Variational Bayesian Blind Image Deconvolution: A review <s> IV. OPEN ISSUES <s> This paper presents a fast deblurring method that produces a deblurring result from a single image of moderate size in a few seconds. We accelerate both latent image estimation and kernel estimation in an iterative deblurring process by introducing a novel prediction step and working with image derivatives rather than pixel values. In the prediction step, we use simple image processing techniques to predict strong edges from an estimated latent image, which will be solely used for kernel estimation. With this approach, a computationally efficient Gaussian prior becomes sufficient for deconvolution to estimate the latent image, as small deconvolution artifacts can be suppressed in the prediction. For kernel estimation, we formulate the optimization function using image derivatives, and accelerate the numerical process by reducing the number of Fourier transforms needed for a conjugate gradient method. We also show that the formulation results in a smaller condition number of the numerical system than the use of pixel values, which gives faster convergence. Experimental results demonstrate that our method runs an order of magnitude faster than previous work, while the deblurring quality is comparable. GPU implementation facilitates further speed-up, making our method fast enough for practical use. <s> BIB001 </s> Variational Bayesian Blind Image Deconvolution: A review <s> IV. OPEN ISSUES <s> In blind deconvolution one aims to estimate from an input blurred image y a sharp image x and an unknown blur kernel k. Recent research shows that a key to success is to consider the overall shape of the posterior distribution p(x, k\y) and not only its mode. This leads to a distinction between MAP x, k strategies which estimate the mode pair x, k and often lead to undesired results, and MAP k strategies which select the best k while marginalizing over all possible x images. The MAP k principle is significantly more robust than the MAP x, k one, yet, it involves a challenging marginalization over latent images. As a result, MAP k techniques are considered complicated, and have not been widely exploited. This paper derives a simple approximated MAP k algorithm which involves only a modest modification of common MAP x, k algorithms. We show that MAP k can, in fact, be optimized easily, with no additional computational complexity. <s> BIB002 </s> Variational Bayesian Blind Image Deconvolution: A review <s> IV. OPEN ISSUES <s> We show in this paper that the success of previous maximum a posterior (MAP) based blur removal methods partly stems from their respective intermediate steps, which implicitly or explicitly create an unnatural representation containing salient image structures. We propose a generalized and mathematically sound L0 sparse expression, together with a new effective method, for motion deblurring. Our system does not require extra filtering during optimization and demonstrates fast energy decreasing, making a small number of iterations enough for convergence. It also provides a unified framework for both uniform and non-uniform motion deblurring. We extensively validate our method and show comparison with other approaches with respect to convergence speed, running time, and result quality. <s> BIB003
Before presenting some BID examples we would like to comment here on some open problems, either on the Variational Bayesian BID (VBBID) or BID itself, that we believe will very likely be explored in the near future: A. Image space versus filter space VB methods can be formulated in either the image or the filter space. Levin et al. BIB002 state that the filter space has better performance for the MOG prior. Xu et al. BIB003 indicate that using the image space  formulation for latent image estimation and filter space formulation for kernel estimation is better than using the same spaces. In our opinion additional work is needed to establish the best spaces for image and kernel estimation. The image space appears to be less sensitive to noise since the noise is amplified in the filter space. Furthermore, the filter space is probably more computationally expensive than the image space. On one hand, utilizing the same number of iterations and L derivative filters, the total computation time in the filter space is about L times that of the image space. On the other hand, it is shown in Cho and Lee BIB001 that the kernel estimation in the image space requires more iterations to converge than in the filter space, since the symmetric matrixX TX of the quadratic program in Eq. (27), is not as diagonally dominant as γX T γX γ , whereX andX γ denote the convolution matrices formed byx andx γ , respectively. Based on the above two factors, it is conceivable that the image space is computationally less expansive than the filter space, when L ≥ 2. Additionally, filter space methods have access to more "observations" to estimate the blur, although with an unrealistic independence assumption on them. The pros and cons of both approaches should be carefully analyzed.