CNN-Based Projected Gradient Descent for Consistent Image Reconstruction

TL;DR

This paper introduces a CNN-enhanced projected gradient descent method for image reconstruction that maintains measurement consistency and improves results over existing techniques, especially in CT imaging.

Contribution

It proposes a novel CNN-based projector within PGD, ensuring convergence and measurement consistency in inverse imaging problems.

Findings

Improved image reconstruction accuracy over TV and CNN methods.

The relaxed PGD with CNN projector always converges.

Effective in both noiseless and noisy CT data.

Abstract

We present a new method for image reconstruction which replaces the projector in a projected gradient descent (PGD) with a convolutional neural network (CNN). CNNs trained as high-dimensional (image-to-image) regressors have recently been used to efficiently solve inverse problems in imaging. However, these approaches lack a feedback mechanism to enforce that the reconstructed image is consistent with the measurements. This is crucial for inverse problems, and more so in biomedical imaging, where the reconstructions are used for diagnosis. In our scheme, the gradient descent enforces measurement consistency, while the CNN recursively projects the solution closer to the space of desired reconstruction images. We provide a formal framework to ensure that the classical PGD converges to a local minimizer of a non-convex constrained least-squares problem. When the projector is replaced with a CNN, we propose a relaxed PGD, which always converges. Finally, we propose a simple scheme to train a CNN to act like a projector. Our experiments on sparse view Computed Tomography (CT) reconstruction for both noiseless and noisy measurements show an improvement over the total-variation (TV) method and a recent CNN-based technique.