Dynamic imaging (such as computed tomography (CT) perfusion, dynamic CT angiography, dynamic positron emission tomography, four-dimensional CT, etc.) is widely used in the clinic. The multiple-scan mechanism of dynamic imaging results in greatly increased radiation dose and prolonged acquisition time. To deal with these problems, low-mAs or sparse-view protocols are usually adopted, which lead to noisy or incomplete data for each frame. To obtain high-quality images from the corrupted data, a popular strategy is to incorporate the composite image that reconstructed using the full dataset into the iterative reconstruction procedure. Previous studies have tried to enforce each frame to approach the composite image in each iteration, which, however, introduces mixed temporal information into each frame. In this paper, we propose an average consistency (AC) model for dynamic CT image reconstruction. The core idea of AC is to enforce the average of all frames to approach the composite image in each iteration, which preserves image edges and noise characteristics while avoids the invasion of mixed temporal information. Experiment on a dynamic phantom and a patient for CT perfusion imaging shows that the proposed method obtains the best qualitative and quantitative results. We conclude that the AC model is a general framework and a superior way of using the composite image for dynamic CT reconstruction.
For a very long time, low-dose computed tomography (CT) imaging techniques have been performed by either preprocessing the projection data or regularizing the iterative reconstruction. The conventional filtered backprojection (FBP) algorithm is rarely studied. In this work, we show that the intermediate data during FBP possess some fascinating properties and can be readily processed to reduce the noise and artifacts. The FBP algorithm can be technically decomposed into three steps: filtering, view-by-view backprojection and summing. The data after view-by-view backprojection is naturally a tensor, which is supposed to contain useful information for processing in higher dimensionality. We here introduce a sorting operation to the tensor along the angular direction based on the pixel intensity. The sorting for each point in the image plane is independent. Through the sorting operation, the structures of the object can be explicitly encoded into the tensor data and the artifacts can be automatically driven into the top and bottom slices of the tensor. The sorted tensor also provides high dimensional information and good low-rank properties. Therefore, any advanced processing methods can be applied. In the experiments, we demonstrate that under the proposed scheme, even the Gaussian smoothing can be used to remove the streaking artifacts in the ultra-low dose case, with nearly no compromising of the image resolution. It is noted that the scheme presented in this paper is a heuristic idea for developing new algorithms of low-dose CT imaging.