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Single image motion deblurring has been a very challenging problem in the field of image processing. Although there are many researches had been proposed to solve this problem, it still has problems on kernel accuracy. In order to improve the kernel accuracy, an effective structure selection method was used to select the salient structure of the blur image. Then a novel kernel estimation method based on *L*0-2 norm was proposed. To guarantee the sparse kernel and eliminate the negative influence of details *L*0-norm was used. And *L*2-norm was used to ensure the continuity of kernel. Many experiments were done to compare proposed method and state-of-the-art methods. The results show that our method can estimate a better kernel and use less time than previous work, especially when the size of blur kernel is large.

Motion blur is caused by the relative displacement between the camera and the target due to the camera or a hand shake. With the popularity of the camera in recent years, the blur is very common in life, so it’s important for the image motion deblurring. However, motion deblurring is a completely challenging problem since it’s an ill-posed problem. Ordinarily, if the motion blur is shift-inva- riant, the image blur process can be modeled as:

where

The kernel estimation is an important step in the deblurring process, since the kernel will impact directly on the restoration of latent image. The awful or inaccurate kernel will produce ringing artifact in the latent image. At the beginning, the researchers used some regularization to estimate the accurate kernel [

Now, we use a more effective image structure extraction algorithm. It avoids the negative effect of the details on the kernel estimation. Meanwhile, we propose a novel method of kernel estimation, it can not only estimate the kernel much faster but also suppress the noise, and guarantee the continuity of kernel. The coarse-to-fine iterative process is taken. The image structure is selected from the blurred image. Then, the kernel can be obtained from the image structure. The latent image, which be got from the estimated kernel and the given blurred image, is prepared for the next finer level.

Image motion deblurring began to be studied in the last century 60’s, in 1967, Helstron et al. proposed the classical Wiener filter. In 70’s, Richardson and Lucy proposed the RL algorithm based on Bayesian theory, but this method couldn't get the satisfying result since they didn’t take into account the effects of noise and the algorithm model was too simple. Since twenty-first Century, researchers have made great progress in the field of image motion deblurring, they utilized the priors of the image and kernel to restore the latent image. Fergus et al. [

Our method focuses on the salient structure selection and the kernel estimation. An effective salient structure extraction method is critical to the kernel estimation, and the accurate kernel is indispensable to the deconvolution.

We find that the effective image structure facilitates the kernel estimation. In previous researches, bilateral filtering and shock filtering are used to predict the image edges [

where

is the

In addition, structures which are smaller than the size of kernel will have a negative impact on the kernel estimation. While, inaccurate kernel fail to restore image. So we add ar(x) to the model which showed as model (1).

Formula (3) is first used in [

The solution of model (4) can be decomposed into two sub problems―

The sub problem about

We can use the Fast Fourier Transforms (FFT) to compute

where

The sub problem about

We add

According to [

Proof details can be found in [

In the last few years, a variety of regularizations were used to estimate the kernel, the most commonly used were

where the first submodel is data fidelity term,

Now, we propose a new kernel estimation method based on

In order to solve model (11), we add two auxiliary variables

We call it model (12) and the solving of it is same to Section 3.2.

To remove noise, we set the kernel elements with the value smaller than 0.075 of the biggest one to zero. Then, the remaining non-zero values are normalized so that their sum becomes one. The experimental results will be compared in Section 4.

The latent image can be restored via the deconvolution operation of the kernel and blurred image. In order to ensure the details and smoothness of the latent image, as well as suppress ringing artifacts produced in process of deconvolution, we use

Formula (13) is a nonconvex function, so IRLS can be used to minimize it.

From Section 3, we can see that our method mainly takes advantage of

For the image structure extraction and the kernel estimation, we both execute in the gradient image. Because of the pixel value of gradient image are all zero in addition to the outline section. It can improve execution efficiency.

There are several parameters in our algorithm. In model (1), we set

The complex building images are challenging for all methods, because the building images contain too many edges, the invalid edges will restrict the image restoration.

a | b | c | d | |
---|---|---|---|---|

Image size | 490 × 288 | 276 × 215 | 593 × 417 | 728 × 470 |

Kernel size | 29 × 39 | 45 × 45 | 55 × 55 | 101 × 57 |

Pan | 213 s | 797 s | 1770 s | 6093 s |

Our | 113 s | 106 s | 386 s | 604 s |

We evaluate our results on the dataset in [

In this paper, an effective image structure extraction algorithm was used to select the salient structure. It eliminated the details of image to avoid the negative effects for the kernel estimation. Meanwhile, a novel kernel estimation method was proposed. It can not only ensure the sparsity of kernel, but also guarantee

a | b | c | d | e | f | |
---|---|---|---|---|---|---|

Xu & Jia | 09336 | 0.9351 | 0.9199 | 0.9120 | 0.9298 | 0.9001 |

Pan | 0.9560 | 0.9591 | 0.97 | 0.9396 | 0.9694 | 0.9666 |

Our | 0.9633 | 0.9661 | 0.9691 | 0.9439 | 0.9707 | 0.9602 |

the connectivity. This kernel estimation model can be translated into convex function, so it can achieve the optimum solution fast. The experimental results show that our algorithm can provide reliable kernel and image. Next stage, we will extend our method to handle non-uniform deblurring.

This work is partially supported by National Natural Science Foundation of China (Grant No. 61472305), Science and technology project of Shaanxi province (Grant No. 2016GY-033).

Zhang, F.W. and Tian, Y.M. (2017) Image Motion Deblurring Based on Salient Structure Selection and L0−2 Norm Kernel Estimation. Journal of Computer and Communications, 5, 24- 32. https://doi.org/10.4236/jcc.2017.53003