CNN-Based Projected Gradient Descent for Consistent Image Reconstruction
This work addresses the challenge of ensuring measurement consistency in CNN-based image reconstruction, which is crucial for diagnostic accuracy in biomedical imaging, though it is incremental as it builds on existing PGD and CNN techniques.
The authors tackled the problem of image reconstruction in inverse problems, particularly in biomedical imaging, by integrating a convolutional neural network (CNN) into a projected gradient descent (PGD) framework to enforce measurement consistency, resulting in improved performance over total-variation and recent CNN-based methods in sparse view CT reconstruction.
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.