Backprojection Implementation 1.1 2005/12/12 00:14:57.600 US/Central 2005/12/12 20:11:50.056 US/Central Deborah Marie Miller dmiller7@rice.edu Warren R Scott wscott@rice.edu Deborah Marie Miller dmiller7@rice.edu Warren R Scott wscott@rice.edu Our implementation uses three pieces of Matlab code: shrinkPR, filtersinc, and backproject.

ShrinkPR The original projection data was greatly over-sampled, taking over 20,000 samples in 400 picoseconds for each of the 360 angles. In order to reduce computation time, we uniformly reduced the number of samples and the number of angles. Our shrinkPR code takes the original PR matrix, a matrix whose columns are the projections, and outputs a smaller PR matrix with fewer samples and angles. It also creates a column vector, theta, which contains the angles of the corresponding projections.

Filtersinc This code takes in the PR matrix and outputs the filtered PR matrix.

It creates the ramp filter |ω| and multiplies it with the FFT of each projection. It then takes the IFFT of each filtered projection.

Backproject Backproject implements the discrete approximation of :

This code backprojects each of the filtered projections over the image plane and sums them together to produce the final reconstructed image. In order to implement the continuous function given discrete data points, the “round” function was used, effectively interpolating the data.

Representative Results The following are reconstructed images: 1500 samples per projection and 360 angles:

From this image you can easily see the original object. 1100 samples per projection and 360 angles:

This image is not as clear since fewer samples were used. 1500 samples and angles 1-180.

From this image you can see the left half of the object since we used the first half of the projections.