A neural network with encoded visible edge prior for limited-angle computed tomography reconstruction

Limited-angle computed tomography is a challenging but important task in certain medical and industrial applications for nondestructive testing. The limited-angle reconstruction problem is highly ill-posed and conventional reconstruction algorithms would introduce heavy artifacts. Various models and methods have been proposed to improve the quality of reconstructions by introducing different priors regarding to the projection data or ideal images. However, the assumed priors might not be practically applicable to all limited-angle reconstruction problems. Convolutional neural network (CNN) exhibits great promise in the modeling of data coupling and has recently become an important technique in medical imaging applications. Although existing CNN methods have demonstrated promising results, their robustness is still a concern. In this paper, in light of the theory of visible and invisible boundaries, we propose an alternating edge-preserving diffusion and smoothing neural network (AEDSNN) for limited-angle reconstruction that builds the visible boundaries as priors into its structure. The proposed method generalizes the alternating edge-preserving diffusion and smoothing (AEDS) method for limited-angle reconstruction developed in the literature by replacing its regularization terms by CNNs, by which the piecewise constant assumption assumed by AEDS is effectively relaxed.

The AEDSNN is derived by unrolling the AEDS algorithm. AEDSNN consists of several blocks, and each block corresponds to one iteration of the AEDS algorithm. In each iteration of the AEDS algorithm, three subproblems are sequentially solved. So, each block of AEDSNN possesses three main layers: data matching layer, $$ -direction regularization layer for visible edges diffusion, and $$ -direction regularization layer for artifacts suppressing. The data matching layer is implemented by conventional ordered-subset simultaneous algebraic reconstruction technique (OS-SART) reconstruction algorithm, while the two regularization layers are modeled by CNNs for more intelligent and better encoding of priors regarding to the reconstructed images. To further strength the visible edge prior, the attention mechanism and the pooling layers are incorporated into AEDSNN to facilitate the procedure of edge-preserving diffusion from visible edges.

We have evaluated the performance of AEDSNN by comparing it with popular algorithms for limited-angle reconstruction. Experiments on the medical dataset show that the proposed AEDSNN effectively breaks through the piecewise constant assumption usually assumed by conventional reconstruction algorithms, and works much better for piecewise smooth images with nonsharp edges. Experiments on the printed circuit board (PCB) dataset show that AEDSNN can better encode and utilize the visible edge prior, and its reconstructions are consistently better compared to the competing algorithms.

A deep-learning approach for limited-angle reconstruction is proposed in this paper, which significantly outperforms existing methods. The superiority of AEDSNN consists of three aspects. First, by the virtue of CNN, AEDSNN is free of parameter-tuning. This is a great facility compared to conventional reconstruction methods; Second, AEDSNN is quite fast. Conventional reconstruction methods usually need hundreds even thousands of iterations, while AEDSNN just needs three to five iterations (i.e., blocks); Third, the learned regularizer by AEDSNN enjoys a broader application capacity, which could work well with piecewise smooth images and surpass the piecewise constant assumption frequently assumed for computed tomography images.