A directional relative TV algorithm for sparse-view CT reconstruction

Objective: Computed tomography (CT) is a widely used medical imaging modality, but its radiation exposure poses potential risks to human health. Sparse-view scanning has emerged as an effective approach to reduce radiation dose; however, images reconstructed using the filtered back-projection (FBP) algorithm from sparse-view projections often suffer from severe streak artifacts. Achieving high-quality CT image reconstructed from sparse-view projections remains a challenging task. Methods: Building on compressed sensing (CS), the total variation (TV) algorithm is applied for high-quality sparse-view reconstruction. We further propose a relative total variation (RTV) algorithm to enhance the accuracy of sparse-view reconstruction. Experimental results indicate that while the RTV algorithm improves accuracy, it has limitations in edge preservation. To address this, inspired by the success of directional TV (DTV) in limited-angle reconstruction, we develop a directional relative TV (DRTV) model. This model applies the RTV technique in both x and y directions independently, and we derive its adaptive steepest descent projection onto convex set (ASD-POCS) solution algorithm. Results: Experiments conducted on simulated phantoms and real CT images demonstrate the correctness, convergence, and superior performance of the DRTV algorithm in sparse-view reconstruction. Compared with the TV, DTV, and RTV algorithm, the DRTV algorithm exhibits superior preservation of structural features and texture details. Significance: The DRTV algorithm represents an advanced method for high-precision sparse-view CT reconstruction, providing stable and accurate results. Moreover, the approach is applicable to other medical imaging modalities.