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Image motion deblurring with unknown blur kernel is an ill-posed problem. This paper proposes a blind motion deblurring approach that solves blur kernel and the latent image robustly. For kernel optimization, an edge mask is used as an image prior to improve kernel update, then an edge selection mask is adopted to improve image update. In addition, an alternative iterative method is introduced to perform kernel optimization under a multiscale scheme. Moreover, for image restoration, a total-variation-(TV-) based algorithm is proposed to recover the latent image via nonblind deconvolution. Experimental results demonstrate that our method obtains accurate blur kernel and achieves better deblurring results than previous works.

Motion deblurring is a type of image restoration problems [

Image motion blur process.

To address such challenging problem, various theories and methods have been proposed. In early days, blind deconvolution recovers sharp images by simple motion and Gaussian blur based on frequency-domain constraints or assumptions [

Even with the estimated kernel, the restoration of the latent image is still a tough problem. In the process of motion blur, the latent image loses much high-frequency information. The traditional methods (inverse filter, wiener filter, etc.) always give undesirable restoration results because of the effect of the additive noise [

In this paper, a complete blind deblurring algorithm is proposed to handle image motion blur with image edge prior. In kernel optimization, an edge mask is used as image prior to improve kernel update and an edge selection mask is adopted to improve image update. Moreover, an alternative iterative method is introduced to implement kernel optimization under a multiscale scheme. For image restoration, a total-variation-based image nonblind deconvolution algorithm is proposed to restore latent image. The rest of the paper is organized as follows. In Section

Motion deblurring is an ill-posed problem where the number of unknowns is more than the number of observed measurements. Generally, the motion blur process can be modeled as

In image processing system, an edge is defined as the continuous boundary pixels that connect two separate regions with changing image amplitude attributes [

In motion deblurring problem, it can be seen that the edge in the blurry image usually appears fuzzy or unsharp, as shown in Figures

Edge features analysis in both motion blurred image and latent image. (a) Edge map before motion blur, (b) close-up of (a), (c) edge map after motion blur, (d) close-up of (c), (e) edge map detected from the blurry image by our edge detection process, and (f) close-up of (e).

The edge detection process finds the presence and locations of the intensity transitions. To find an ideal edge map from the blurry image, a modified edge detection process is used and described as follows. First the blurry image is convolved by the derivatives of Gaussian. Then, the magnitude and orientation of its gradient are computed. Thirdly, a nonmaxima suppression method is used to get the thinned gradient magnitudes. Finally, hysteresis is used to get the sharp edge map by doing threshold operation on the gradient magnitude. Especially, two adaptive thresholds are used to suppress the false edges. As shown in Figures

Before kernel estimation, the blurry image and the initial kernel, which are later used as the inputs of our algorithm, need to be preprocessed. More specifically, the bilateral filter and the shock filter are used to smooth the noise and keep the edge details, respectively [

For kernel optimization, an iterative optimization problem model is constructed, and its task is to optimize the blur kernel and the latent image alternately under a multiscale scheme. The edge map mentioned above is introduced as image prior, which adds mask on both latent image and blurry image. On the other hand, the

For latent image optimization, an edge selection mask mentioned in [

To solve for the kernel accurately, a multiscale scheme is introduced to implement the whole blind deblurring algorithm. Under this scheme, blur kernel and latent image are estimated by using a coarse-to-fine pyramid of image resolutions. The number of scale levels is computed by the size of blur kernel and the scale level step is

Given the estimated blur kernel, the latent image can be restored by using a nonblind image deconvolution algorithm. As mentioned above, a clear image should have sharp edge details. For this reason, an image restoration model with TV regularization term is built to recover the latent image. This model is a minimum optimization problem:

It can be seen that (

At first, an auxiliary variable

To solve these two sub-problems, an alternative minimization method (AMD) is used to optimize them. In each iteration, (

In this Section, the proposed blind deblurring algorithm was tested with both synthetic motion blurred images and real-life motion blurred images. In the kernel estimation process, the parameters

To verify the validity of our algorithm, the synthetic blurry images were generated by convolving the synthetic images with a

Testing our algorithm with the synthetic images. (a)–(c) In order from left to right, the images are the original synthetic images, the synthetic images after motion blur, restored results and estimated kernels by using our algorithm, and the close-ups of them (the red rectangle in the blurry image shows the location of close-ups).

On the other hand, the proposed algorithm was compared with the approach described in [

Testing our algorithm with real-life motion blurry images. (a)–(c) In order from left to right, the images are original blurry images, restored results and estimated kernels by our algorithm, restored results and estimated kernels by using the algorithm in [

In this paper, a novel blind deblurring algorithm is presented for motion blur occurring in photography. The approach consists of two stages: kernel estimation and image reconstruction. The edge information in blurry images is explored as an image prior for obtaining accurate blur kernel and the use of total variation regularization keeps image details during image recovery. The proposed algorithm was tested with synthetic and really captured motion blur images. The experimental results demonstrated the efficacy of our algorithm in image motion deblurring. On the other hand, there still exist some defects (cartoon effect and unclear texture detail) in the restored images. Our future work is to extend the current research by considering more complex blurs (such as blur with rotation and shift-variant blur) and other image analysis problems [

This work was supported by the China Special Fund for Meteorological-scientific Research in the Public Interest (GYHY201106044), NSFC (Grant nos. 61103130, 61070120, 61141014); National Program on Key basic research Project (973 Programs) (Grant nos. 2010CB731804-1, 2011CB706901-4).