An analytical form of ring artifact correction for computed tomography based on directional gradient domain optimization

Abstract Background Ring artifact is a common problem in Computed Tomography (CT), which can lead to inaccurate diagnoses and treatment plans. It can be caused by various factors such as detector imperfections, anti‐scatter grids, or other nonuniform filters placed in the x‐ray beam. Physics‐based corrections for these x‐ray source and detector non‐uniformity, in general cannot completely get rid of the ring artifacts. Therefore, there is a need for a robust method that can effectively remove ring artifacts in the image domain while preserving details. Purpose This study aims to develop an effective method for removing ring artifacts from reconstructed CT images. Methods The proposed method starts by converting the reconstructed CT image containing ring artifacts into polar coordinates, thereby transforming these artifacts into stripes. Relative Total Variation is used to extract the image's overall structural information. For the efficient restoration of intricate details, we introduce Directional Gradient Domain Optimization (DGDO) and design objective functions that make use of both the image's gradient and its overall structure. Subsequently, we present an efficient analytical algorithm to minimize these objective functions. The image obtained through DGDO is then transformed back into Cartesian coordinates, finalizing the ring artifact correction process. Results Through a series of synthetic and real‐world experiments, we have effectively demonstrated the prowess of our proposed method in the correction of ring artifacts while preserving intricate details in reconstructed CT images. In a direct comparison, our method has exhibited superior visual quality compared to several previous approaches. These results underscore the remarkable potential of our approach for enhancing the overall quality and clinical utility of CT imaging. Conclusions The proposed method offers an analytical solution for removing ring artifacts from CT images while preserving details. As ring artifacts are a common problem in CT imaging, this method has high practical value in the medical field. The proposed method can improve image quality and reduce the difficulty of disease diagnosis, thereby contributing to better patient care.