基于改进的期望值最大化自适应光学图像多帧迭代去卷积算法

为提高自适应光学图像复原的效果，基于期望值最大化理论，提出了一种基于改进期望值最大化（EM）算法的自适应光学（AO）图像多帧联合去卷积算法。通过建立多帧AO图像退化的数学模型，推导出基于相位误差并随时间变化的点扩散函数(PSF)模型，根据图像功率谱密度及约束图像支持域的方法对AO图像进行去噪处理。应用AO成像系统参数与正则化技术相结合对EM算法进行改进，建立多帧AO图像联合去卷积的代价函数及其参数估计的优化模型。利用所建模型对模拟图像和实际观测的AO图像进行图像复原实验验证文中算法的复原效果。实验结果表明，与Wiener迭代盲去卷积、Richardson-Lucy迭代盲去卷积算法相比，文中算法迭代次数减少14.3%，估算精度有了明显提高，辨识出了AO图像的PSF，复原出了清晰的观测目标图像。研究结果对实际AO图像复原有一定的应用价值。

Multi-frame Iteration Blind Deconvolution Algorithm Based on Improved Expectation Maximization for Adaptive Optics Image Restoration

To improve the effect of adaptive optics image restoration, a deconvolution algorithm based on the improved expectation-maximization (EM) algorithm is proposed according to the EM theory. A mathematical model for degenerating the multi-frame adaptive optics images is built. The point spread function (PSF) model changed over time based on phase error is deduced. The AO images are de-noised using the image power spectrum density and the support constraints. The EM algorithm is improved by combining the AO imaging system parameters and regularization technique. A cost function for the joint-deconvolution of multi-frame AO images is given, and an optimization model for their parameter estimation is built. The image-restoration experiments of the analog images and the real AO images are performed to verify the image restoration effect of the proprosed algorithm. The experimental results show that, compared with the Wiener-IBD or RL-IBD algorithm, the iterations of the proposed algorithm is decreased by 14.3%, and its estimation accuracy is significantly improved. The model distinguishes PSFs of the AO images and recovers the observed target images clearly.