Line 29: | Line 29: | ||

A straight line with slope <math>\mu_0</math> | A straight line with slope <math>\mu_0</math> | ||

− | <math>< | + | <math></math> |

==Problem 2== | ==Problem 2== | ||

− | a)Since U is | + | a)Since U is <math>p \times N</math>, <math>\Sigma</math> and V are <math>N \times N</math> |

## Revision as of 18:23, 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 $