Research on Adaptive Optics Image Restoration Algorithm by Improved Expectation Maximization Method

Abstract

To improve the effect of adaptive optics images’ restoration, we put forward a deconvolution algorithm improved by the EM algorithm which joints multiframe adaptive optics images based on expectation-maximization theory. Firstly, we need to make a mathematical model for the degenerate multiframe adaptive optics images. The function model is deduced for the points that spread with time based on phase error. The AO images are denoised using the image power spectral density and support constraint. Secondly, the EM algorithm is improved by combining the AO imaging system parameters and regularization technique. A cost function for the joint-deconvolution multiframe AO images is given, and the optimization model for their parameter estimations is built. Lastly, the image-restoration experiments on both analog images and the real AO are performed to verify the recovery effect of our algorithm. The experimental results show that comparing with the Wiener-IBD or RL-IBD algorithm, our iterations decrease 14.3% and well improve the estimation accuracy. The model distinguishes the PSF of the AO images and recovers the observed target images clearly.

Robust Multi-Frame Adaptive Optics Image Restoration Algorithm Using Maximum Likelihood Estimation with Poisson Statistics

“…In our algorithm, the parameters $\beta =1.31$ and $\xi =1.35$ were selected experimentally for visually acceptable results. Table 2 gives the results of our algorithm and those of the ML-EM [10], CPF-adaptive [11], RT-IEM [12], and VBBD-TV [9] methods, and the number of iterations for the four algorithms is 300. Our algorithm ranks on the top of the list, and the results demonstrate the superiority of our method.…”

“…The estimated PSF model for an AO image is under the following conditions: the full field-of-view for the system is ${20}^{″}$; the Zernike model for the fully corrected turbulence effect is with the first 35 orders; the field-of-view is ${10}^{″}$; the size of the space-variant PSF is $5\times 5$ pixels; and the isoplanatic angle $\theta$ is $2^{″}$. The AO image restoration experiments based on the ML-EM algorithm [10], the CPF-adaptive algorithm [11], the RT-IEM algorithm [12], the VBBD-TV algorithm [9], and our algorithm are compared.…”

“…To avoid excessive noise amplification, regularization on the cost function is required. We combine Equation (27) with regularization parameters to establish the cost function for joint deconvolution for multi-frame AO images, which is $J_{\mathrm{multi}}(o,\left\{h_k\right\})=J_1^{\prime }(o,\left\{h_k\right\})+\frac{|\nabla \stackrel{false^}{o}(x,y)|}{\gamma \left(\nabla v\right)},$ where the second term is a regularization term that can be defined as $|\nabla \stackrel{false^}{o}(x,y)|=\sqrt{{\left(\nabla o_x(x,y)\right)}^2+{\left(\nabla o_y(x,y)\right)}^2}$ and $\gamma \left(\nabla v\right)=exp(-\frac{{\left|\nabla v\right|}^2}{2{\xi }^2}),$ where $\gamma \left(\nabla v\right)$ has a variable regularization coefficient associated with the gradient of each point with $0<\gamma \left(\nabla v\right)\le 1$ [12,27]; parameter $\xi$ is the smoothing coefficient; and $\nabla v$ is the gradient for point $v(x,y)$, where v is a gray pixel value.…”

Adaptive Optics Image Restoration via Regularization Priors With Gaussian Statistics

“…In order to handle the ill-posed nature of blind deconvolution to a great extent of considering multiple images, Tian et al presented another multiframe restoration algorithm based on the frame selection techiques [17]. Approaches based on improved expectation maximization for AO image restoration was proposed in [18]. An adaptive image restoration method based on hierarchical neural network is proposed by Yap et al [19].…”

Complex System Blind Equalization Algorithm for Equivalent Multichannel CT Image Restoration

“…These blind image restoration methods can be divided into two classes. The first class contains methods that separate PSF identification as a disjoint procedure from restoration, such as maximum likelihood, 1 generalized cross-validation, 2 zero sheet separation, 3 Bayesian estimation, 4 maximum a-posteriori, 5 and expectation maximization, 6 etc. The algorithm has low computational complexity, but the precision heavily depends on model.…”