3D volumetric reconstruction from incomplete or noisy measurements is a fundamental problem in medical imaging and computational tomography. Deep image prior (DIP)-based methods have recently shown strong capability for solving inverse problems without requiring large training datasets. However, directly extending DIP to 3D reconstruction by fully 3D networks can incur high computational cost, while slice-by-slice 2D DIP approaches may lead to inter-slice inconsistencies due to the lack of explicit regularization along the third direction. In this paper, we propose a novel volumetric reconstruction framework, Fractional-gradient Autoencoding Sequential Tomography DIP (FAST-DIP), which integrates input-adaptive sequential deep image prior modeling of slices with fractional sparsity regularization to capture inter-slice dependencies. Specifically, we introduce a fractional l1/l2-based sparsity prior on the gradients along the slice (z) direction to explicitly enforce inter-slice structural consistency. We further provide theoretical analysis of the proposed alternating minimization algorithm under the majorization-minimization (MM) framework, establishing monotonic descent of the objective function and convergence to a critical point under the Kurdyka-Lojasiewicz (KL) property. Experimental results for 3D X-ray computed tomography (CT) reconstruction demonstrate that the proposed method improved reconstruction quality and structural consistency compared with existing DIP-based approaches.

翻译：三维体素重建是医学成像和计算断层成像中从不完整或含噪声测量中恢复结构的基础问题。基于深度图像先验（DIP）的方法近年展现出无需大规模训练数据集即可解决逆问题的强大能力。然而，直接通过全三维网络将DIP扩展到三维重建会带来高计算成本，而逐层的二维DIP方法因缺乏沿第三方向的显式正则化可能导致层间不一致。本文提出一种创新的体素重建框架——分数梯度自编码序贯断层成像DIP（FAST-DIP），该框架将输入自适应序贯深度图像先验建模与分数稀疏正则化相结合，以捕捉层间依赖关系。具体而言，我们引入基于分数l1/l2范数的梯度稀疏先验作用于切片（z）方向，显式强化层间结构一致性。同时，在主导最小化（MM）框架下对交替最小化算法进行理论分析，证明目标函数的单调下降性以及基于Kurdyka-Lojasiewicz（KL）性质收敛至临界点。三维X射线计算机断层成像（CT）重建实验表明，相较于现有DIP方法，所提方法在重建质量与结构一致性方面均有显著提升。