提出一种带保证的多尺度图像恢复模型，提升重建精度与稳定性。
MAP Image Recovery with Guarantees using Locally Convex Multi-Scale Energy (LC-MUSE) Model
- 用局部凸能量模型建模图像先验，通过CNN参数化负对数先验。
- 在并行MRI重建中优于经典凸正则化方法，性能媲美端到端方法。
- 理论保证解唯一性、收敛性及对噪声鲁棒，适合医学成像等高可靠性场景。
我们提出一种多尺度深度能量模型，其在数据流形附近的局部邻域内具有强凸性，用于表示概率密度，并应用于图像逆问题。具体地，将负对数先验表示为由卷积神经网络（CNN）参数化的多尺度能量模型，并限制CNN梯度为局部单调，从而构建局部凸多尺度能量（LC-MuSE）模型。该模型在基于图像的逆问题中具有若干优良性质：(i) 解的唯一性，(ii) 收敛至逆问题最小值的保证，(iii) 对输入扰动的鲁棒性。在并行磁共振（MR）图像重建任务中，所提方法表现优于当前最先进的凸正则化方法，性能可与插件式正则化和端到端训练方法相媲美。
原文摘要 · Abstract (English)
We propose a multi-scale deep energy model that is strongly convex in the local neighbourhood around the data manifold to represent its probability density, with application in inverse problems. In particular, we represent the negative log-prior as a multi-scale energy model parameterized by a Convolutional Neural Network (CNN). We restrict the gradient of the CNN to be locally monotone, which constrains the model as a Locally Convex Multi-Scale Energy (LC-MuSE). We use the learned energy model in image-based inverse problems, where the formulation offers several desirable properties: i) uniqueness of the solution, ii) convergence guarantees to a minimum of the inverse problem, and iii) robustness to input perturbations. In the context of parallel Magnetic Resonance (MR) image reconstruction, we show that the proposed method performs better than the state-of-the-art convex regularizers, while the performance is comparable to plug-and-play regularizers and end-to-end trained methods.
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