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Overview: Atmospheric turbulence is a major factor limiting the imaging resolution of ground-based telescopes. Adaptive optics (AO) is commonly used to compensate for the wavefront distortion caused by turbulence to obtain higher resolution. However, due to the limitations of the system itself, such as the fitting error of the deformed mirror and the residual error caused by the time bandwidth, the closed-loop image still has residual errors, thus AO postprocessing technique is needed to further improve the image quality.
Blind deconvolution (BD) could recover a sharp image only from several degraded images. However, BD problems have the difficulties of ill-conditioned and infinite solutions, it is necessary to add prior knowledge to avoid undesired solutions. Traditional Wiener filtering based iterative blind deconvolution method assumes that the intensity of the image obeys the Gaussian distribution, while Chan et al. employ total variation prior, which assumes the gradient of the image obeys the Laplacian distribution. Given the fact that the gradient distribution of natural images is a sparse one with heavy tails, both of Gaussian and Laplacian model cannot approximate this sparse model greatly. Therefore, this paper draws on the image gradient sparse priori derived from blind motion deblurring, and applied it to the blind restoration of turbulence-degraded images.
In order to cope with the non-convex cost function caused by sparse prior, this paper uses split Bregman and look-up table method to solve effectively. Secondly, a two-step estimation strategy is adopted including kernel estimation and non-blind restoration. This paper employs the deconvolution method of Krishnan to reconstruct a sharp image with the kernel from the former step, and this strategy is essential to avoid the ringing effect reported by Fergus.
Firstly, the simulation experiment is carried out. To model the atmospheric turbulence degradation, the Zernike polynomials are used to generate the point spread function, and the OCNR5 satellite image is used as an object for observing. This paper adopts the relative error to evaluate the kernel estimation error and the signal to noise ratio (SNR) to evaluate image quality of degraded and restored ones. Both simulations and experiments on the real degraded images show that: 1) compared with the traditional Wiener filtering method and total variation prior, the sparse prior is beneficial to kernel estimation, produces sharp edges and removes ringing, thus improving the restoration quality. 2) After employing split Bregman optimization, restoration with sparse prior can converge rapidly and steadily, hence the proposed algorithm in this paper is robust and stable. 3) It is worth noting that the value of p should not be too large or too small, smaller p will amplify the noise.
Natural images statistical model. (a) Real natural image gradient distribution; (b) Parametric model
Simulated Zernike coefficient distribution of point spread function
Blind deconvolution of simulated turbulence-degrade image.
Convergence performance of algorithms
Restored image SNRs and kernel error RE under different p values
Real ISS restoration. (a) Degraded image; (b) Total variation restoration; (c) Sparse prior restoration with p=0.5; (d) Sparse prior restoration with p=0.1; (e) Local details of (a), (b), (c) and (d)