  This paper investigates the application of unsupervised learning methods for
computed tomography (CT) reconstruction. To motivate our work, we review
several existing priors, namely the truncated Gaussian prior, the $l_1$ prior,
the total variation prior, and the deep image prior (DIP). We find that DIP
outperforms the other three priors in terms of representational capability and
visual performance. However, the performance of DIP deteriorates when the
number of iterations exceeds a certain threshold due to overfitting. To address
this issue, we propose a novel method (MCDIP-ADMM) based on Multi-Code Deep
Image Prior and plug-and-play Alternative Direction Method of Multipliers.
Specifically, MCDIP utilizes multiple latent codes to generate a series of
feature maps at an intermediate layer within a generator model. These maps are
then composed with trainable weights, representing the complete image prior.
Experimental results demonstrate the superior performance of the proposed
MCDIP-ADMM compared to three existing competitors. In the case of parallel beam
projection with Gaussian noise, MCDIP-ADMM achieves an average improvement of
4.3 dB over DIP, 1.7 dB over ADMM DIP-WTV, and 1.2 dB over PnP-DIP in terms of
PSNR. Similarly, for fan-beam projection with Poisson noise, MCDIP-ADMM
achieves an average improvement of 3.09 dB over DIP, 1.86 dB over ADMM DIP-WTV,
and 0.84 dB over PnP-DIP in terms of PSNR.
