Accelerated Optimization of Implicit Neural Representations for CT Reconstruction

Inspired by their success in solving challenging inverse problems in computer vision, implicit neural representations (INRs) have been recently proposed for reconstruction in low-dose/sparse-view X-ray computed tomography (CT). An INR represents a CT image as a small-scale neural network that takes spatial coordinates as inputs and outputs attenuation values. Fitting an INR to sinogram data is similar to classical model-based iterative reconstruction methods. However, training INRs with losses and gradient-based algorithms can be prohibitively slow, taking many thousands of iterations to converge. This paper investigates strategies to accelerate the optimization of INRs for CT reconstruction. In particular, we propose two approaches: (1) using a modified loss function with improved conditioning, and (2) an algorithm based on the alternating direction method of multipliers. We illustrate that both of these approaches significantly accelerate INR-based reconstruction of a synthetic breast CT phantom in a sparse-view setting.

Towards a Sampling Theory for Implicit Neural Representations

Implicit neural representations (INRs) have emerged as a powerful tool for solving inverse problems in computer vision and computational imaging. INRs represent images as continuous domain functions realized by a neural network taking spatial coordinates as inputs. However, unlike traditional pixel representations, little is known about the sample complexity of estimating images using INRs in the context of linear inverse problems. Towards this end, we study the sampling requirements for recovery of a continuous domain image from its low-pass Fourier coefficients by fitting a single hidden-layer INR with ReLU activation and a Fourier features layer using a generalized form of weight decay regularization. Our key insight is to relate minimizers of this non-convex parameter space optimization problem to minimizers of a convex penalty defined over an infinite-dimensional space of measures. We identify a sufficient number of samples for which an image realized by a width-1 INR is exactly recoverable by solving the INR training problem, and give a conjecture for the general width-$W$ case. To validate our theory, we empirically assess the probability of achieving exact recovery of images realized by low-width single hidden-layer INRs, and illustrate the performance of INR on super-resolution recovery of more realistic continuous domain phantom images.