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It is known that the less the salient edges are used in kernel estimation, the more unreliable the estimated blur kernel is. We take the following strategies to guarantee the reliability of the estimated blur kernel: Firstly, as the initial value of �� is critical to kernel estimation [7], we take the method of [6] to set the value of �� adaptively at the beginning of the iterative restoration process. Four directions of the image gradients are taken into account to guarantee enough information of the salient edges are used to estimate the blur kernel. Additionally, the value of �� for later iterations is set to allow that at least 0.5PIPk pixels take part in the kernel estimation Dasatinib in vivo in each group. Pk and PI are the total number of pixels of the blur kernel and input image, respectively. Secondly, as more edges are needed to estimate the blur kernel in higher level of the pyramid, the parameters �� and ��s are decreased to bring more edge information into the kernel estimation. Our strategies allow the recovery of fine structures during kernel refinement. Figure 5d�Cf show some interim ?S maps in different Selleckchem Gefitinib levels. It is obvious that the higher the level is, the more the sharp edges participate in kernel estimation. Figure 5 Results comparison of [7] and our method. (a) Blurred image and truth kernel; (b) result of [7]; (c) result of our method; and (d�Cf) interim ?S maps with our method. Our result shown in (c) is better. 3.2. Kernel Estimation and Refinement As motion blur ascribes to the relative motion between the subject and image sensors within the exposure time period, the blur kernel delineates the motion trace between them and should be continuous and sparse. We employ a two-step Oxygenase method to guarantee the sparsity and continuity, respectively. Estimation. We combine the strictly-selected edges ?S with a Hyper-Laplacian prior regularization term by the MAP estimation criterion to estimate the blur kernel with sparsity. The energy function is formulated as follow: E(k)?=?��S*,B*��*��S*?k???B*��22?+?�ơ�k���æ� (7) s.t.?k(x,?y)?��?0,?��(x,y)k(x,?y)?=?1 (8) where ��* is the weight for each partial derivative, �� is the weight for the Hyper-Laplacian regularization term with 0