Imaging by an optimizing method

The imaging problem can be described as an optimizing problem in mathematics. Thus optimizing theory and algorithms can be used to solve it. In this paper we present an optimizing method, in which we take the imaging problem as an optimizing problem with linear constraints. We-choose the objective function carefully. Both the mathematical expectation and the variance of the observed data are considered. Upper and lower limit source and background intensities can be conveniently considered. We adopt an algorithm very similar to the affine scaling approach in convex programming. Computer simulations of rotating modulation collimator imaging show that the quality of images from this method is better than that from the traditional cross-correlation method. Both point and extended sources can be imaged in the same held of view. We also apply the algorithm to ROSAT PSPC pointed observation data of the Crab nebula. The image quality is improved significantly. The extended structure of the Crab nebula can clearly be seen.