Maximum cross-entropy generalized series reconstruction

This paper addresses the classical image reconstruction problem from limited Fourier data. Here, we assume that a high-resolution reference which provides an initial estimate of the desired image is available. A new algorithm is described which represents the desired image using a family of basis functions derived from 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 and can also account for relative rotation and translation between the reference and the measured data.