We propose a greedy inversion method for a spatially localized, high-resolution Radon transform. The kernel of the method is based on a conventional iterative algorithm, conjugate gradient (CG), but is utilized adaptively in amplitude-prioritized local model spaces. The adaptive inversion introduces a coherence-oriented mechanism to enhance focusing of significant model parameters, and hence increases the model resolution and convergence rate. We adopt the idea in a time-space domain local linear Radon transform for data interpolation. We find that the local Radon transform involves iteratively applying spatially localized forward and adjoint Radon operators to fit the input data. Optimal local Radon panels can be found via a subspace algorithm which promotes sparsity in the model, and the missing data can be predicted using the resulting local Radon panels. The subspacing strategy greatly reduces the cost of computing local Radon coefficients, thereby reducing the total cost for inversion. The method can handle irregular and regular geometries and significant spatial aliasing. We compare the performance of our method using three simple synthetic data sets with a popular interpolation method known as minimum weighted norm Fourier interpolation, and show the advantage of the new algorithm in interpolating spatially aliased data. We also test the algorithm on the 2D synthetic data and a field data set. Both tests show that the algorithm is a robust antialiasing tool, although it cannot completely recover missing strongly curved events.