用深度网络学习图像边缘自适应的正则化参数，提升去噪和MRI重建效果。
Deep unrolling for learning optimal spatially varying regularisation parameters for Total Generalised Variation
- 结合CNN与算法展开框架，联合学习空间变化的TGV参数。
- 在去噪和MRI重建中显著优于固定参数与无监督方法。
- 参数图在边缘处呈现三重结构，适合医学图像处理研究者。
我们将近期提出的深度展开框架扩展至总广义变分（TGV）情形，用于学习空间变化的正则化参数。该框架将一个深度卷积神经网络（CNN）与展开的算法求解器相结合，联合端到端训练以使重建图像尽可能接近真实值。在图像去噪和MRI重建任务中，结果表明其性能显著优于最优的标量参数TGV方法及其他采用无监督方式计算的空间变化参数方法。此外，推断出的空间变化参数图在图像边缘附近具有稳定结构：第一阶TGV权重呈现高低高交替的三重边缘特征，第二阶权重在边缘周围大范围区域取小值，提示需进一步开展理论分析。
原文摘要 · Abstract (English)
We extend a recently introduced deep unrolling framework for learning spatially varying regularisation parameters in inverse imaging problems to the case of Total Generalised Variation (TGV). The framework combines a deep convolutional neural network (CNN) inferring the two spatially varying TGV parameters with an unrolled algorithmic scheme that solves the corresponding variational problem. The two subnetworks are jointly trained end-to-end in a supervised fashion and as such the CNN learns to compute those parameters that drive the reconstructed images as close to the ground truth as possible. Numerical results in image denoising and MRI reconstruction show a significant qualitative and quantitative improvement compared to the best TGV scalar parameter case as well as to other approaches employing spatially varying parameters computed by unsupervised methods. We also observe that the inferred spatially varying parameter maps have a consistent structure near the image edges, asking for further theoretical investigations. In particular, the parameter that weighs the first-order TGV term has a triple-edge structure with alternating high-low-high values whereas the one that weighs the second-order term attains small values in a large neighbourhood around the edges.
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