Fourier-enhanced high-order total variation (FeHOT) iterative network for interior tomography

Objective. Determining a satisfactory solution for different computed tomography (CT) fields has been a long-standing challenge in the interior tomography, Traditional methods like FBP suffer from low contrast, while deep learning approaches often lack data consistency. The goal is to leverage high-order total variation (HOT) regularization and Fourier-based frequency domain enhancement to achieve high-precision reconstruction from truncated projection data while overcoming limitations such as slow convergence, over-smoothing, and loss of high-frequency details in existing methods.Approach. The proposed Fourier-enhanced HOT (FeHOT) network employs a coarse-to-fine strategy. First, a HOT-based unrolled iterative network accelerates coarse reconstruction using a learned primal-dual algorithm for data consistency and implicit high-order gradient constraints. Second, a Fourier-enhanced U-Net module selectively attenuates low-frequency components in skip connections while amplifying high-frequency features from filtered back-projection (FBP) results, preserving edge and texture details. Frequency-dependent scaling factors are introduced to balance spectral components during refinement.Main Results. Experiments on the AAPM and clinical medical datasets demonstrate FeHOT's superiority over competing methods (FBP, HOT, AG-Net, PD-Net). For the medical dataset, FeHOT achieved PSNR = 41.17 (noise-free) and 39.24 (noisy), outperforming PD-Net (33.42/31.08) and AG-Net (33.41/31.31). Meanwhile, For the AAPM dataset, where imaged objects exhibit piecewise constant properties, first-order total variation achieved satisfactory results. In contrast, for clinical medical datasets with non-piecewise-constant characteristics (e.g. complex anatomical structures), FeHOT's second-order regularization better aligned with the high-quality requirements of interior tomography. Ablation studies confirmed the necessity of Fourier enhancement, showing significant improvements in edge preservation (e.g. SSIM increased from 0.9877 to 0.9976 for noise-free cases). The method achieved high-quality reconstruction within five iterations, reducing computational costs.Significance. FeHOT represents a paradigm shift in interior tomography by: 1) Bridging classical HOT theory with deep learning through an iterative unrolling framework. 2) Introducing frequency-domain operations to overcome the limitations of polynomial/piecewise-constant assumptions in CT images. 3) Enabling high-quality reconstruction in just five iterations, balancing computational efficiency with accuracy. This method offers a promising solution for low-dose, precise imaging in clinical and industrial applications.