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One of the most important issues in 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 problem 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 - α 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, a fraction gradient operator is used instead of the ordinary gradient operator. The proposed method is investigated on different kinds of images such as text, face and natural. The output of the proposed method reflects the effectiveness of the proposed algorithm in restoring images from blind problems. [ABSTRACT FROM AUTHOR]

In this paper, a new 4D chaos system is introduced based on the mathematical structure through composing and transferring. The behavior of the proposed chaotic system is studied using different tests, such as Lyapunov exponent, bifurcation diagram and histogram. In order to show the advantage of the new chaos system, the proposed system is used for image encryption. In the proposed algorithm, in addition to the new chaos system, cellular automata is also used to improve the security of the algorithm. The proposed algorithm has a separate structure for encryption key, which increases the security of the proposed algorithm. The security of the proposed environment which is evaluated using different types of security tests shows the efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]