We present preliminary results from a comparison of image estimation and recovery algorithms developed for use with advanced telescope instrumentation and adaptive optics systems. Our study will quantitatively compare the potential of these techniques to boost the resolution of imagery obtained with undersampled or low-bandwidth adaptive optics; example applications are optical observations with JR-optimized AO, AO observations in severe turbulence, and AO observations with dim guidestars. We will compare the algorithms in terms of morphological and relative radiometric accuracy as well as computational efficiency. Here, we present qualitative comments on image results for two levels each of seeing, object brightness, and AO compensation/wavefront sensing.

Adaptive optics image data acquired on large telescopes nearly always need postdetection processing. We have designed a new algorithm for fast phase estimation from the bispectrum. Our innovative "part-bispectrum" approach to phase estimation addresses the large, instantaneous memory required to form the bispectrum of data measured on large-format detectors. The part-bispectrum approach has been further extended to run on parallel machines, hence the name "parallel part-bispectrum" algorithm. We describe the concept, design, and optimization of the algorithm and provide execution times for a variety of scenarios.

We use blind deconvolution methods in optical diffusion tomography to reconstruct images of objects imbedded in or located behind turbid media from continuous-wave measurements of the scattered light transmitted through the media. In particular, we use a blind deconvolution imaging algorithm to determine both a deblurred image of the object and the depth of the object inside the turbid medium. Preliminary results indicate that blind deconvolution produces better reconstructions than can be obtained using backpropagation techniques. Moreover, it does so without requiring prior knowledge of the characteristics of the turbid medium or of what the blur-free target should look like: important advances over backpropagation.

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We analyze the quality of reconstructions obtained when using the multi-frame blind deconvolution (MFBD) algorithm and the bispectrum algorithm to reconstruct images from atmospherically-degraded data that are corrupted by detector noise. In particular, the quality of reconstructions is analyzed in terms of the fidelity of the estimated Fourier phase spectra. Both the biases and the mean square phase errors of the Fourier spectra estimates are calculated and analyzed. The reason that the comparison is made by looking at the Fourier phase spectra is because both the MFBD and bispectrum algorithms can estimate Fourier phase information from the image data itself without requiring knowledge of the system transfer function, and because Fourier phase plays a dominant role in image quality. Computer-simulated data is used for the comparison in order to be able to calculate true biases and mean square errors in the estimated Fourier phase spectra. For the parameters in this study, the bispectrum algorithm produced less-biased phase estimates in all cases than the MFBD algorithm. The MFBD algorithm produced mean square phase errors comparable to or lower than the bispectrum algorithm for good seeing and few data frames, while the converse is true for many data frames and poor seeing.