Correlated statistical uncertainties in coded-aperture imaging

Abstract

a b s t r a c tIn nuclear security applications, coded-aperture imagers can provide a wealth of information regarding the attributes of both the radioactive and nonradioactive components of the objects being imaged. However, for optimum benefit to the community, spatial attributes need to be determined in a quantitative and statistically meaningful manner. To address a deficiency of quantifiable errors in coded-aperture imaging, we present uncertainty matrices containing covariance terms between image pixels for MURA mask patterns. We calculated these correlated uncertainties as functions of variation in mask rank, mask pattern over-sampling, and whether or not anti-mask data are included. Utilizing simulated point source data, we found that correlations arose when two or more image pixels were summed. Furthermore, we found that the presence of correlations was heightened by the process of over-sampling, while correlations were suppressed by the inclusion of anti-mask data and with increased mask rank. As an application of this result, we explored how statistics-based alarming is impacted in a radiological search scenario.

Exploiting fission chain reaction dynamics to image fissile materials

“…In the decoding process, G (i , j ) is the complement of A(i , j ); i.e., each open element is +1 and each closed element is −1, with the central element being set to +1 [11]. By defining G (i , j ) this way, its correlation with A(i , j ) approximates a delta function.…”

“…The image shown is reconstructed from a measurement of a 252 Cf point source. The following discussion of estimating the uncertainty in an ROI sum was originally presented by Fleenor [11]. The variance of a single reconstructed object image pixel σ 2Ô…”

“…The covariance term is dependent on mask rank, whether or not mask and anti-mask data are used in reconstructing the object image, and whether or not the encoded picture is double-sampled. In the case of the NCAI, the normalized covariance is 0.5 for pixels that share an edge and 0.25 for pixels that share a corner 2 [11]. The total variance for an ROI is therefore determined by accounting for the variance of each pixel, as well as its covariance with each of its nearest neighbors.…”

Final Report: Non-Visible, Automated Target Acquisition and Tracking

“…Because of the anti-aliasing approach used by the system, there is covariance in the error for neighboring pixels. (This has only recently been explored for 2D images [11] and that work has not been extended to the 1D images used here.) That means that one cannot just add data from a set of pixels and calculate a total uncertainty based on adding the individual uncertainties in quadrature (the normal approach for uncorrelated errors).…”

“…By the time that the hardware was up and running, suitable data were collected, but the project had advanced to a point where it was no longer feasible to implement the changes. The recent work on calculating the covariance terms from neighboring pixels correctly [11] should provide both an easier fix, and also allow using the data from several neighboring pixels to enhance the sensitivity from the individual trailers. However, such improvements are left to future development.…”