Communication, Networking, Signal and Image Processing (CS)

Question 5: Image Processing

August 2016 (Published in Jul 2019)

## Problem 1

1. Calcualte an expression for $\lambda_n^c$, the X-ray energy corrected for the dark current

$\lambda_n^c=\lambda_n^b-\lambda_n^d$

1. Calculate an expression for $G_n$, the X-ray attenuation due to the object's presence

$G_n = \frac{d\lambda_n^c}{dx}=-\mu (x,y_0+n * \Delta d)\lambda_n^c$

1. Calculate an expression for $\hat{P}_n$, an estimate of the integral intensity in terms of $\lambda_n$, $\lambda_n^b$, and $\lambda_n^d$

$\lambda_n = (\lambda_n^b-\lambda_n^d) e^{-\int_{0}^{x}\mu(t)dt}d)\lambda_n^c$

$\hat{P}_n = \int_{0}^{x}\mu(t)dt= -log(\frac{\lambda_n}{\lambda_n^b-\lambda_n^d})$

1. For this part, assume that the object is of constant density with $\mu(x,y) = \mu_0$. Then sketch a plot of $\hat{P}_n$ versus the object thickness, $T_n$, in mm, for the $n^{th}$ detector. Label key features of the curve such as its slope and intersection.

## Problem 2

1. Specify the size of $YY^t$ and $Y^tY$. Which matrix is smaller

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