Point spread function estimation for blind image deblurring problems based on framelet transform

Abstract: One of the most important issues in the image processing is the approximation of the image that has been lost due to the blurring process. These types of matters are divided into non-blind and blind problems. The second type of problem is more complex in terms of calculations than the first problems due to the unknown of original image and point spread function estimation. In the present paper, an algorithm based on coarse-to-fine iterative by $l_0-\alpha l_1$ regularization and framelet transform is introduced to approximate the spread function estimation. Framelet transfer improves the restored kernel due to the decomposition of the kernel to different frequencies. Also in the proposed model fraction gradient operator is used instead of ordinary gradient operator. The proposed method is investigated on different kinds of images such as text, face, natural. The output of the proposed method reflects the effectiveness of the proposed algorithm in restoring the images from blind problems.