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Pure Mathematics 2026
基于范围–零空间分解与扩散先验的线性逆问题求解
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Abstract:
近年来，扩散模型在通过单一扩散先验解决逆问题方面表现出显著的能力，消除了对任务特定重新训练的需求。现有的方法聚焦于反向生成的过程但却忽略了反向生成存在的隐式规律，导致它们的有效性往往会受到影响。在本文中，我们提出了一种新的范围零空间融合方法，该方法协同地将数据保真度约束与影像先验约束相结合，从而确保数据一致性和感知真实性，从而有效改善隐式规律的影响。该方法显著提高了扩散模型在逆问题中的性能，达到与前沿方法高度竞争的结果。我们提出的方法为解决图像重建挑战提供了一种多功能且高效的解决方案。
In recent years, diffusion models have demonstrated remarkable capabilities in solving inverse problems through a single diffusion prior, thereby eliminating the need for task-specific retraining. However, existing methods focus primarily on the reverse generation process while neglecting the implicit patterns inherent in this process, which often compromises their effectiveness. In this paper, we propose a novel Range null-space fusion method that synergistically integrates data fidelity constraints with image prior constraints, thereby ensuring data consistency and perceptual authenticity, and effectively mitigating the impact of these implicit patterns. This method significantly enhances the performance of diffusion models in solving inverse problems, achieving highly competitive results compared with state-of-the-art approaches. The proposed method provides a versatile and efficient solution for addressing image reconstruction challenges.
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