Accelerating Deep Unrolling Networks via Dimensionality Reduction

• URL: http://arxiv.org/abs/2208.14784v1
• Date: Wed, 31 Aug 2022 11:45:21 GMT
• Title: Accelerating Deep Unrolling Networks via Dimensionality Reduction
• Authors: Junqi Tang, Subhadip Mukherjee, Carola-Bibiane Sch\"onlieb
• Abstract summary: Deep unrolling networks are currently the state-of-the-art solutions for imaging inverse problems. For high-dimensional imaging tasks, such as X-ray CT and MRI imaging, the deep unrolling schemes typically become inefficient. We propose a new paradigm for designing efficient deep unrolling networks using dimensionality reduction schemes.
• Score: 5.73658856166614
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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