LAUSR

Dynamic imaging is essential for analyzing various biological processes but faces two main challenges: data incompleteness and computational burden. For many imaging systems, high frame rates and short acquisition times require severe undersampling, leading to data incompleteness. Multiple images may then be compatible with the data, thus requiring special techniques (regularization) to ensure uniqueness of the reconstruction. Computational and memory requirements are particularly burdensome for three-dimensional applications requiring high spatiotemporal resolution. Exploiting redundancies in the object's spatiotemporal features is key to addressing both challenges. This contribution investigates neural fields, or implicit neural representations, to model the sought-after dynamic object. Neural fields are a particular class of neural networks that represent the dynamic object as a continuous function of space and time, thus avoiding the burden of storing a full-resolution image at each time frame. The proposed approach integrates the neural field representation of the object into the imaging model to formulate the dynamic image reconstruction problem as a self-supervised learning problem. Specifically, the network parameters are estimated by minimizing a regularized data discrepancy functional by use of accelerated first-order stochastic optimization algorithms. Once trained, the neural field is evaluated at arbitrary locations in space and time, allowing for high-resolution rendering of the object. Key advantages of the proposed approach are that neural fields automatically learn redundancies in the sought-after object to both regularize the reconstruction and significantly reduce memory requirements. The proposed framework is illustrated with an application to dynamic image reconstruction from severely undersampled circular Radon transform data.