Rotational Scanning Computed Laminography (RCL) is widely utilized for the Non-Destructive Testing (NDT) of large planar components. However, to facilitate rapid inspection, continuous sparse-view scanning is often employed, where the angular integration effect during exposure induces rotational blur in the projection domain. Furthermore, the data incompleteness inherent in sparse sampling manifests as sparse artifacts in the reconstructed image domain. To address these cross-domain degradations, this paper proposes RCL-Mamba, a measurement-oriented dual-domain State Space Model (SSM)-based image restoration network. The framework adopts a cascaded joint processing strategy: it first corrects the rotational blur in the projection domain and subsequently suppresses the sparse artifacts in the image domain. Additionally, we design a Mamba-CNN dual-branch module to adaptively balance large-scale blur correction with local detail recovery. Evaluations on both simulated datasets and real-world Printed Circuit Board (PCB) scans demonstrate that RCL-Mamba outperforms existing baselines in blur removal, artifact suppression, and structural preservation. Line-profile-based structural measurement further verifies that the proposed method better preserves via/pad boundaries and slender trace profiles. Crucially, by reducing the required scanning views from 512 to 64, our method enhances inspection efficiency by approximately 8-fold without compromising reconstruction quality, offering a robust measurement-oriented restoration solution for high-throughput RCL inspection with improved structural measurement fidelity.

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