Oracle-Net 用于电阻抗断层成像重建问题中的非线性压缩感知
Oracle-Net for nonlinear compressed sensing in Electrical Impedance Tomography reconstruction problems
AI总结：
本文针对非线性、含噪且欠采样的电阻抗断层成像逆重建问题，提出用图神经网络 Oracle-Net 预测稀疏支撑并嵌入正则化恢复模型，结合约束近端梯度求解，给出误差界并验证可提升重建质量。
摘要：
稀疏恢复原理在求解许多非线性不适定逆问题中发挥着重要作用。本文研究一种带有支撑 Oracle 的变分框架，用于压缩感知稀疏重建，其中可用测量是非线性的，并且可能受到噪声污染。文中提出了一个名为 Oracle-Net 的图神经网络，用于从非线性测量中预测支撑，并将其集成到正则化恢复模型中以强制稀疏性。随后，通过一种约束近端梯度法高效求解所导出的非光滑优化问题。在不适定的电阻抗断层成像（EIT）问题背景下，本文给出了所提出的基于 Oracle 的优化问题近似解的误差界。EIT 非线性逆重建问题的数值解证实了该方法的潜力：在稀疏性假设下，它能够利用欠采样测量提升重建质量。
英文摘要：
Sparse recovery principles play an important role in solving many nonlinear ill-posed inverse problems. We investigate a variational framework with support Oracle for compressed sensing sparse reconstructions, where the available measurements are nonlinear and possibly corrupted by noise. A graph neural network, named Oracle-Net, is proposed to predict the support from the nonlinear measurements and is integrated into a regularized recovery model to enforce sparsity. The derived nonsmooth optimization problem is then efficiently solved through a constrained proximal gradient method. Error bounds on the approximate solution of the proposed Oracle-based optimization are provided in the context of the ill-posed Electrical Impedance Tomography problem. Numerical solutions of the EIT nonlinear inverse reconstruction problem confirm the potential of the proposed method which improves the reconstruction quality from undersampled measurements, under sparsity assumptions.
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