规整化人脸图像超分辨率重建的数值解法

摘要

提出了基于特征子空间规整化的人脸图像超分辨率重建(SRR)算法并给出了三种数值解法.在仿射变换运动模型下,将图像的四邻域插值方法拓展为图像的梯度场估计问题,推导出了待求高分辨率(HR)图像关于运动参数的雅科比矩阵;并根据对SRR代价函数的全微分和偏微分展开,将非线性的SRR问题转换为线性问题迭代求解,讨论了三种运动参数与HR图像的联合迭代估计算法.给出了SRR规整化参数的自适应计算方法以实现自动SRR.仿真结果证实:采用的人脸子空间规整化方法优于传统规整化方法(拉普拉斯、全变差),尤其在低信噪比时可以获得良好的人脸图像SRR效果.%This paper proposes an eigen-subspace based regularization method for face image Super-Resolution Reconstruction (SRR),and presents three numerical solutions to the SRR problem.Under the affine motion model, it extends the interpola tion of image using the four-neighbor interpolation to the estimation of image gradient field,and derives the Jacobian of the High Resolution (HR) image with respect to the motion parameters.By means of the total and partial differential expansions of the SRR cost functional, it reduces the nonlinear SRR problem to a linear problem and presents three iterative algorithms for the joint estimation of motion parameters and HR image.An adaptive calculation method for the SRR regularization pa rameter is proposed to fulfill the automatic SRR of facial imagery.Simulation results verify the superiority of the proposed face sub-space regularized method over the traditional regularization methods (Laplacian and Total Variation (TV)) and demon strate good face image SRR performance even in the case of low signal to noise ratio.