Image-reconstruction tool challenges maximum entropy
To remove the diffraction patterns inherent in telescope-based imaging systems without incurring the complexities of Fourier deconvolution and maximum entropy restoration approaches, Richard Puetter and Robert Piña at the University of California, San Diego (La Jolla, CA), have developed the Pixon method of modeling underlying, unblurred, noise-free images. To commercialize this development, Puetter and Amos Yahil, a cosmologist at the State University of New York at Stony Brook (Stony Brook, NY) have formed a company called Pixon (Stony Brook, NY) to license the technology to interested third-party companies.
In the restoration of imaging data, the best estimate of underlying quantities encoded into data can be accomplished by prequantifying the image deterioration and noise. For example, images can be blurred by unfocused optics or a turbulent atmosphere, and noise can be added by a recording device. From the blurry image, the best estimate of the unblurred object must be sought.
In operation, the Pixon approach assigns a priori probabilities to different image models. Therefore, a function that zigzags through noisy data would have a low probability, whereas a smooth function would have a high a priori probability. In Bayesian fashion, this approach maximizes not the usual maximum likelihood of the data but the product of that likelihood and the a priori probability of the model.
In execution, the Pixon method develops a set of basis functions into which images are decomposed. These functions contain a set of elements whose number exceeds the number of data points but does not include functions that zigzag through noise. The Pixon method then selects the smallest number of basis functions that adequately fit the data.
"Each collection of basis functions represents the minimum number of parameters needed to describe the data," says Puetter, now co-managing director at Pixon. "This can increase spatial resolution and sensitivity, and ensure rejection of spurious sources."
The Pixon method has been tested in a variety of imaging applications at the University of Hawaii (Honolulu, HI), University of Texas (Austin, TX), University of California at Riverside (Riverside, CA), University of Chicago (Chicago, IL), and Lawrence Livermore National Laboratory (Livermore, CA). "In all cases, the Pixon method exceeded the performance of other methods," says Puetter.
To correct image blurring over large dynamic ranges, the Pixon method was applied to enhanced, near-infrared imaging data obtained from the Near Infrared Camera and Multi-Object Spectrometer (NICMOS) instrument aboard the Hubble Space Telescope. Although the NICMOS instrument provides near optimal performance, diffraction effects do hide many of the details of the underlying nebula. Using the Pixon method revealed the properties of the underlying nebula in detail (see figure).
Recently, an accelerated Pixon method has been developed that works faster than the original. Although the Quick Pixon method sacrifices local photometric accuracy for computational speed, its performance rivals that of the Wiener-filter Fourier deconvolution method. With the addition of special-purpose hardware, the Quick Pixon method can reach real-time image restoration at video speed. Consequently, the Pixon company is now planning the development of hardware that will be able to reconstruct 640 x 480-pixel images in real time.