Back projection reconstruction
Back projection is a simple method of reconstruction for data from PET, SPECT and CT scans.
For PET, for example, the raw data are the number of counts in the detectors. These give the number of gamma rays traveling in a straight line between any two detectors. The simplest way to recover an image corresponding to these data is to first, make an image which covers the space of the inside of the scanner and the position of the detectors, then, for each count (corresponding to a pair of detectors)m draw a line on the image between the position of the two detectors with an intensity proportional to the count. Once this has been done for all pairs of detectors, you will get a rather crude image of whatever was generating the counts inside the scanner.
Here's a more detailed tutorial with some of the processing that can improve this method: http://www.physics.ubc.ca/~mirg/home/tutorial/fbp_recon.html