Feature constrained compressed sensing CT image reconstruction from incomplete data via robust principal component analysis of the database

In computed tomography (CT), incomplete data problems such as limited angle projections often cause artifacts in the reconstruction results. Additional prior knowledge of the image has shown the potential for better results, such as a prior image constrained compressed sensing algorithm. While a pre-full-scan of the same patient is not always available, massive well-reconstructed images of different patients can be easily obtained from clinical multi-slice helical CTs. In this paper, a feature constrained compressed sensing (FCCS) image reconstruction algorithm was proposed to improve the image quality by using the prior knowledge extracted from the clinical database. The database consists of instances which are similar to the target image but not necessarily the same. Robust principal component analysis is employed to retrieve features of the training images to sparsify the target image. The features form a low-dimensional linear space and a constraint on the distance between the image and the space is used. A bi-criterion convex program which combines the feature constraint and total variation constraint is proposed for the reconstruction procedure and a flexible method is adopted for a good solution. Numerical simulations on both the phantom and real clinical patient images were taken to validate our algorithm. Promising results are shown for limited angle problems.