Study of CT image reconstruction algorithm based on high order total variation

The traditional total variation (TV) minimization algorithm is an image reconstruction algorithm based on compressed sensing, which can accurately reconstruct images from sparse data or highly noisy data and has been widely used in low-dose computed tomography (CT). Sometimes it may lead to staircase effect if the reconstructed image has not obvious piecewise constant feature. Recently, researches in the field of image processing suggested that the high order total variation (HOTV) can effectively suppress staircase effect. Whereas the HOTV reconstruction algorithm has not been carried out deeply and extensively in image reconstruction. Herein, we propose a HOTV reconstruction model and design its adaptive steepest descent-projection onto convex sets (ASD-POCS) solving algorithm, and then characterize its reconstruction performance. We construct the second order TV norm using the second order gradient, and design the data fidelity constrained, second order TV minimization model, and derive the its ASD-POCS algorithm. In order to characterize its reconstruction performance, we use the Shepp-Logan simulation phantom of wavy background, the gray-changing simulation phantom and the chest X-ray image simulation phantom to perform reconstructions. Sparse reconstruction results show that compared to the traditional TV algorithm, the HOTV algorithm can effectively suppress the staircase effect and improve the reconstruction accuracy. Noisy-projections reconstruction results show that the traditional TV algorithm and the HOTV algorithm both have good denoising effect but the HOTV algorithm is slightly better for it can better protect the image edge information. The HOTV algorithm is a better reconstruction algorithm than the TV algorithm in image reconstruction if the piecewise constant feature of the reconstructed image is not so obvious but the grayscale fluctuation feature is prominent. The proposed HOTV algorithm can be extended to various CT configurations and other imaging modalities.