Least squares image estimation for large data in the presence of noise and irregular sampling

We consider an acquisition system where a continuous, band-limited image is reconstructed from a set of irregularly distributed, noisy samples. An optimal estimator can be obtained by exploiting Least Squares, but it is not practical to compute when the data size is large. A simpler, widely used estimate can be obtained by properly rounding off the pointing information, but it is suboptimal and is affected by a bias, which may be large and thus limits its applicability. To solve this problem, we develop a mathematical model for the acquisition system, which accounts for the pointing information round off. Based on the model, we derive a novel optimal estimate, which has a manageable computational complexity and is largely immune from the bias, making it a better option than the suboptimal one. Moreover, the model opens a new, fruitful point of view on the estimation performance analysis. Finally, we consider the application of the novel estimate to the data of the Photodetector Array Camera and Spectrometer instrument. In this paper, we discuss several implementation aspects and investigate the performance by using both true and simulated data.