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求解低秩矩阵融合高动态范围图像

朱雄泳,陆许明,李智文,吴炆芳,谭洪舟,陈强(广东第二师范学院计算机科学系, 广州 510303;中山大学电子与通信工程学院, 广州 510006)

摘 要
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(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,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(SSIM)指标均优于对比方法:对于无噪声的Memorial Church图像序列,RPCA方法的PSNR、SSIM值分别为28.117 dB与0.935,而PSSV方法的分别为30.557 dB与0.959,本文方法的分别为32.550 dB与0.968。当为该图像序列添加均匀噪声后,RPCA方法的PSNR、SSIM值为28.115 dB与0.935,而PSSV方法的分别为30.579 dB与0.959,本文方法的为32.562 dB与0.967。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。
关键词
High dynamic range image fusion with low rank matrix recovery

Zhu Xiongyong,Lu Xuming,Li Zhiwen,Wu Wenfang,Tan Hongzhou,Chen Qiang(Department of Computer Science, Guangdong University of Education, Guangzhou 510303, China;School of Electronic and Information Engineering, Sun Yat-sen University, Guangzhou 510006, China)

Abstract
Objective Most traditional methods used to merge sequential multi-exposure low dynamic range (LDR) images into a high dynamic range (HDR) image are sensitive to certain problems, such as noise and object motion, and must address large-scale data, which hinder the application and further development of HDR image acquisition technology. Low-rank matrix recovery can extract an aligned low-rank image with linear correlation from a sparse noise-corrupted data matrix. A new method that exploits the abovementioned feature based on the low-rank matrix recovery is proposed to merge sequential multi-exposure LDR images into an HDR image and improve the anti-noise and de-artifact performances in capturing HDR images. Method First, the sequential multi-exposure LDR images are inputted and mapped to the linear luminance space by a calibrated camera response function (CRF). Second, a partial sum of singular values (PSSV) is used as an optimization objective function to build a low-rank matrix mathematical model for HDR image fusion method, which is used to merge the captured sequential multi-exposure LDR images. With the help of the proposed method, the data matrix is decomposed into low-rank and sparse matrices through the exact augmented Lagrange multiplier method, where the PSSV is the objective function. This algorithm is optimized given the motivation for an alternating direction multiplier method. An adaptive penalty factor is set to address different singular values. If a singular value tends to 0, then the algorithm will update the low-rank and sparse matrices with a new partial singular value thresholding (PSVT); otherwise, the algorithm will update the low-rank and sparse matrices with the classical PSVT. Moreover, the augmented Lagrange multiplier and penalty factor are updated simultaneously. The algorithm will terminate when the optimal solution concentrates within the space of the maximum singular value as much as possible after a finite number of iteration steps. Thus, a low-rank matrix with the light information of an entire scene, where the noises and artifacts are eliminated, is obtained. This obtained low-rank matrix is also the final merged HDR image from the captured sequential multi-exposure LDR images. Result The convergence and anti-noise performance are first evaluated. The proposed method and two other comparison methods are applied to the randomly generated data matrices with a size of 10 000×50 pixels and rank from 1 to 4. Simultaneously, a sparse noise is added to each data matrix with a ratio from 0.1 to 0.4. The comparison methods refer to robust principal component analysis (RPCA) and the PSSV. Simulation results indicate that the proposed method has better convergence and anti-noise performance than the two other comparison methods. The experimental results of various matrices with different ranks and sparse noise ratios show that the proposed method achieves low normalized mean square and solution errors. Furthermore, the proposed algorithm guarantees that the rank of the result is sufficiently lower than the original matrix. Thus, the singular value of the main information will not be considerably attenuated. This finding indicates that the new method can obtain low-rank results even when the reconstruction error is low. The performance of HDR image fusion is evaluated by analyzing the values of peak signal-to-noise ratio (PSNR) and structural similarity index metric based on perceptually uniform mapping. The experiments run with the classical sequential multi-exposure LDR images, such as memorial church and arch, to acquire the HDR images. The experimental results show that the expectation is achieved. The proposed method can eliminate the artifacts in dynamic scenes with sparse noise and improve the quality of the fused HDR images compared with the recovering high dynamic range radiance maps from photographs (RHDRRMP), RPCA, and PSSV algorithms. The RHDRRMP method cannot suppress the sparse noise and artifacts and produces poor brightness and contrast. The RPCA method cannot suppress artifacts well, and missing details and even inaccurate results have emerged. The PSSV method can obtain better results but fewer details than the proposed method. The index metrics of the PSNR and SSIM of the results obtained through the proposed method from the objective indicators are higher than those of the comparison algorithms. For the memorial church sequence without noise, the PSNR and SSIM of the RPCA method are 28.117 dB and 0.935, respectively; those of the PSSV method are 30.557 dB and 0.959, correspondingly; and those of our method are 32.550 dB and 0.968, respectively. The PSNR and SSIM of the RPCA method are 28.115 dB and 0.935, correspondingly; those of the PSSV method are 30.579 dB and 0.959, respectively; and those of the proposed method are 32.562 dB and 0.967, correspondingly. The proposed algorithm can recover the low-rank matrix to obtain the HDR image, even with few images in the multi-exposure image sequence. In this situation, the RPCA method cannot obtain the optimal solution to the low-rank matrix. The PSSV method only ensures that the variance of the singular value vectors in the data, rather than the low-rank data, is not the largest and cannot guarantee that the low-rank data have the maximum variance on the singular value vector. Overall, the results show that the proposed algorithm has better robustness than the traditional fusion methods. Conclusion In this study, a new method based on low-rank matrix recovery optimization theory is proposed. The proposed method can merge sequential multi-exposure LDR images into an HDR image. With the help of the proposed method, the HDR image can be obtained with a low reconstruction error in the case of few datasets, and the interference of the noise and artifacts can be removed in a dynamic scene. Thus, the proposed method has better robustness than the traditional experimental methods. The demand for high-quality images can be satisfied by improving HDR images. However, the proposed method depends on the CRF, that is, an accurate CRF indicates an improved quality of the result of image fusion. The proposed method also requires the aligned sequential multi-exposure LDR images to further eliminate the serious problems of image displacement or high-speed moving objects in a scene. Otherwise, the ghost and blur phenomena will affect the fused HDR image.
Keywords
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