Abstract

Issues in the application of spectral least-squares methods to Fourier transform infrared spectrophotometry are discussed with emphasis on collinearity problems in vapor and gas reference spectra. Excessive collinearity may degrade the accuracy and reliability of prediction. Several methods that detect and diagnose collinearity are developed and tested with the use of numerical experiments. The condition number is based on the singular values in the reference spectra matrix and provides a stable and composite measure of collinearity. Variance-decomposition proportions and auxiliary regressions identify the spectra that form dependencies. Application of the methods to spectra of common vapors and gases shows complex and potentially degrading dependencies that would not be seen by examining correlation coefficients or other statistics measuring only pair-wise dependencies. A method to estimate the precision of results for specified signal-to-noise ratios and degree of collinearity is evaluated.

Analysis of a photoacoustic imaging system by the crosstalk matrix and singular value decomposition

Michael Roumeliotis, Robert Z. Stodilka, Mark A. Anastasio, Govind Chaudhary, Hazem Al-Aabed, Eldon Ng, Andrea Immucci, and Jeffrey J.L. Carson
Opt. Express 18(11) 11406-11417 (2010)

Image restoration by singular value decomposition

T. S. Huang and P. M. Narendra
Appl. Opt. 14(9) 2213-2216 (1975)

Singular value decomposition ghost imaging

Xue Zhang, Xiangfeng Meng, Xiulun Yang, Yurong Wang, Yongkai Yin, Xianye Li, Xiang Peng, Wenqi He, Guoyan Dong, and Hongyi Chen
Opt. Express 26(10) 12948-12958 (2018)

Bidirectional texture function image super-resolution using singular value decomposition

Wei Dong, Hui-Liang Shen, Zhi-Wei Pan, and John H. Xin
Appl. Opt. 56(10) 2745-2753 (2017)

Singular-value decomposition of a tomosynthesis system

Anna Burvall, Harrison H. Barrett, Kyle J. Myers, and Christopher Dainty
Opt. Express 18(20) 20699-20711 (2010)