Due to shading of clouds and objects on the ground and due to the performance of sensors, the part region of field inversion data by remote sensing may be incomplete, which makes it harmful to use these data for further study. The way to recover the incomplete field inversion data accurately and quickly seems to be significant. Matrix completion (MC) has been proposed in recent years, which is mainly used for low rank matrix. Because of the quality of low rank, the data of the matrix has high correlation, so the matrix can be high accurately recovered with MC. SVT (Singular Value Thresholding) algorithm is one method of MC, which could recover missing values in the matrix rapidly and accurately. In this paper, we introduced the SVT algorithm for matrix completion and we used this algorithm to complete the missing data points which were selected in different regions. Making the missing data points be the center of a region of square and the size of the square is selected by the criteria of the smallest variance. Use SVT algorithm to complete this square region and name this method local SVT algorithm (LSVT). Comparing with the SVT algorithm for the whole region data that is named WSVT which is based on the whole experiment area, inversing distance weighting method (IDW) and Kriging method respectively, we conclude that the precision for LSVT is higher than WSVT and IDW method. Also, the precision changing trend for LSVT is similar with Kriging method and the precision for LSVT is higher than Kriging method in sea front region.
PING Bo, SU Fenzhen, ZHOU Chenghu, GAO Yi
. Based on Local SVT Algorithm to Recover Field Data Inversion by Remote Sensing[J]. Journal of Geo-information Science, 2011
, 13(5)
: 651
-655
.
DOI: 10.3724/SP.J.1047.2011.00651
[1] Williams D., Liao X J, et al. On Classification with Incomplete Data . // IEEE transactions on pattern analysis and machine intelligence, 2007,427-436.
[2] 赵地, 李光强, 李晶晶. 空间不完备数据及其填补方法研究[J]. 西部探矿工程, 2009, 21(1): 137-140.
[3] 汤国安, 杨昕. ArcGIS 地理信息系统空间分析实验教程[M]. 北京:科学出版社,2006.
[4] 陈宝政,蔡德利.普通 Kriging 插值算法研究[J]. 测绘与空间地理信息, 2009, 32(3): 7-9.
[5] 汤国安, 刘学军, 闾国年. 数字高程模型及地学分析的原理与方法[M]. 北京: 科学出版社,2005.
[6] 王乘, 周均清, 李利军. Creator可视化仿真建模技术[M]. 长沙: 华中科技大学出版社,2005.
[7] 舒娱琴, 唐丽玉, 彭国均. 采用 Creator 生成三维地形[J]. 测绘信息与工程, 2003, 28(5): 9-11.
[8] Harvey N J A, Karger D R, and Yekhanin S. The Complexity of Matrix Completion . ACM, 2006.
[9] Candes E J and Recht B. Exact Matrix Completion via Convex Optimization[J]. Foundations of Computational Mathematics, 2009, 9(6): 717-772.
[10] Cai J F, Candes E J, and Shen Z W. A Singular Value Thresholding Algorithm for Matrix Completion[J]. Arxiv preprint arXiv:2008,10:3286.
[11] Ji H, Liu C, Shen Z,et al. Robust Video Denoising Using Low Rank Matrix Completion . // Proceedings of CVPR, 2010,1791-1798.
[12] 靳国栋, 刘衍聪, 牛文杰. 距离加权反比插值法和克里金插值法的比较[J]. 长春工业大学学报: 自然科学版, 2003, 24(3): 53-57.