GPR interpretation processing: Single Value Decomposition (SVD)

*직교 행렬 (orthogonal matrix) : 모든 Column 들이 orthonomal set을 이루는 행렬

-> orthogonal: 모든 column 벡터들이 서로 직교한다. 수식적으로는 내적 (inner product)이 0 이라는 것이다. 

-> normal 모든 벡터의 크기가 1로 맞춰져 있다는 것이다. 

Q = [q_{1}, q_{2}, \cdots q_{n}]

\newline

\\

(q_{i}, q_{j}) =\left\{\begin{matrix} 1 \ (i = j)

\\ 0 \ (i \neq j)

\end{matrix}\right.

*대칭 행렬 (symmetric matrix)

*반대칭 행렬 (skew symmetric matrix)

*단위 행렬

Singular value decomposition can be used to compress images by truncating SVD matrices to lower dimensions. Since the components with the most important information are ordered to be in the front, we can use the first r rows and columns to compress an image to reduce not-as-important information in the picture, by truncating the SVD matrices to rank r.

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reference: 

https://m.blog.naver.com/crm06217/221723294379

https://darkpgmr.tistory.com/105

https://www.cs.cmu.edu/~16385/s17/Slides/11.5_SVD.pdf

https://angeloyeo.github.io/2019/08/01/SVD.html

https://angeloyeo.github.io/2020/11/19/eigen_decomposition.html

 

https://nextjournal.com/yuewangpl/svd-and-eigenfaces 

=> This one is great!