Fast Phase Spectrum Estimation Using the Parallel Part‐Bispectrum Algorithm

Abstract

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.

Gauss–Newton Optimization for Phase Recovery From the Bispectrum

“…This structure can be implemented to exploit the symmetries in the phase for real-valued images in Fourier space, which increases computational efficiency. We base our indexing structure on the work presented by [28].…”

“…Numerous algorithms for phase recovery from the modulo-2π bispectrum have been proposed which build upon the relationship in (1). These can be separated into two categories: recursive algorithms; see, e.g., [5], [6], [10], [23], [24], [25], [26], [27], [28], and nonlinear least-squares formulations; see, e.g., [7], [25], [26], [29], [30], [31]. We look at the second category.…”

“…Recursive strategies fix a small set of known phase values near the center of the Fourier domain and use these known phase values along with the collected bispectrum to recursively compute the remainder of the reconstructed phase. Such strategies are well explored in the literature [5], [6], [10], [23], [24], [25], [26], [27], [28]. One limitation of recursive strategies is poor performance when attempting to reconstruct the phase values associated with high frequency information when using noisy data [7].…”

Parallel hybrid bispectrum-multi-frame blind deconvolution image reconstruction technique

“…Previous attempts at parallelizing bispectrum SI have been limited to techniques where ensembles of small, overlapping sub-images are processed in parallel [21,26]. Further, previous parallelization techniques employ multitude of CPUs to parallelize processing of multiple frames or tiles [26].…”

“…Further, previous parallelization techniques employ multitude of CPUs to parallelize processing of multiple frames or tiles [26]. These techniques allow for real-time processing but at the expense of reduced image quality compared to full-frame SI technique.…”