目的 由拟合项与正则项组成的海森矩阵,如果不具有特殊结构,其逆矩阵计算比较困难,为克服此缺点,提出一种海森矩阵可分块对角化的牛顿投影迭代算法。方法 首先,用L₂范数描述拟合项,用自变量是有界变差函数的复合函数刻画正则项,建立能量泛函正则化模型。其次,引入势函数,将正则化模型转化为增广能量泛函。再次,构造预条件矩阵,使得海森矩阵可分块对角化。最后,为防止牛顿投影迭代算法收敛到局部最优解,采用回溯线性搜索算法和改进的Barzilai-Borwein步长更新准则使得算法全局收敛。结果 针对图像去模糊正则化模型容易使边缘平滑和产生阶梯效应“两难”问题,提出一种新的正则化模型和牛顿投影迭代算法。仿真结果表明,“两难”问题通过本文算法得到了很好的解决。结论 与其他正则化图像去模糊模型相比,本文算法明显改善图像的质量,如有效地保护图像的边缘,抑制阶梯效应,相对偏差和误差较小,较高的峰值信噪比和结构相似测度。

Objective The Hessian matrix comprises fidelity and regularization terms. Without a special structure, the inverse Hessian matrix is difficult and expensive to compute. To overcome these shortcomings, a Newton projection iterative algorithm with a block diagonal Hessian matrix is proposed. Method The fidelity term is described by the L₂ norm. The regularization term is established by considering the bounded variation function as a variable of the compound function. The energy function of the regularization model is established. The regularization model is converted into an augmentation energy function by using the potential function. Constructing preconditioned matrix makes the Hessian matrix diagonal and easy to compute. A retrospective linear search algorithm and an improved Barzilai-Borwein step length update criterion are adopted for complete convergence to prevent the Newton projection iterative algorithm from trapping the local optimal solution.Result For the problem of image deblurring regularization models easily smoothing edges and producing the stair effect, a new image deblurring model and Newton projection iterative algorithm are proposed. The simulation shows that the problem is fairly solved by the proposed method.Conclusion Compared with other regularization image deblurring models, the proposed model exhibits better image improvement, such as effectively protecting image edges, alleviating the stair effect, and achieving lower relative error and deviation as well as higher peak signal-to-noise ratio and structural similarity index measure.