Characterization of statistical prior image constrained compressed sensing. I. Applications to time-resolved contrast-enhanced CT.

Purpose: Prior image constrained compressed sensing (PICCS) is an image reconstruction framework that takes advantage of a prior image to improve the image quality of CT reconstructions. An interesting question that remains to be investigated is whether or not the introduction of a statistical model of the photon detection in the PICCS reconstruction framework can improve the performance of the algorithm when dealing with high noise projection datasets. The goal of the research presented in this paper is to characterize the noise properties of images reconstructed using PICCS with and without statistical modeling. This paper investigates these properties in the clinical context of time-resolved contrast-enhanced CT. Methods: Both numerical phantom studies and an Institutional Review Board approved human subject study were used in this research. The conventional filtered backprojection (FBP), and PICCS with and without the statistical model were applied to each dataset. The prior image used in PICCS was generated by averaging over FBP reconstructions from different time frames of the time-resolved CT exam, thus reducing the noise level. Numerical studies were used to evaluate if the noise characteristics are altered for varying levels of noise, as well as for different object shapes. The dataset acquired in vivo was used to verify that the conclusions reached from numerical studies translate adequately to a clinical case. The results were analyzed using a variety of qualitative and quantitative metrics such as the universal image quality index, spatial maps of the noise standard deviations, the noise uniformity, the noise power spectrum, and the model-observer detectability. Results: The noise characteristics of PICCS were shown to depend on the noise level contained in the data, the level of eccentricity of the object, and whether or not the statistical model was applied. Most differences in the characteristics were observed in the regime of low incident x-ray fluence. No substantial difference was observed between PICCS with and without statistics in the high fluence domain. Objects with a semi-major axis ratio below 0.85 were more accurately reconstructed with lower noise using the statistical implementation. Above that range, for mostly circular objects, the PICCS implementation without the statistical model yielded more accurate images and a lower noise level. At all levels of eccentricity, the noise spatial distribution was more uniform and the model-observer detectability was greater for PICCS with the statistical model. The human subject study was consistent with the results obtained using numerical simulations. Conclusions: For mildly eccentric objects in the low noise regime, PICCS without the noise model yielded equal or better noise level and image quality than the statistical formulation. However, in a vast majority of cases, images reconstructed using statistical PICCS have a noise power spectrum that facilitated the detection of model lesions. The inclusion of a statistical model in the PICCS framework does not always result in improved noise characteristics.