Comparing Implicit Neural Representations and B-Splines for Continuous Function Fitting from Sparse Samples

A research team from the University of Michigan has published a preliminary empirical study directly comparing the representation capabilities of Implicit Neural Representations (INRs) against the classical cubic B-spline model. The core question addressed is which method is better at reconstructing a continuous signal—critical for medical imaging like MRI and CT—from only sparse, random samples. The study isolates the pure representation capacity by using only coefficient-domain Tikhonov regularization, removing other confounding factors. Results show that with oracle hyperparameter selection, the INR model consistently outperforms the B-spline baseline.

The technical findings are significant: the coordinate-based neural network with positional encoding achieved a lower normalized root-mean-squared error (NRMSE). Visually, this translated to reconstructions with sharper edge transitions and significantly fewer oscillatory artifacts, which are common pitfalls of traditional spline-based methods. Furthermore, the researchers demonstrated that a practical bilevel optimization framework for tuning the INR hyperparameters based on a split of the measurement data can effectively approximate this oracle performance. This moves the result from a theoretical ideal to a practically achievable one, empirically supporting the shift towards neural representations for sparse data fitting in scientific and medical applications.