论文标题
通过多阶段草图的梯度加速插件图像重建
Accelerating Plug-and-Play Image Reconstruction via Multi-Stage Sketched Gradients
论文作者
论文摘要
在这项工作中，我们提出了一种新的范式，用于设计使用尺寸降低技术的快速插件（PNP）算法。与使用随机梯度迭代进行加速的现有方法不同，我们提出了新型的多阶段草绘制梯度迭代，该迭代首先在图像空间中降低了降采样尺寸，然后使用低维空间中的概述梯度有效地近似真正的梯度。该草图的梯度方案也可以与PNP-SGD方法自然合并，以进一步改善计算复杂性。作为通用加速方案，它可以应用于加速任何现有的PNP/RED算法。我们在X射线风扇束CT上进行的数值实验证明了我们方案的显着有效性，即可以使用图像空间中的这种维度降低来获得计算自由午餐。
In this work we propose a new paradigm for designing fast plug-and-play (PnP) algorithms using dimensionality reduction techniques. Unlike existing approaches which utilize stochastic gradient iterations for acceleration, we propose novel multi-stage sketched gradient iterations which first perform downsampling dimensionality reduction in the image space, and then efficiently approximate the true gradient using the sketched gradient in the low-dimensional space. This sketched gradient scheme can also be naturally combined with PnP-SGD methods for further improvement on computational complexity. As a generic acceleration scheme, it can be applied to accelerate any existing PnP/RED algorithm. Our numerical experiments on X-ray fan-beam CT demonstrate the remarkable effectiveness of our scheme, that a computational free-lunch can be obtained using this dimensionality reduction in the image space.
