Neural fields for dynamic imaging

Dynamic imaging systems monitor physiological processes that evolve or change over time. However, image reconstruction from dynamic data is made difficult by data incompleteness and significant computational burden. Data incompleteness, in particular, arises from severe undersampling often necessary to increase frame rate by reducing data acquisition time and leads to ill-posedness of the reconstruction problem. Computational cost and memory requirements are particularly burdensome for three-dimensional problems, especially for applications in which high-resolution in space and time is needed. Two main approaches exist for dynamic image reconstruction. Frame-by-frame approaches solve a sequence of image reconstruction problems (one for each frame). Spatiotemporal approaches instead directly reconstruct the dynamic object using data from all imaging frames at once. Although statistically suboptimal, frame-by-frame approaches have often been advocated because of the ease of implementation and lower memory requirements. This work explores a new spatiotemporal dynamic reconstruction approach that uses neural fields, a special class of neural networks, to drastically reduce the computational complexity and memory requirements while exploiting the object's spatiotemporal redundancies. As a feasibility study, a simple dynamic image reconstruction problem whose forward operator is given by the circular Radon transform is considered. Numerical results demonstrate that the proposed approach is more accurate and uses less memory than the classical frame-by-frame approach.