## 1 Introduction  
Image deblurring is important in many fields, such as surveillance, traffic control, astronomy, and remote sensing [1; 2; 3]. Blurs occur due to a variety of reasons, such as moving objects, focus issues, and atmospheric turbulence. They significantly deteriorate the quality of the image. The blurring procedure is always described by a point spread function (PSF), also known as blur kernel. When the PSF is known, the blur can be removed by conventional deconvolution methods, such as Weiner filtering and the Lucy-Richardson algorithm. However, when the PSF is unknown, the issue constitutes a blind-deconvolution problem, which is a notoriously vague inverse problem that has perplexed the scientific community for decades. Therefore, recovering an approximated latent image from a blurred observation is essential for improving the performance of an imaging system, in addition to having several applications [4; 5; 6]. One approach to handle this problem is to build parameterized models for specific blur types, i.e., employ motion length and angle to describe a motion blur, the radius of a disk to model the defocus blur, and a Gaussian model to simulate the atmospheric turbulence blur. Subsequently, [PERSON] and [PERSON] suggested a radial basis function neural network with image features based on the magnitude of Fourier coefficients to estimate the motion lengths [7]. [PERSON] et al. exploited the maximum likelihood estimator on the entire dataset available to estimate the parameters for a Gaussian model [8]. [PERSON] et al. utilized the Tchebycheff moment to estimate the variance of a Gaussian model [9]. [PERSON] and [PERSON] combined the non-Gaussianity measures for independent component analysis to estimate the parameters for the motion length, disk radius, and turbulence degrees [10]. However, the methods based on parameter estimation fail when dealing with a random PSF. Because the blind deconvolution problem is ambiguous, it could be regularized by some image priors, which favor the original nature of images over noisy and blurry ones. In this perspective, numerous image priors have been proposed in recent years. The Gaussian prior is one of the simplest and most commonly used priors because it implements ridge regularization in the image gradient domain as the penalty term in the cost functions and turns the problem into a quadratic convex optimization problem, which can be solved by a number of numerical methods [11]. However, the Gaussian prior is not adequately effective because natural images are mainly non-Gaussian [12; 13]. Recent advances in digital image processing and sparse representation have led to the development of new methods based on the statistical characteristics of natural images. [PERSON] et al. asserted that the distribution of gradient magnitudes of a natural image has a heavy tail and sharp top, and proposed an effective method based on the variational Bayesian approach [14]. [PERSON] et al. introduced a hyper-Laplacian prior to the image gradient and used the iterative reweighted least squares to solve the cost function [15]. [PERSON] et al. put forward a prior on local color statistics with the hyper-Laplacian prior for denoising and deblurring [16]. [PERSON] et al. proposed a prior based on total variation [17]. [PERSON] and [PERSON] combined the total variation with an \(\ell_{\mathbf{1}}\) constraint deconvolution method to efficiently reduce outliers and preserve image structures [18]. [PERSON] et al. restored the latent image in the dark channel [19]. [PERSON] et al. proposed an \(\ell_{\mathbf{1}}\)-based constrained method combined with a genetic algorithm to restore a clear image [20]. These methods adopt the \(\ell_{\mathbf{p}}\)-norm or quasi-norm forms as the image priors, which achieve high quality results. Furthermore, learning-based methods are also practical approaches in this field. [PERSON] et al. proposed a method that reveals the priors from Gibbs sampling [21]. [PERSON] et al.