紧框架域混合正则化模型在图像恢复中的应用

Applying a hybrid regularization model in a tight frame domain to image restoration

目的有界变差函数容易造成恢复图像纹理信息丢失，并产生虚假边缘，为克服此缺点，在紧框架域，提出一种保护图像纹理信息，抑制虚假边缘产生的混合正则化模型，并推导出交替方向迭代乘子算法。方法首先，在紧框架域，对系统和泊松噪声模糊的图像，用Kullback—Leibler函数作为拟合项，用有界变差函数半范数和L1范数组成混合正则项，二者加权组成能量泛函正则化模型。其次，分析混合正则化模型解的存在性和唯一性。再次，通过引入辅助变量，利用交替方向迭代乘子算法，将混合正则化模型最小化问题分解为4个容易处理的子问题。最后，子问题交替迭代形成有效的优化算法。结果紧框架域混合正则化模型有效地克服有界变差函数容易导致纹理信息丢失、产生虚假边缘的不足。相对经典算法，本文算法提高峰值信噪比大约0．1～0．7dB。结论与其他图像恢复正则化模型相比，本文算法有利于保护图像的纹理，抑制虚假边缘，取得较高的峰值信噪比和结构相似测度，适用于恢复系统和泊松噪声模糊的图像。

Objective To overcome the texture loss and false edge caused by a bounded variation function, a mixing regular- ization model in a tight frame domain that protects image texture information and reduces false edge is proposed. An alterna- ting-direction iteration multiplier algorithm is introduced. Method First, in the tight frame domain, for images blurred by system and Poisson noises, the fitting term is described by the Kallback-Leibler function, the mixing regularization terms are composed of the semi-norm of the bound variation function and the L1 norm, and the fitting and weight regularization terms constitute the energy functional regularization model. Second, the solution and uniqueness of the mixing regularization model are analyzed. Third, the minimum problem of the mixing regularization model is decomposed into four easily solved sub-problems by introducing auxiliary variables and utilizing the alternating-direction iteration multiplier algorithm. Finally, an effective optimization algorithm is constructed with the four sub-problems via alterative iteration. Result The mixing reg- ularization of the tight frame domain can effectively overcome the texture information loss and false edge caused by the bound variation function. Compared with traditional algorithms, the proposed algorithm can increase the peak signal-to-noise ratio to approximately 0. 1 dB to 0. 7 dB. Conclusion The proposed model can protect image texture information, alle- viate false edges, achieve higher peak signal-to-noise ratio and structural similarity index measure, and restore images blurred by system and Poisson noises compared with other regnlarization models.