Jump to: navigation, search

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!