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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. 

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 a 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. 

The majority of iterative algorithms for CT reconstruction rely on discrete-to-discrete modeling, where both the sinogram measurements and image to be estimated are discrete arrays. However, tomographic projections are ideally modeled as line integrals of a continuous attenuation function, i.e., the true inverse problem is discrete-to-continuous in nature. Recently, coordinate-based neural networks (CBNNs), also known as implicit neural representations, have gained traction as a flexible type of continuous domain image representation in a variety of inverse problems arising in computer vision and computational imaging. Using standard neural network training techniques, a CBNN can be fit to measurements to give a continuous domain estimate of the image. In this study, we empirically investigate the potential of CBNNs to solve the continuous domain inverse problems in CT imaging. In particular, we experiment with reconstructing an analytical phantom from its ideal sparse-view sinogram measurements. Our results illustrate that reconstruction with a CBNN are more accurate than filtered back projection and algebraic reconstruction techniques at a variety of resolutions, and competitive with total variation regularized iterative reconstruction.