Neural Proximal Gradient Descent for Compressive Imaging

TL;DR

This paper introduces a neural proximal gradient method using residual networks for compressive imaging, achieving faster and more accurate high-resolution image reconstructions from limited data, outperforming traditional methods.

Contribution

It develops a recurrent ResNet-based proximal gradient framework that improves reconstruction quality and speed in compressive imaging tasks, with theoretical convergence analysis.

Findings

Recurrent ResNet with a single residual block effectively reconstructs MRI images.

The proposed method outperforms non-recurrent ResNets by 2dB SNR and traditional wavelet-based methods by 4dB SNR.

Reconstruction speed is improved by 100 times compared to state-of-the-art methods.

Abstract

Recovering high-resolution images from limited sensory data typically leads to a serious ill-posed inverse problem, demanding inversion algorithms that effectively capture the prior information. Learning a good inverse mapping from training data faces severe challenges, including: (i) scarcity of training data; (ii) need for plausible reconstructions that are physically feasible; (iii) need for fast reconstruction, especially in real-time applications. We develop a successful system solving all these challenges, using as basic architecture the recurrent application of proximal gradient algorithm. We learn a proximal map that works well with real images based on residual networks. Contraction of the resulting map is analyzed, and incoherence conditions are investigated that drive the convergence of the iterates. Extensive experiments are carried out under different settings: (a) reconstructing abdominal MRI of pediatric patients from highly undersampled Fourier-space data and (b) superresolving natural face images. Our key findings include: 1. a recurrent ResNet with a single residual block unrolled from an iterative algorithm yields an effective proximal which accurately reveals MR image details. 2. Our architecture significantly outperforms conventional non-recurrent deep ResNets by 2dB SNR; it is also trained much more rapidly. 3. It outperforms state-of-the-art compressed-sensing Wavelet-based methods by 4dB SNR, with 100x speedups in reconstruction time.