Techniques for tomographic reconstruction using non-linear diagonal estimators are disclosed. In a preferred embodiment, tomographic data from a tomographic device is decomposed in a wavelet vector family. Regularization of the tomographic data is accomplished by performing a thresholding operation on coefficients of the decomposed data. The regularized data is reconstructed into image data that may he displayed. In another preferred embodiment, a wavelet packet vector family is used to decompose the tomographic data. The wavelet packet is selected from a dictionary of wavelet packets using the best basis algorithm.