目的 利用低秩矩阵恢复方法可从稀疏噪声污染的数据矩阵中提取出对齐且线性相关低秩图像的优点，提出一种新的基于低秩矩阵恢复理论的多曝光高动态范围(HDR)图像融合的方法，以提高HDR图像融合技术的抗噪声与去伪影的性能。方法 以部分奇异值和(PSSV)作为优化目标函数，可构建通用的多曝光低动态范围(LDR)图像序列的HDR图像融合低秩数学模型。然后利用精确增广拉格朗日乘子法，求解输入的多曝光LDR图像序列的低秩矩阵，并借助交替方向乘子法对求解算法进行优化，同时对不同的奇异值设置自适应的惩罚因子，使得最优解尽量集中在最大奇异值的空间，从而得到对齐无噪声的场景完整光照信息，即HDR图像。结果 本文求解方法具有较好的收敛性，抗噪性能优于鲁棒主成分分析(RPCA)与PSSV方法，且能适用于多曝光LDR图像数据集较少的场合。通过对经典的Memorial Church与Arch多曝光LDR图像序列的HDR图像融合仿真结果表明，本文方法对噪声与伪影的抑制效果较为明显，图像细节丰富，基于感知一致性(PU)映射的峰值信噪比(PSNR)与结构相似度指标均优于对比方法。结论 本文方法将多曝光HDR图像融合问题与低秩最优化理论结合，不仅可以在较少的数据量情况下以较低重构误差获取到HDR图像，还能有效去除动态场景伪影与噪声的干扰，提高融合图像的质量，具有更好的鲁棒性，适用于需要记录场景真实光线变化的场合。
High dynamic range image fusion with low rank matrix recovery
zhuxiongyong,luxuming,lizhiwen,wuwenfang,tanhongzhou,chenqiang(Guangdong University of Education;Sun Yat-Sen University)
Objective The traditional methods which merge the sequential multi-exposure low dynamic range (LDR) images into a high dynamic range (HDR) image are sensitive to problems such as noise and object motion, and have to deal with large scale data, which hinders the further development of HDR image acquisition technology. The algorithm of low rank matrix recovery can extract the aligned low rank image with linear correlation and without noise from the data matrix which polluted by sparse noise. Take advantage of this feature, this paper proposed a new method which merge the sequential multi-exposures LDR images into a HDR image based on low rank matrix recovery theory, to improving the performance of anti-noise and artifact in HDR image fusion technology. Method First of all, the partial sum of singular values (PSSV) are taken as the optimization objective function, to help build a low rank matrix mathematical model of HDR image fusion method from a sequential multi-exposure LDR images. Then decomposes the data matrix into the low rank matrix and sparse matrix by the exact augmented Lagrange multiplier method (EALM) with PSSV as the objective function. The algorithm is optimized by the idea of alternating direction method of multipliers method. At the same time, the adaptive penalty factor is set to deal with different singular values, and make the optimal solution concentrated in the space of maximum singular value as possible. Finally, the light information of the whole scene without noise and artifact is obtained, i.e. HDR image. Result The method of this paper has better convergence, and the anti-noise performance is better than the robust principal component analysis (RPCA) and PSSV methods. It also can be applied to the situations where there are a few LDR images in the sequential data sets. The simulation results with the classical multi-exposure LDR image sequences of Memorial Church and Arch show that the proposed method has a good performance of on the suppression of noise and artifact, and can keep the image details. It has the better objective indicators of peak signal-to-noise ratio (PSNR) and structural similarity index metric based on perceptually uniform (PU) mapping function by compared with other algorithms. Conclusion In this paper, the sequential multi-exposure LDR images can be merged into a HDR image based on the low rank matrix recovery optimization theory. It not only the HDR image can be obtained with a lower reconstruction error in the case of a small amount of data sets, also can remove the interference from the noise and artifact in the dynamic scene, and has better robustness. With the improvement of HDR image, the demand for high-quality images would been met.