Estimating Signal Features from Noisy Images with Stochastic Backgrounds

Abstract

Imaging is often used in scientific applications as a measurement tool. The location of a target, brightness of a star, and size of a tumor are all examples of object features that are sought after in various imaging applications. A perfect measurement of these quantities from image data is impossible because of, most notably, detector noise fluctuations, finite resolution, sensitivity of the imaging instrument, and obscuration by undesirable object structures. For these reasons, sophisticated image-processing techniques are designed to treat images as random variables. Quantities calculated from an image are subject to error and fluctuation; implied by calling them estimates of object features.This research focuses on estimator error for tasks common to imaging applications. Computer simulations of imaging systems are employed to compare the estimates to the true values. These computations allow for algorithm performance tests and subsequent development. Estimating the location, size, and strength of a signal embedded in a background structure from noisy image data is the basic task of interest. The estimation task's degree of difficulty is adjusted to discover the simplest data-processing necessary to yield successful estimates.Even when using an idealized imaging model, linear Wiener estimation was found to be insufficient for estimating signal location and shape. These results motivated the investigation of more complex data processing. A new method (named the scanning-linear estimator because it maximizes a linear functional) is successful in cases where linear estimation fails. This method has also demonstrated positive results when tested in realistic simulations of tomographic SPECT imaging systems. A comparison to a model of current clinical estimation practices found that the scanning-linear method offers substantial gains in performance.