Meshless super-resolution of scattered data via constrained radial basis functions and K-nearest-neighbors-driven densification

We propose a novel meshless method to achieve super resolution from scattered data obtained from sparse, randomly positioned sensors such as the particle tracers of particle tracking velocimetry. The method combines K Nearest Neighbor Particle Tracking Velocimetry (KNN PTV, Tirelli et al. 2023) with meshless Proper Orthogonal Decomposition (meshless POD, Tirelli et al. 2025) and constrained Radial Basis Function regression (c RBFs, Sperotto et al. 2022). The main idea is to enhance the spatial resolution of flow fields by blending data from locally similar flow regions available in the time series. This similarity is assessed in terms of statistical coherency with leading features identified by meshless POD applied directly to scattered data, without interpolation onto a grid and relying instead on RBFs to compute the relevant inner products. The denser scattered distributions are then used within a constrained RBF framework to derive an analytical representation of the flow fields that incorporates physical constraints. The approach is fully meshless and does not require a grid at any stage, offering flexibility in complex geometries. An ablation study highlights the role of penalties and physical constraints in regularizing the regression and ensuring physically consistent reconstructions. The method is validated using three dimensional measurements of a jet flow in air. The assessment focuses on statistics, spectra, and modal analysis. Performance is evaluated against standard Particle Image Velocimetry, KNN PTV, and c RBFs. The results show improved accuracy, with an average error of about ten percent compared to twelve to thirteen percent for the other methods, nearly halved errors in reduced order reconstructions, and a higher frequency cutoff based on the noise floor.