Abstract
All optical systems that operate in or through the atmosphere suffer from turbulence induced image blur. Both military and civilian surveillance, gun sighting, and target identification systems are interested in terrestrial imaging over very long horizontal paths, but atmospheric turbulence can blur the resulting images beyond usefulness. This work explores the mean square error (MSE) performance of a multiframe blind deconvolution (MFBD) technique applied under anisoplanatic conditions for both Gaussian and Poisson noise model assumptions. The technique is evaluated for use in reconstructing images of scenes corrupted by turbulence in long horizontal-path imaging scenarios. Performance is evaluated via the reconstruction of a common object from three sets of simulated turbulence degraded imagery representing low, moderate, and severe turbulence conditions. Each set consisted of 1000 simulated turbulence degraded images. The MSE performance of the estimator is evaluated as a function of the number of images, and the number of Zernike polynomial terms used to characterize the point spread function. A Gaussian noise model-based MFBD algorithm reconstructs objects that showed as much as 40% improvement in MSE with as few as 14 frames and 30 Zernike coefficients used in the reconstruction, despite the presence of anisoplanatism in the data. An MFBD algorithm based on the Poisson noise model required a minimum of 50 frames to achieve significant improvement over the average MSE for the data set. Reconstructed objects show as much as 38% improvement in MSE using 175 frames and 30 Zernike coefficients in the reconstruction.
Highlights
The goal of this article is to use a parameterized, multiframe blind deconvolution (MFBD) technique to reconstruct an object estimate from a set of simulated anisoplanatic images, and examine the mean square error (MSE) performance of the estimator as the parameters are varied
We provide an estimate of the optimum number of images and Zernike coefficients to use in the future work with MFBD reconstructions
The performance of an unconstrained optimization-based MFBD estimator was evaluated in terms of the MSE between the reconstructed object and a diffraction limited image
Summary
The goal of this article is to use a parameterized, multiframe blind deconvolution (MFBD) technique to reconstruct an object estimate from a set of simulated anisoplanatic images, and examine the mean square error (MSE) performance of the estimator as the parameters are varied. In addition to phase errors at the aperture, light propagating over longer distances or through stronger turbulence, will cause images to suffer from anisoplanatic, and possibly scintillation effects as well. In a stack of K turbulence corrupted, but measurement noise-free images, the k’th image can be described as the convolution of an unchanging object in space convolved with the PSF of the optical system sð~xÞ. This can be expressed as[13] gkð~xÞ 1⁄4 oð~xÞ⋆skð~xÞ; (1). These relationships are given by skð~xÞ 1⁄4 jhkð~xÞj2 1⁄4 jF −11⁄2Hkð~uÞj2;
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