It has been known for a long time that, in order to reconstruct a streak-free image in tomography, the sampling of view angles should satisfy the Shannon/Nyquist criterion. When the number of view angles is less than the Shannon/Nyquist limit, view aliasing artifacts appear in the reconstructed images. Most recently, it was demonstrated that it is possible to accurately reconstruct a sparse image using highly undersampled projections provided that the samples are distributed at random. The image reconstruction is carried out via an L1 norm minimization procedure. This new method is generally referred to as compressed sensing (CS) in literature. Specifically, for an N × N image with S significant image pixels, the number of samples for an accurate reconstruction of the image is O(S ln N) . In medical imaging, some prior images may be reconstructed from a different scan or from the same acquired time-resolved data set. In this case, a new image reconstruction method, Prior Image Constrained Compressed Sensing (PICCS), has been recently developed to reconstruct images using a vastly undersampled data set. In this paper, we introduce the PICCS algorithm and demonstrate how to use this new algorithm to solve problems in medical imaging.