Four-dimensional computed tomography (4D-CT) has been widely used in preoperative evaluation and radiotherapy planning of lung tumors. To reduce the damage to healthy tissue, it is a better way to limit the scan time and the number of CT slices. Yet, it leads to the reduction of CT image resolution in the superior-inferior direction. To improve the resolution of the 4D-CT image, we propose a super-resolution (SR) algorithm based on tensor product and nuclear norm optimization. The proposed cost function includes a tensor fidelity term and a nuclear norm regularization term. The tensor fidelity term consists of low-resolution (LR) and high-resolution (HR) image tensors, as well as SR operators. The nuclear norm regularization term is used to preserve the operators’ low-rank. The optimization problem can be effectively solved by an alternative direction method of the multipliers (ADMM) technique. The SR operators can extract useful information from each dimension of LR image tensors to enhance the equality of 4D-CT SR reconstruction. Experimental results show that the proposed method can preserve the edge details of the 4D-CT image. Moreover, quantitative comparisons show that the proposed method increases peak signal-to-noise ratio from 1.5 dB to 5.5 dB, structural similarity index from $2\%$ to $11\%,$ visual information fidelity from $6\%$ to $20\%,$ edge model-based blur metric from $5\%$ to $15\%,$ and decreases the spatial-spectral entropy-based quality index from $1\%$ to $5\%,$ compared with conventional 4D-CT SR algorithms.

四维计算机断层扫描（4D-CT）已广泛应用于肺肿瘤的术前评估和放射治疗计划。为了减少对健康组织的损伤，限制扫描时间和CT切片数量是更好的方法。然而，它导致CT图像上下方向分辨率的降低。为了提高 4D-CT 图像的分辨率，我们提出了一种基于张量积和核范数优化的超分辨率 (SR) 算法。提议的成本函数包括张量保真度项和核范数正则化项。张量保真度项由低分辨率 (LR) 和高分辨率 (HR) 图像张量以及 SR 算子组成。核范数正则化项用于保持算子的低秩。优化问题可以通过乘法器（ADMM）技术的替代方向方法有效解决。SR 算子可以从 LR 图像张量的每个维度中提取有用的信息，以增强 4D-CT SR 重建的平等性。实验结果表明，该方法可以保留4D-CT图像的边缘细节。此外，定量比较表明，所提出的方法将峰值信噪比从 1.5 dB 提高到 5.5 dB，结构相似性指数从$2\%$ 到 $11\%,$ 视觉信息保真度来自 $6\%$ 到 $20\%,$ 基于边缘模型的模糊度量来自 $5\%$ 到 $15\%,$ 并将基于空间光谱熵的质量指数从 $1\%$ 到 $5\%,$ 与传统的 4D-CT SR 算法相比。