Maximum cross-entropy generalized series reconstruction

This article addresses the classical image reconstruction problem from limited Fourier data. In particular, we deal with the issue of how to incorporate constraints provided in the form of a high-resolution reference image which approximates the desired image. A new algorithm is described which represents the desired image using a family of basis functions derived from translated and rotated versions of the reference image. The selection of the most efficient basis function set from this family is guided by the principle 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-sequential magnetic resonance imaging applications, for which significant improvement in temporal resolution can be obtained, even as the object undergoes bulk motion during the acquisition.