۱- Introduction

۲- Related work and discussion

۳- The proposed model and algorithm

۴- Experimental results and analysis

۵- Conclusion

References

Abstract

Various image prior based regularization techniques have been proposed for image deblurring. By utilizing existing image smoothing operators, the method-noise provides a new way to formulate image regularizers. The method noise is defined as the difference of an image and its smoothed version, obtained by an image smoothing operator such as the non-local means(NLM). Therefore, the method noise mainly contains edges, small scaled details and noise (if exists). The l2-NLM method noise regularization has been successfully used in image denoising. However, the restored image exists over-smoothed edges and noise in smooth areas cannot be perfectly removed. In this work, we propose a weighted-l1-method-noise regularization model for image deblurring. We analyze the advantages of the proposed model in terms of variational form and its solution. Specifically, the l1 penalty of the method noise is better than the l2 penalty in removing noise in smooth areas. The incorporated gradient based weight can better preserve image edges. Experimental results show that the proposed method can obtain better results than other method noise based regularization methods.

Introduction

Image deblurring aims to estimate a sharp clean image from a blurred noisy image, which is one of the most basic problems in image processing. In general, image blurring can be described by the following mathematical formulation [1]: f = A ∗ u + k (1) where f and u ∈ RN (N = m × n) denotes the observed image and the original image respectively, A stands for the blurring convolution kernel, ∗ denotes the convolution operation, and k ∈ RN is the white Gaussian noise with variance σ ۲٫ In recent years, many image deblurring methods have been presented based on the following variational framework [2–۶]: uˆ = arg minu A ∗ u − f۲ ۲ + λJ(u) (2) where ·۲ ۲ stands for square of l2 norm in RN. The first term is the data fitting term which ensures the blurred version of the restored image close to the observed image. The second term J(u) is called regularization term, which imposes smoothness or some kind of structure constraint on the estimated image and can be deduced from the prior of the real image. λ > 0 is a tuning parameter to balance the data fitting term and the regularization term.