Mean Squared and Worst Case performance of multiple spacecraft interferometric imaging systems : A Feature Based Approach

Abstract

The problem of quantifying minimum acceptable performance of multi-spacecraft interferometric imaging systems is considered. The noise corrupting the measurements is critical in the design of these systems and is dependent on the motion of the constituent spacecrafts. Minimum acceptable performance is defined in terms of the misclassification error of an image given that the set of images has been partitioned into two distinct classes. Two measures of the noise corrupting the measurements are considered: mean squared error(MSE) and the worst case error(WCE). It is shown that these are consistent with the goal of image classification in the sense that as image estimates converge in the MSE/WCE sense, the probability of misclassifying the image tends to zero. Error bounds are obtained on the MSE/WCE such that some minimum acceptable performance, in terms of the probability of correctly classifying an image, is acheived. An example is presented where the bandedness of the image of a planet is sought to be detected. Bounds on the noise corrupting the measurements are obtained such that a pre-specified level of performance is achieved for this case.