Since wavefront distortions cannot be directly measured from an image, a wavefront sensor (WFS) can use intensity variations from a point source to estimate slope or curvature of a wavefront. However, processing of measured aberration data from WFSs is computationally intensive, and this is a challenge for real-time image restoration or correction. A multi-resolutional method, known as the ridgelet transform, is explored to estimate wavefront distortions from astronomical images of natural source beacons (stars). Like the curvature sensor, the geometric WFS is relatively simple to implement but computationally more complex. The geometric WFS is extended by incorporating the sparse and multi-scale geometry of ridgelets, which are analyzed to optimize the performance of the geometric WFS. Ridgelets provide lower wavefront errors, in terms of root mean square error, specifically over low photon flux levels. The simulation results further show that by replacing the Radon transform of the geometric WFS with the ridgelet transform, computational complexity is reduced.