A folder named Code that contains your

code in Python $(.$py or Jupyter Notebook$)$

or Matlab.

Detailed instructions on how to run the

code $($in a

readme.md$/$readme$.$txt file$)$

should be included under the Code

folder. These instructions should

include required libraries and packages

with version numbers $($e$.$g$.,$

requirements.txt file$).$Tasks:

Q$1.$ Modify the Shepp$-$Logan phantom: Start with the source code of the phantom$()$

function in Matlab or other language of choice.

Q$\mathrm{.}1\mathrm{.}1$ Implement a function that takes the following parameters: Phantom Matrix

Size $($N$),$ Number of ellipses $($M$),$ and for each ellipse, the center position $(x,$

$Y),$ rotation angle $($ANGLE$),$ size $($width$,$ height$)$ and signal intensity $($SI$).$ The

function generates a Shepp$-$Logan phantom using these input values. $(40$

pts$)$

Q$\mathrm{.}1\mathrm{.}2$ What is the signal intensity of the background? $(5$ pts $)$

Q$\mathrm{.}1\mathrm{.}3$ What would you expect the signal intensity of the background to be in the real

world? $(5$ pts$)$

Q$2$: Test the Code: Run the code you generated in Q$1$ to create three phantoms:

Q$\mathrm{.}2\mathrm{.}1$ One with $n{o}_{?}$ overlapping structures. As an example: make structure $(1)$

smaller, move structure $(2)$ positioned lower, etc. $(10$ pts $)$

Q$\mathrm{.}2\mathrm{.}2$ Start with the output of Q$\mathrm{.}2\mathrm{.}1($modified phantom$)$ and add two circular

structures outside the brain in the empty space. $(10$ pts $)$

Q$\mathrm{.}2\mathrm{.}3$ Create a phantom that is composed of three concentric circles. $(10$ pts$)$

Example phantom: