Abstract

An algorithm for recovering a function from essentially localized values of its Radon transform, and sparse non-local values was outlined in [12]. 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 paper we utilize alternative time-frequency projections which were introduced by Coifman and Meyer in [4]. 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 [12]. Finally we present numerical results supporting this work. Running Head: Localized tomography Key words: Local tomography, medical imaging, x-ray tomography, Radon transform, wavelets, local trigonometric bases 1 Introduction 1.1 Historical Notes Computerized tomography (CT) refers to the recovery of a two-dimensional density f(x; y) from the one dimens...

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