Image Estimation in the Presence of Irregular Sampling, Noise, and Pointing Jitter

We consider an acquisition system where a continuous image is reconstructed from a set of irregularly distributed noisy samples. Moreover, the system is affected by a random pointing jitter which makes the actual sampling positions different from the nominal ones. We develop a model for the system and derive the optimal, minimum variance unbiased (MVU) estimate. Unfortunately, the latter estimate is not practical to compute when the data size is large. Therefore, we develop a simplified, low resolution model and derive the corresponding MVU estimate, which has a drastically lower complexity. Moreover, we analyze the estimators' performance by using both theoretical analysis and simulations. Finally, we discuss the application to the data of the Photodetector Array Camera and Spectrometer (PACS) instrument, which is an infrared photometer on board the Herschel satellite.