title: Image reconstruction and multidimensional field estimation from randomly scattered sensors.
abstract: Many important problems in statistical signal processing can be formulated as function estimation from randomly scattered sensors in a multidimensional space, e.g., image reconstruction from photon-limited images and field estimation from scattered sensors. We present a novel approach to the study of signal reconstruction from random samples in a multidimensional space. In particular, we study a classical iterative reconstruction method and demonstrate that it forms a sequence of unbiased estimates for band-limited signals, which converge to the true function in the mean-square sense. We subsequently rely on the iterative estimation method for multidimensional image reconstruction and field estimation from sensors scattered according to a multidimensional Poisson and uniform distribution. Computer simulation experiments are used to demonstrate the efficiency of the iterative estimation method in image reconstruction and field estimation from randomly scattered sensors.
authors.forename: Pan
authors.initials: P
authors.lastname: Pan
authors.forename: Dan
authors.initials: D
authors.lastname: Schonfeld
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D007089:Image Enhancement / Q000295:instrumentation / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000295:instrumentation / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000295:instrumentation / Q000379:methods*; D015233:Models, Statistical; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity; D014159:Transducers