In this work we propose a new paradigm for designing efficient deep unrolling networks using dimensionality reduction schemes, including minibatch gradient approximation and operator sketching. The deep unrolling networks are currently the state-of-the-art solutions for imaging inverse problems. However, for high-dimensional imaging tasks, especially X-ray CT and MRI imaging, the deep unrolling schemes typically become inefficient both in terms of memory and computation, due to the need of computing multiple times the high-dimensional forward and adjoint operators. Recently researchers have found that such limitations can be partially addressed by unrolling the stochastic gradient descent (SGD), inspired by the success of stochastic first-order optimization. In this work, we explore further this direction and propose first a more expressive and practical stochastic primal-dual unrolling, based on the state-of-the-art Learned Primal-Dual (LPD) network, and also a further acceleration upon stochastic primal-dual unrolling, using sketching techniques to approximate products in the high-dimensional image space. The operator sketching can be jointly applied with stochastic unrolling for the best acceleration and compression performance. Our numerical experiments on X-ray CT image reconstruction demonstrate the remarkable effectiveness of our accelerated unrolling schemes.
翻译:在这项工作中,我们提出了一个新的范例,用于设计高效的深潜流网络,使用维度减少计划,包括小型梯度近似和操作者草图等,设计高效的深深潜流网络。深潜流网络目前是成像反问题的最新解决方案。然而,对于高维成像任务,特别是X射线CT和MRI成像,深深深层的滚动计划通常在记忆和计算两方面都变得效率低下,因为需要多次计算高维前和协作操作者。最近研究人员发现,通过在高维图像空间成功随机梯度梯度下降(SGD)的模拟技术(SGD),可以部分解决这些局限性。在这项工作中,我们进一步探索了这一方向,并首先提出一个更清晰和实用的探索性原创性原始的无滚动性方案,其基础是,因为需要多次计算高维度前和连接操作者(LPDD)网络,以及进一步加快了随机质原始的原始不动性原始不动脉动脉动脉冲,同时使用光谱技术将产品近似近似于高度图像空间中。我们X级的加速的加速度图像的加速模型,可以共同展示。