Current x-ray technologies provide security personnel with non-invasive sub-surface imaging and contraband detection in various portal screening applications such as checked and carry-on baggage as well as cargo. Computed tomography (CT) scanners generate detailed 3D imagery in checked bags; however, these scanners often require significant power, cost, and space. These tomography machines are impractical for many applications where space and power are often limited such as checkpoint areas. Reducing the amount of data acquired would help reduce the physical demands of these systems. Unfortunately this leads to the formation of artifacts in various applications, thus presenting significant challenges in reconstruction and classification. As a result, the goal is to maintain a certain level of image quality but reduce the amount of data gathered. For the security domain this would allow for faster and cheaper screening in existing systems or allow for previously infeasible screening options due to other operational constraints. While our focus is predominantly on security applications, many of the techniques can be extended to other fields such as the medical domain where a reduction of dose can allow for safer and more frequent examinations. This dissertation aims to advance data reduction algorithms for security motivated x-ray imaging in three main areas: (i) development of a sensing aware dimensionality reduction framework, (ii) creation of linear motion tomographic method of object scanning and associated reconstruction algorithms for carry-on baggage screening, and (iii) the application of coded aperture techniques to improve and extend imaging performance of nuclear resonance fluorescence in cargo screening. The sensing aware dimensionality reduction framework extends existing dimensionality reduction methods to include knowledge of an underlying sensing mechanism of a latent variable. This method provides an improved classification rate over classical methods on both a synthetic case and a popular face classification dataset. The linear tomographic method is based on non-rotational scanning of baggage moved by a conveyor belt, and can thus be simpler, smaller, and more reliable than existing rotational tomography systems at the expense of more challenging image formation problems that require special model-based methods. The reconstructions for this approach are comparable to existing tomographic systems. Finally our coded aperture extension of existing nuclear resonance fluorescence cargo scanning provides improved observation signal-to-noise ratios. We analyze, discuss, and demonstrate the strengths and challenges of using coded aperture techniques in this application and provide guidance on regimes where these methods can yield gains over conventional methods.