arXiv subjects
Publications and source records attributed to Weston Baines.
In this work we consider the Conical Radon Transform, which integrates a function on $\R^n$ over families of circular cones. Transforms of this type are known to arise naturally as models of Compton camera imaging and single-scattering optical tomography (in the latter case, when $n=2$). The main results (which depend on the parity of $n$) provide a description of the range of the transform on the space $C_0^\infty(\R^n)$
Methods for source detection in high noise environments are important for single-photon emission computed tomography (SPECT) medical imaging and especially crucial for homeland security applications, which is our main interest. In the latter case, one deals with passively detecting the presence of low emission nuclear sources with significant background noise (with Signal To Noise Ratio ($SNR$) $1\%$ or less). In passive emission problems, direction sensitive detectors are needed, to match the dimensionalities of the image and the data. Collimation, used for that purpose in standard Anger $γ$-cameras, is not an option. Instead, Compton $γ$-cameras (and their analogs for other types of radiation) can be utilized. Backprojection methods suggested before by two of the authors and their collaborators enable detection in the presence of a random uniform background. In most practical applications, however, cargo packing in shipping containers and trucks creates regions of strong absorption and scattering, while leaving some streaming gaps open. In such cases backprojection methods prove ineffective and lose their detection ability. Nonetheless, visual perception of the backprojection pictures suggested that some indications of presence of a source might still be in the data. To learn such features (if they do exist), a deep neural network approach is implemented in 2D, which indeed exhibits higher sensitivity and specificity than the backprojection techniques in a low scattering case and works well when presence of complex cargo makes backprojection fail completely.
We present a novel technique based on deep learning and set theory which yields exceptional classification and prediction results. Having access to a sufficiently large amount of labelled training data, our methodology is capable of predicting the labels of the test data almost always even if the training data is entirely unrelated to the test data. In other words, we prove in a specific setting that as long as one has access to enough data points, the quality of the data is irrelevant.