Maximum cross-entropy generalized series reconstruction

This article addresses the classical image reconstruction problem from limi ted Fourier data. In particular, we deal with the issue of how to incorpora te constraints provided in the form of a high-resolution reference image wh ich approximates the desired image. A new algorithm is described which repr esents the desired image using a family of basis functions derived from tra nslated and rotated versions of the reference image. The selection of the m ost efficient basis function set from this family is guided by the principl e of maximum cross-entropy. Simulation and experimental results have shown that the algorithm can achieve high resolution with a small number of data points while accounting for relative misregistration between the reference and measured data. The technique proves to be useful for a number of time-s equential magnetic resonance imaging applications, for which significant im provement in temporal resolution can be obtained, even as the object underg oes bulk motion during the acquisition. (C) 1999 John Wiley & Sons, Inc.