Deep Convolutional Neural Network for Inverse Problems in Imaging

TLDR

Regularized iterative algorithms are the standard for ill‑posed inverse problems but are computationally costly and hard to tune, and unrolled iterative methods resemble CNNs when the normal operator is a convolution. The paper proposes a CNN‑based algorithm that combines direct inversion with a CNN to solve normal‑convolutional ill‑posed inverse problems. The method uses direct inversion to model the physics, then a CNN employing multiresolution decomposition and residual learning to remove artifacts and preserve structure. The network achieves superior sparse‑view CT reconstruction, outperforming TV‑regularized iterative methods on realistic phantoms and reconstructing 512×512 images in under a second on GPU.

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.