In this paper we introduce an algorithm for imaging a time varying object f(x,t) from its projections at different fixed times. We show that the reconstruction of coarse features, corresponding to low spatial-frequency data, can be made nearly instantaneously in time from the evolving data. A temporal sequence of these low spatial-frequency reconstructions can be used to estimate the motion of the object. Once the motion is estimated, we may use the estimate to compensate for some of the motion of fine scale features. This enables accurate reconstructions of the time varying fine structure in several cases. The algorithm is demonstrated for a selection of phantoms and actual MRI studies. In general, this technique shows promise for a wide variety of applications in MRI, as well as for heart imaging using x- ray CT. Clinical applications should include both functional MRI such as dynamic imaging of oxygen usage and blood flow in the brain, and motion imaging of joints, angiography in the lungs, and heart imaging.