Optimal Time-Frequency Projections for Localized Tomography
An algorithm for recovering a function from essentially localized values of its Radon transform and sparse nonlocal values was outlined in . That algorithm utilized the time-frequency properties of wavelets, coupled with the range theorems for the Radon transform to essentially localize the dependence of the Radon transform. In this chapter we utilize alternative time-frequency projections which were introduced by Coifman and Meyer in . We present evidence that these bases are optimal according to our criterion for localized tomography. These bases require significantly less data than the wavelet bases which were used in . Finally we present numerical results supporting this work.