Term Paper

Due Apr 29, 2020 by 11:59pm
Points 100
Submitting a file upload

Biophysics 430 Winter 2020: Term Paper

Use the following neuroimaging datasets:

It's recommended that you try to use Rmarkdown Links to an external site., modify this Rmd example Links to an external site. and it's knitted HTML output Links to an external site..

Using a single Rmd source would allow you to export your report, include all data import, processing, and output results. Alternatively, you can opt to use GoogleDocs, PDF, raw LaTeX, MS Word, etc. Your paper submission on Canvas should include 2 upload files: Rmd source and knitted output (HTML, PDF, DOCX, etc.)

General Hint: See this Canvas Discussion Thread. A complete RMD source and the corresponding HTML output of a starting hint are provided in the course canvas site (Biophysics_Rmd_TermPaperProjectTempate):

RMD source
HTML Output (generated by the RStudio knitter).

(1) Problem 1 (Visualization):

Show graphs, plots, visualizations of each volume in 1D (linear section), 2D (planar cross-sections), and 3D (volume rendering).
Show some color-map examples (e.g., hot-metal, spectral, cool, etc.)
Use pseudo colors to enhance some views of the data.
Show the effects of thresholding, gamma correction through exponentiation, and transposition and rotation of 2D images.
Generate histograms of the 3D volumes and some 2D image sections.
Save some of the graphs in PNG, TIFF, or JPG rasterized image files.

[Hint: see these examples Links to an external site.].

(2) Problem 2 (Filtering): Try various image processing techniques.

Smooth (blur, low-pass filter), denoise (median filter), and sharpen (contour detect, Laplacian filter) the images.
Apply watershed image segmentation.
Try Voronoi tesselation.
Display the Raw image , Fourier Transform of the image, filter the FT(image), e.g., threshold, low or high pass filter, and invert the processed image back in spacetime.
Can you empirically show these FT properties using 2D image cross-sections:
- Linearity property: $LaTeX: af\left(x,y\right)+bg\left(x,y\right)=a\:F\left(x,y\right)+bG\left(x,y\right),\:where\:FT\left(f\right)=F,\:FT\left(g\right)=G$ $af\left(x,y\right)+bg\left(x,y\right)=a\:F\left(x,y\right)+bG\left(x,y\right),\:where\:FT\left(f\right)=F,\:FT\left(g\right)=G$
- Multiplication property (FT of a convolution is a product of FTs): $LaTeX: FT\left(f\ast g\right)=FT\left(f\right)\cdot\:FT\left(g\right)$ $FT\left(f\ast g\right)=FT\left(f\right)\cdot\:FT\left(g\right)$ , use the R method fft(x).
- For a single 2D sMRI slice (plane), try to replicate the results of removing either the central (removing low-frequency Fourier components below $LaTeX: k_{\:x,\:\left(\frac{1}{4}\right)\max}$ $k_{\:x,\:\left(\frac{1}{4}\right)\max}$ and $LaTeX: k_{\:y,\:\left(\frac{1}{4}\right)\max}$ $k_{\:y,\:\left(\frac{1}{4}\right)\max}$ ) or the peripheral (remove high-frequency Fourier
  components above $LaTeX: k_{x,\left(\frac{1}{2}\right)\max}$ $k_{x,\left(\frac{1}{2}\right)\max}$ and are removed) components, see Chapter 12, figures 12.8 - 12.10 $LaTeX: k_{y,\left(\frac{1}{2}\right)\max}$ $k_{y,\left(\frac{1}{2}\right)\max}$ .

[Hint: see the examples in this HTML page and the Rmd source-code].

(3) Problem 3 (Modeling & Analysis): Use the longitudinal fMRI (4D real-valued functional MRI hyper-volume) Links to an external site. data.

Extract the (160-point) fMRI time-series at a couple of (x,y,z) spatial locations Links to an external site..
Fit ARIMA models Links to an external site. on training data ( $LaTeX: 1\le time \le 140$ $1\le time \le 140$ ) and assess the model predictions against the testing data ( $LaTeX: 141\le time \le 160$ $141\le time \le 160$ ).
Suppose the stimulus $X$ is an alternating ON vs. OFF visual input where each ON or OFF epoch continues for 10 time-points. Thus, there are 8 ON intertwined with 8 OFF stimulus conditions: $X=(0,0,0,0,0,0,0,0,0,0, 1,1,1,1,1,1,1,1,1, 1, 0,0,0,0,0,0,0,0,0,0, ... , 1,1,1,1,1,1,1,1,1,)$ .
Fit a linear model $LaTeX: Y=X\beta+\epsilon$ $Y=X\beta+\epsilon$ and report the coefficient (parameter) estimates, where $LaTeX: Y'=\left(y_1,\:y_2,\:...,\:y_{160}\right)$ $Y'=\left(y_1,\:y_2,\:...,\:y_{160}\right)$ , is the fMRI time-course at a fixed voxel location, $LaTeX: X=\left(1,\:x\right)$ $X=\left(1,\:x\right)$ is the intercept vector and the stimulus condition, $LaTeX: \beta$ $\beta$ is the effect-size (parameter to be estimated by linear model/OLS), and the residual error is $LaTeX: \epsilon$ $\epsilon$ .