# Blind Deconvolution with Scale Ambiguity
## 2 Related Work  
Blind image deblurring is an important low-level vision topic which has attracted tremendous research attention. It is an ill-posed problem, and still remains a challenging task. To make the problem tractable, plenty of deblurring methods aim to introduce additional information to constrain the solution space.  
Following the study on natural image statistics [22], a number of deblurring methods have adapted the regularization terms to encourage the sparsity of image gradient. [PERSON] et al. [19] presented detailed analysis that the method based on variational Bayesian inference was able to avoid trivial solutions in comparison to other naive MAP based methods. Unfortunately, this approach is computationally expensive. It is also proven to be effective to introduce an explicitly edge selecting step for kernel estimation [1; 23] within the conventional MAP framework. However, strong edges may not always be available, such as face images. Recently, a wide variety of efficient methods based on MAP framework have been proposed. Many of them focused on designing different data terms [4; 24] and various kinds of image priors [3; 5; 7; 25; 26; 27; 28]. In addition, patch-based methods [13; 29; 30] have been developed to sidestep classical regularizers and had shown impressive performance. These methods usually searched for similar patches [13] or exploited sharp patches in an external dictionary [29; 30], which both required heavy computation.  
On the other hand, some methods employed different blur kernel priors [12; 31; 32; 33], either encouraging the estimated the blur kernel to be sparse or discouraging the delta kernel. In addition, [PERSON] et al. [21] imposed a unit Frobenius norm constraint on the blur kernel. However, an explicit solution of the latent image, which was very critical to their method, was often not easy to achieve. In comparison, [PERSON] et al. [17] considered the blur kernel normalization for the convex isotropous TV regualizer with no requirement of explicit solution. Our work is motivated by this work. Our main difference from this method is that we incorporate a non-convex hyper-Laplacian prior in this paper.  
Recently, the amazing success of deep learning provides new ideas for image deblurring. Generally, deep learning based deblurring methods, such as [34; 35; 36; 37; 38; 39], train end-to-end systems on large datasets, seeking the implicit mapping functions between the blurred images and the corresponding blur-free images. [PERSON] et al. [34] train a multi-scale Convolutional Neural Network (CNN) to progressively restore sharp images in an end to-end manner without explicitly estimating the blur kernel. [PERSON] et al. [35] develop an end-to-end learning method for motion deblurring based on a conditional Generative Adversarial Network (GAN) and the content loss. [PERSON] et al. [37] propose a scale-recurrent network which is equipped with a Convolutional Long Short-Term Memory Network (ConvLSTM) layer [40] to further ensure hidden information flow between different resolution images. Different from conventional blind deblurring methods which output both the blur kernel and the clear image, this kind of methods do not make any effort to estimating the blur kernel. There are two main limitations for them. One is that the essential training process is very time-consuming. The other is that most existing deep learning based methods depend on the consistency between the training datasets and the testing datasets, which can hinder the generalization ability. These methods are less effective in facial images with large blur kernels. In this regard, conventional deblurring methods still have certain superiority on some level.