Deep Convolutional Neural Network for Inverse Problems in Imaging

TL;DR

This paper introduces a CNN-based approach for solving ill-posed inverse imaging problems, leveraging direct inversion and deep learning to improve reconstruction quality and computational efficiency.

Contribution

It proposes a novel CNN architecture that combines direct inversion with residual learning to effectively address artifacts in ill-posed inverse problems with convolutional normal operators.

Findings

Outperforms total variation-regularized iterative reconstruction in synthetic and real data.

Reconstructs 512x512 images in less than a second on GPU.

Effective in sparse-view X-ray computed tomography with as few as 50 views.

Abstract

In this paper, we propose a novel deep convolutional neural network (CNN)-based algorithm for solving ill-posed inverse problems. Regularized iterative algorithms have emerged as the standard approach to ill-posed inverse problems in the past few decades. These methods produce excellent results, but can be challenging to deploy in practice due to factors including the high computational cost of the forward and adjoint operators and the difficulty of hyper parameter selection. The starting point of our work is the observation that unrolled iterative methods have the form of a CNN (filtering followed by point-wise non-linearity) when the normal operator (H*H, the adjoint of H times H) of the forward model is a convolution. Based on this observation, we propose using direct inversion followed by a CNN to solve normal-convolutional inverse problems. The direct inversion encapsulates the physical model of the system, but leads to artifacts when the problem is ill-posed; the CNN combines multiresolution decomposition and residual learning in order to learn to remove these artifacts while preserving image structure. We demonstrate the performance of the proposed network in sparse-view reconstruction (down to 50 views) on parallel beam X-ray computed tomography in synthetic phantoms as well as in real experimental sinograms. The proposed network outperforms total variation-regularized iterative reconstruction for the more realistic phantoms and requires less than a second to reconstruct a 512 x 512 image on GPU.