Illumination pattern optimization in compressive X-ray Compton backscattering imaging

Compressive X-ray Compton backscattering imaging (CXBI) is a recently proposed technique where coded illumination patterns are projected onto a target for security inspection scans while the needed radiation dose decreases. CXBI resembles the well-known concept of single-pixel imaging, as the number of backscattered photons per illumination pattern is captured in large scintillation plates with null spatial resolution. Although CXBI represented a paradigm change in Compton scanning, no further studies to explore optimal coding structures have been yet released. In this sense, this paper proposes an in-depth analysis of the CXBI sensing matrix, to formulate model-based and data-driven solutions to find adequate coding patterns that maximize the quality of the recovered scenes. The proposed cost functions, in both cases, are guided through defined features such as transmittance, mutual coherence, a binary restriction, and dispersion of ON pixels. The non-data-driven approach is conceived as a gradient-descent problem with reconstructions done through the alternating direction method of multipliers (ADMM) with block-matching and 3D filtering (BM3D) as a prior denoiser. Data-driven, on the other hand, uses a sampling stage combined with residual U-blocks for training while residual U-blocks for reconstruction. Training data consists of human silhouette images, hand-written letters, and self-generated scenes, which are contaminated with <i>Geant-4</i> noise similar to the one that affects CXBI in a real scenario. The encountered optimal patterns were tested using the <i>Geant-4 Application for Tomographic Emissions (GATE)</i> under realistic conditions and compared against randomly generated patterns. Our results demonstrate that non-data- and data-driven designed codes outperform random codes, with the data-driven solution yielding superior quality metrics.