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Accurate spatiotemporal image reconstruction methods are needed for a wide range of biomedical research areas but face challenges due to data incompleteness and computational burden. Data incompleteness arises from the undersampling often required to increase frame rates and reduce acquisition times, while computational burden emerges due to the memory footprint of high-resolution images with three spatial dimensions and extended time horizons. Neural fields, an emerging class of neural networks that act as continuous representations of spatiotemporal objects, have previously been introduced to solve these dynamic imaging problems by reframing image reconstruction to a problem of estimating network parameters. Neural fields can address the twin challenges of data incompleteness and computational burden by exploiting underlying redundancies in these spatiotemporal objects. This work proposes ProxNF, a novel neural field training approach for spatiotemporal image reconstruction leveraging proximal splitting methods to separate computations involving the imaging operator from updates of the network parameter. Specifically, ProxNF evaluates the (subsampled) gradient of the data-fidelity term in the image domain and uses a fully supervised learning approach to update the neural field parameters. By reducing the memory footprint and the computational cost of evaluating the imaging operator, the proposed ProxNF approach allows for reconstructing large, high-resolution spatiotemporal images. This method is demonstrated in two numerical studies involving virtual dynamic contrast-enhanced photoacoustic computed …