spacewatch images good candidates for enhancement using the Pixon method, since faint objects will be more easily detected if all of their total signal is concentrated into a central pixel.

Because there are many more faint objects in the sky than bright ones, any small improvement in the detection limit would produce large numbers of discoveries. With that goal in mind, SwRI scientists tested the Pixon pipeline by enhancing Spacewatch images automatically, first extracting stars in the image to serve as the PSF, then estimating the noise at each pixel, and finally Pixon-processing the image.

In practice, the Pixon pipeline improves the Strehl ratio by a factor of 2, and the detection limit is lowered by about a magnitude (roughly a factor of 2 in flux). This incremental improvement in the detection limit translates to a doubling in the expected number of detected asteroids, simply because there are exponentially more faint asteroids than there are bright ones.

Conclusion

SwRI scientists will continue working with the Pixon pipeline it helped develop to enhance Hubble telescope and ground-based adaptive optics images. In general, the Pixon pipeline has proven to be successful at improving spatial resolutions, often beyond a telescope's diffraction limit. The Pixon pipeline also has applications in detecting faint features in images. SwRI scientists will soon apply this technology to the search for satellites of asteroids and to the direct imaging of Pluto.

Comments about this article? Contact Young at (303) 546-6807 or efy@boulder.swri.edu.

Acknowledgements: The author would like to acknowledge the contributions of Spacewatch investigators Jeff Larsen and Robert McMillan and the IRTF pipeline team of Richard Puetter, Amos Yahil and Alan Tokunaga.

Published in the Spring 2002 issue of Technology Today®, published by Southwest Research Institute. For more information, contact Joe Fohn.

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