A reconstruction-algorithm that might be more reliable and precise than the existing ones might be a hybrid of a zonal and a modal algorithm:
First, a modal zernike-reconstruction could be done, reconstructing all the low-frequent parts of the wavefront. The remaining gradient could then be fed into a zonal algorithm, e.g. southwell, to reconstruct the high-frequent parts.
Before adding the high-frequent parts, they should be passed through a zernike-filter to remove all the low-frequent reconstruction errors.