RBP-DIP: Residual back projection with deep image prior for ill-posed CT reconstruction

The success of deep image prior (DIP) in a number of image processing tasks has motivated their application in image reconstruction problems in computed tomography (CT). In this paper, we introduce a residual back projection technique (RBP) that improves the performance of deep image prior framework in iterative CT reconstruction, especially when the reconstruction problem is highly ill-posed. The RBP-DIP framework uses an untrained U-net in conjunction with a novel residual back projection connection to minimize the objective function while improving reconstruction accuracy. In each iteration, the weights of the untrained U-net are optimized, and the output of the U-net in the current iteration is used to update the input of the U-net in the next iteration through the proposed RBP connection. The introduction of the RBP connection strengthens the regularization effects of the DIP framework in the context of iterative CT reconstruction leading to improvements in accuracy. Our experiments demonstrate that the RBP-DIP framework offers improvements over other state-of-the-art conventional IR methods, as well as pre-trained and untrained models with similar network structures under multiple conditions. These improvements are particularly significant in the few-view and limited-angle CT reconstructions, where the corresponding inverse problems are highly ill-posed and the training data is limited. Furthermore, RBP-DIP has the potential for further improvement. Most existing IR algorithms, pre-trained models, and enhancements applicable to the original DIP algorithm can also be integrated into the RBP-DIP framework.