| Line 30: | Line 30: | ||
<math></math> | <math></math> | ||
| − | |||
==Problem 2== | ==Problem 2== | ||
| − | a)Since U is <math>p \times N</math>, <math>\Sigma</math> and V are <math>N \times N</math> | + | a)Since U is <math>p \times N</math>, <math>\Sigma</math> and V are <math>N \times N</math>] |
| + | |||
| + | <math>Y = U \Sigma V^t = p \times N</math> | ||
| + | |||
| + | <math>YY^t = (p\times N)(N\times p) = p \times p</math> | ||
| + | |||
| + | <math>Y^tY = (N\times p)(p\times N) = N \times N</math> | ||
Revision as of 18:25, 9 July 2019
Communication, Networking, Signal and Image Processing (CS)
Question 5: Image Processing
August 2016 (Published in Jul 2019)
Problem 1
a) $ \lambda_n^c=\lambda_n^b-\lambda_n^d $
b) $ G_n = \frac{d\lambda_n^c}{dx}=-\mu (x,y_0+n\Delta d)\lambda_n^c $
c) $ \lambda_n = \lambda_n^c e^{-\int_{0}^{x}\mu(t)dt} \Longrightarrow \hat{P}_n = \int_{0}^{x}\mu(t)dt= -ln(\frac{\lambda_n}{\lambda_n^c}) = -ln(\frac{\lambda_n}{\lambda_n^b-\lambda_n^d}) $
d) $ \hat{P}_n = \int_{0}^{T_n}\mu_0dt = \mu_0 T_n $
A straight line with slope $ \mu_0 $
Problem 2
a)Since U is $ p \times N $, $ \Sigma $ and V are $ N \times N $]
$ Y = U \Sigma V^t = p \times N $
$ YY^t = (p\times N)(N\times p) = p \times p $
$ Y^tY = (N\times p)(p\times N) = N \times N $
