Prior Image Constrained Compressed Sensing (PICCS)

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.