BIOENG1340 Assignment 3 — Part 1 Biomedical Imaging Solution

Instructions
Please show your solutions to each problem in full, writing them neatly. For computer programs, please remember to turn in your code through the course's blackboard session, as well as any plots / figures that are requested
LEARNING GOALS;
Understanding Signal to Noise and Contrast to Noise Visualizing the output of an MRI scanner: Experiencing k-space in 2D!
1. Part 1 (20 points) — Exploring SNR and CNR: In this question you will be attempting to recreate the in-class demonstration of signal to noise (SNR) improvement using an average of N time series images.
a.
b.
Please quantify SNR in the infarction portion of the image (after first cropping a region which contains only pixels in the "yellow" infarction region from the images), using the formulation learned in class, delineating your steps and any assumptions. Please repeat this exercise for each time in the provided time series of TIFF images representing cranial-caudal projections of ADC MRI signal from the rat brain and tabulate your results.
Compute the average image of the provided N image. Does the image clarity / SNR improve..? If so, verify that the sqrt(N) relationship for improvement in SNR holds good.
Part 2 (20 points) Compute the contrast to noise (CNR) ratio between the infarct (yellow) and the rest of the brain (red) in the original images as well as the time-series averaged image. By what specific percentage does contrast to noise ratio improve as a result of time series image averaging..?
2. (20 points) In this question you will be visualizing k-space of the 20 Shepp- Logan 1974 head phantom image. This phantom consists of several ellipses of
different sizes, orientations, locations, and signal intensities (i.e. gray levels). Attached with this assignment is the 2D complex k-space of the 2D Shepp- Logan phantom, as a *MAT file. This k-space is "simulated MRI data" i.e. what we might expect to see from as the output of the MRI system prlor to Fourier reconstruction back into image space.
Write separate Matlab scripts to read the Phantom image into the Matlab workspace and compute the image-space version of the k-space data (after appropriate Fourier-transform reconstruction activities, based on the class ectures). Visualize the 2D image space result, 12, using the "imshow" and
"imagesc" functions in Matlab. Insert plots and describe your observations. Also, visualize the k-space which you began with after first using the function in Matlab to center the k-space origin to the center of your plot. Insert a plot of this with your report.
In your reports, please insert screenshots of your results along with the steps taken to reconstruct the image data in each case, with the code. HINT: Recall that you can plot a matrix of complex numbers as an image by take the absolute value of the numbers. Plot the "real" and "imaginary" components of your reconstructed image and the original k-space for this question!