Multi-limited-angle spectral CT image reconstruction based on average image induced relative total variation model

In recent years, spectral computed tomography (CT) has attracted extensive attention. The purpose of this study is to achieve a low-cost and fast energy spectral CT reconstruction algorithm by implementing multi-limited-angle scans. General spectral CT projection data are collected over a full-angular range of 360 degrees. We simulate multi-source spectral CT by using a pair of X-ray source/detector. To speed up scanning, multi-limited-angle scanning was used in each energy channel. On this basis, an average image induced relative total variation (Aii-RTV) with multi-limited-angle spectral CT image reconstruction model is proposed. The iterative algorithm is used to solve Aii-RTV. Before iteration, the weighted average projection data of the multi-limited-angle energy spectral is carried out. In each step of the iterative algorithm flow is as follows: First, the relative total variation (RTV) reconstruction model is used to reconstruct the average image using average projection data. Then, the partial derivative of the average image is used to calculate the inherent variation in RTV model due to the integrity of the average image, and take its reciprocal as the weight coefficient of the windowing total variation of each energy channel reconstruction image. Finally, the average energy image is used to guide the multi-limited-angle projection data to reconstruct the image of each energy channel so as to suppress the limited-angle artifact of each energy channel image. In addition, we also discuss the influence of parameter selection on reconstructed image quality, which is important for regularization model. Through the reconstruction of multi-limited-angle spectral CT projection data, quantitative results and reconstructed images show that our algorithm has better performance than prior image constrained compressed sensing (PICCS) and RTV. The average PSNR of our reconstruction results in different channels was 35.6273, 4.533 and 2.301 higher than RTV (31.0943) and PICCS (33.3263), respectively.