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Blind image deconvolution is an ill-posed problem, which is mainly addressed by the regularization methods. Wavelet transform is an effective denoising method related to regularized inversion. In this paper, wavelet transform is utilized to decompose and extract the low- and high-frequency information of the blurred image, which is taken as the first step of the presented deblurring methods in this paper. However, when the process highlights the approximate portion of the image feature, the blurry image will be smoothed so that the image is distorted. Simultaneously, the overall wavelet transform will result in excessive data redundancy for the image. Thus, in the second step, based upon the recursive convolution neural network, a deep recursive convolutional neural network (R-DbCNN) is designed, which can eliminate or weaken the characteristics of high data redundancy and image smoothness caused by wavelet transform to remove the blur of corrupted image. Comparing with the traditional convolution neural network in image restoration, R-DbCNN has better performance in deblurring with fast training speed. Thereafter, a novel loss function is built to attain the best deblurring effect of the proposed method based on the L<sub>2</sub> regularization term. The experiment results demonstrate that our method has practical applicability for image restoration with different blurs, such as the motion blur, Gaussian blur, and out-of-focus by camera.

Blind Deblurring via a Novel Recursive Deep CNN Improved by Wavelet Transform