SGD-Net: Efficient Model-Based Deep Learning with Theoretical Guarantees

TL;DR

SGD-Net introduces a stochastic approximation approach to deep unfolding networks, significantly reducing computational complexity while maintaining performance in large-scale imaging inverse problems.

Contribution

It proposes SGD-Net, a novel method that enhances deep unfolding efficiency with theoretical guarantees, enabling scalable imaging inverse problem solutions.

Findings

SGD-Net matches batch network performance in tomography tasks.

It reduces training and testing complexity substantially.

Theoretical analysis confirms approximation accuracy.

Abstract

Deep unfolding networks have recently gained popularity in the context of solving imaging inverse problems. However, the computational and memory complexity of data-consistency layers within traditional deep unfolding networks scales with the number of measurements, limiting their applicability to large-scale imaging inverse problems. We propose SGD-Net as a new methodology for improving the efficiency of deep unfolding through stochastic approximations of the data-consistency layers. Our theoretical analysis shows that SGD-Net can be trained to approximate batch deep unfolding networks to an arbitrary precision. Our numerical results on intensity diffraction tomography and sparse-view computed tomography show that SGD-Net can match the performance of the batch network at a fraction of training and testing complexity.