Vesselness-constrained robust PCA for vessel enhancement in x-ray coronary angiograms

Effective vessel enhancement in x-ray coronary angiograms (XCA) is essential for the diagnosis of coronary artery disease, yet challenged by complex background structures of varying intensities as well as motion patterns. As a typical layer-separation method, robust principal component analysis (RPCA) has been proposed to automatically improve vessel visibility via sparse and low-rank decomposition. However, the attenuated motion of vessels in x-ray angiograms leads to the unsatisfactory vessel enhancement performance of the decomposition framework. To address this problem, we propose a vesselness-constrained RPCA method (VC-RPCA), where a vessel-like appearance prior is incorporated into the layer separation framework for accurate vessel enhancement. We first pre-compute the vessel-like appearance prior based on a Frangi filter to highlight the curvilinear structures. After removing large-scale background structures via a morphological closing operation, we then integrate the pre-computed vessel-like appearance prior into a low-rank decomposition framework to separate the fine vessel structures. In addition, we develop an adaptive regularization strategy that imposes structured-sparse constraints to solve the scale issue and capture vessels without salient motion. The proposed method was validated on 13 clinical XCA sequences containing 777 images in total. The contrast-to-noise ratio, Dice coefficient and area under the ROC curve were employed for quantitative evaluation of the vessel enhancement performance. Experiments show that (1) the adaptive regularization strategy helps to obtain a complete coronary tree in the separated vessel layer; (2) our low-rank decomposition framework is robust against false positive/negative responses of the Frangi filter; and (3) the proposed VC-RPCA is computationally fast and outperforms other state-of-the-art RPCA methods for vessel enhancement in the full-contrast and low-contrast scenarios. The results demonstrate that the proposed VC-RPCA can accurately separate coronary arteries and prominently improve vessel visibility in x-ray angiograms.