# User:Amiller1

## Contents

## Personal Information

I am a rising junior at Harding University in Searcy, Arkansas. I am working toward my B.S. in Mathematics and Computer Science, and will hopefully continue my education in mathematics.

## Goals for Summer

- Learn Fourier Transform (in particular the Discrete Fourier Transform)
- Be able to program in MatLab
- Create functions to perform the Fourier Transform and Inverse Fourier Transform
- Be able to test these functions with simulated data
- Integrate my work with Shelby's work
- Potentially, be able to take real data and work with it

## Week One

**Tuesday, May 29**

- Orientation
- All the necessarily paperwork was filled out
- Tour of the campus
- Met mentor and other REU students

**Wednesday, May 30**

- Library meeting, where the library and some of its resources were shown
- Met with mentor, Dr. Rowe, about what the next few weeks I would be working on
- At this time, I received his book on the Fourier Transform
- Brushed up on any previous math that I thought would be helpful
- Began to get a basic overview of Fourier Transformations
- Read the Preface of the book

**Thursday, May 31**

- Began to work through Dr. Rowe's book on the Fourier Transform
- Meeting on Good Research Practice by Dr. Factor
- Attempted to familiarize myself with Matlab
- Continued working through the Fourier Transform book
- Began some problems on the Fourier Series (Chapter One)

**Friday, June 1**

- Spent the day working on teaching myself about Fourier Transformation which consisted off:
- Worked on the problems on the Fourier Series (Chapter One)
- Taking notes and doing the problems on the Continuous Fourier Transformation (Chapter Two)
- I also looked up additional problems and examples online to ensure that I understood what I was doing

## Week Two

**Monday, June 4**

- Spent the day further working on the Fourier Transformation which included:
- Taking notes and doing the problems for Chapter Three of the book "Specific Fourier Transform Pairs"
- Taking notes and doing the problems for Chapter Four of the book "Continuous Fourier Transform Properties"
- Looked up more information on convolution and correlation

**Tuesday, June 5**

- Spent the day working through the Fourier Transformation book:
- Finished up a few problems from Chapter Four
- Finished taking notes of Chapter Five "2/3D Fourier Transform"
- Finished the problems for Chapter Five

**Wednesday, June 6**

- Spent the morning working with MatLab attempting to become more familiar with it
- The afternoon I worked on more of the Fourier book:
- Took notes on Chapter Six Discrete Sampling
- Finished the problems for Chapter Six

**Thursday, June 7**

- Began taking notes on Chapter Seven "Discrete Fourier Transform"
- Attended the working lunch with the other REU students
- Met with my mentor, Dr. Rowe, to further discuss our Goals and Milestones
- Finished taking notes on Chapter Seven

**Friday, June 8**

- Because the Discrete Fourier Transform is very important, I spent the day focused on it
- Working on problems from the book (Chapter Seven)
- Looking up additional problems and examples to gain more understanding

## Week Three

**Monday, June 11**

- Continued to look at the one dimensional finite discrete Fourier transform
- Began to take notes on Chapter 8 about two and three dimensions
- I used both problems from the book, as well as additional problems on line

**Tuesday, June 12**

- Looked through several books about Matlab
- Continued to familiarize myself with it
- Began working on a function that would perform a 1D finite discrete Fourier transform

**Wednesday, June 13**

- Took time to explore the Memorial Library a little
- Continued taking notes on Chapter 8, focusing on the properties of 2/3D Fourier Transforms
- Looked through a book on MatLab

**Thursday, June 14**

- Worked on MatLab
- Finished working on the function I started working with on Tuesday
- This function would sample a continuous function and then perform the finite discrete Fourier transform

- Finished working on a function that is given sampled data (sampled at a consistent rate) and performs the Fourier transform on it
- Then I went back and had both functions compute the magnitude and phase
- The phase part is having a little trouble, and will need to be fixed, otherwise the 1D Fourier Transforms functions are done
- I also did a sample graph of the original function, the real part of the Fourier Transform, the imaginary part, the magnitude and the phase

**Friday, June 15**

- Continued to work with MatLab, specifically with graphics
- Looked through the books on MatLab
- Began to look into colormaps a little bit more

## Week Four

**Monday, June 18**

- Continued trying to learn more about MatLab
- Attempted at first to look into two dimensional graphing
- Became distracted with colormapping
- Loaded an image and looked into changing its format
- Performed first two dimensional fourier transform (using the preset fft2 function unfortunately)
- Used this information to graph the real and imaginary parts of the image
- Then performed the fourier transform on the already transformed image and got the original image (with slight scaling changes)

**Tuesday, June 19**

- Created a two dimensional sampling function
- Tested the function on several images
- Created a two dimensional fourier transform function
- Tested the function on several images
- Created a two dimensional inverse fourier transform function to further test the other function
- Tested the function on several images

**Wednesday, June 20**

- Attended the LaTex meeting by Dr. Corliss
- Spent the day downloading LaTex and starting to getting used to it

**Thursday, June 21**

- Working lunch
- Began to collect my thoughts for the talk next week
- Started to create a list of what needs to be in slides
- Began going over previous material to refresh my mind
- Created rough outline for talk
- Made a list of diagrams and formulas that need to be collected

**Friday, June 22**

- Started reading Chapter Ten "Temporal and Spatial Filtering"

## Week Five

**Monday, June 25**

- Worked on presentation
- Created powerpoint
- Ran through it
- Created images for it
- Met with mentor to answer questions and talk about presentation

**Tuesday, June 26**

- Mini-presentations!

**Wednesday, June 27**

- Began working on a filtering function
- Started off with a 3x3 mean filter mask
- Ran through a small test

**Thursday, June 28**

- Spent the day creating a larger test case for the mean filter mask

**Friday, June 29**

- Tested the larger test and made adjustments accordingly
- Started using other 3x3 filters such as a smoothing and sharpening filter
- Saved images and compared their appearances, as well as their matrices

## Week Six

**Monday, July 2**

- Went back to work on the mean filter more, trying to tweak it a little
- Created a median filter
- Had to tweak the median filter, once I had finished with the mean filter
- Create a Gaussian filter generator
- Tested all of these

**Tuesday, July 3**

- Looked up information to gain more understanding
- Now have a better understanding of what I'm doing
- Smoothed an image using a Gaussian filter
- Figured out how to sharpen an image (using convolution)
- Created a function to accept a kernel and then sharpen the image corresponding to that
- Talk: What makes a good poster

**Wednesday, July 4**

- Holiday

**Thursday, July 5**

- Working lunch
- Began gathering additional information and books about the Fourier Transform

**Friday, July 6**

- Continued gathering information and began reading

## Week Seven

**Monday, July 9**

- Looked through more information
- Began thinking about paper

**Tuesday, July 10**

- Continued reading books, seeing what would be helpful

**Wednesday, July 11**

- Continued reading

**Thursday, July 12**

- Working lunch
- Started to work on my power point for final presentation
- Continued reading

**Friday, July 13**

- Worked on an outline for paper
- Created a rough outline for powerpoint
- Read Chapter 10 through 12 again to refresh memory

## Week Eight

**Monday, July 16**

- Began filling in some of the spaces for the powerpoint
- Created a basic outline for the poster
- Began to collect ideas and different information that would need to go on it

**Tuesday, July 11**

- Continued working on the poster
- Added a few titles and rough info where it needed to go
- Made a list of images that would need to be either created or simply used
- Went over work for paper

**Wednesday, July 12**

- Created several images for poster
- Went through previous images
- Started to put the images into the poster
- Played around with the graphics of the poster
- Meeting with Dr. Rowe

**Thursday, July 12**

- Working lunch
- Worked on sample data for Shelby
- Created a 96x96 matrix from phantom with 128 slices
- Added noise to slices to give it a more realistic feeling

**Friday, July 13**

- Worked on adding pictures to my poster
- Wrote a rough draft abstract
- Continued working on my paper

## Week Nine

**Monday, July 23**

- Worked on poster
- Created images for it in MatLab
- Finished the with everything but a few last touches on the poster

**Tuesday, July 24**

- Finished up those last touches for poster
- Worked on the different slices, attempting to make them play in a sort of movie
- Once I figured out how to get them to play, I tried to develop different ways to make it easier

**Wednesday, July 25**

- Poster and abstract due
- Finished up my abstract, reading over the rough draft and changing a few things
- I looked at several examples of abstracts
- Continued working on my paper and power point for next week

**Thursday, July 26**

- Working lunch
- Worked on my paper

**Friday, July 27**

- Spent the day working on paper

## Week Ten

**Monday, July 30**

- Finished rough draft of paper!

**Tuesday, July 31**

- Worked on presentation for Thursday
- Poster Session
- Began editing my paper

**Wednesday, August 1**

- Finished up presentation
- Went through all the slides
- Practiced a few times
- Edited paper a little more, trying my hand at BibTex

**Thursday, August 2**

- Presentations!

**Friday, August 3**

- Finished adding the citations to the LaTex with BibTex
- Finished up with the paper!