User:Amiller1

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!