In geophysics the ionosphere has an important role due to its interaction with satellite signals. The ionosphere can be imaged through computerized tomography using observations from ground based receivers. However, the uneven and sparse distribution of limited-angle observations makes this inverse problem particularly challenging. To help solve this, a sparse regularization technique is applied to wavelet basis functions. Advantages over a more conventional approach using Tikhonov regularization with spherical harmonics are presented.