Use of singular value decomposition for analyzing repetitive measurements

✍ Scribed by L. Unonius; P. Paatero

• Book ID: 103046619
• Publisher: Elsevier Science
• Year: 1990
• Tongue: English
• Weight: 975 KB
• Volume: 59
• Category: Article
• ISSN: 0010-4655
• DOI: 10.1016/0010-4655(90)90172-w

✦ Synopsis

Situations are analyzed where repetitive measurements are performed on similar physical Situations. One measurement is assumed to produce one column vector of numbers. Together, the measurements produce a matrix A 1~. By "similar" we mean that the columns of matrix A can be represented as linear combinations of some possibly unknown basis vectors plus noise. It is shown how the singular value decomposition (SVD) of matrix A is used to analyze the contents of the matrix: the amount of noise-like experimental error is revealed, and more importantly, the presence or non-presence of any kind of distortions from the ideal situation is quantitatively estimated. The result of this analysis is summarized as the "quality number" Q of a matrix. A low Q is a warning: there is something wrong in your data. A high Q is a positive indication of the quality of the data.

Experimental examples from X-ray physics are studied. It is demonstrated how SVD aids in a correction process, whereby the distortions are removed from matrix A.