We study the problem of recovering an object from noisy limited-angle tomographic data---a problem which arises in many important medical applications. We argue that curvelets, a recently developed multiscale system, may have a great potential in this setting. Conceptually, curvelets are multiscale elements with a useful microlocal structure which makes them especially adapted to limited-angle tomography. We develop a theory of optimal rates of convergence which quantifies that features which are microlocally in the "good" direction can be recovered accurately and which shows that adapted curvelet-biorthogonal decompositions with thresholding can achieve quantitatively optimal rates of convergence. We hope to report on early numerical results.
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