Coded x-ray diffraction imaging (CXRDI) is an emerging computational imaging approach that aims to solve the phase retrieval problem in x-ray crystallography based on the intensity measurements of encoded diffraction patterns. Boolean coding masks (BCMs) with complementary structures have been used to modulate the diffraction pattern in CXRDI. However, the optimal spatial distribution of BCMs still remains an open problem to be studied in depth. Based on the spectral initialization criterion, we provide a theoretical proof for the premise that the optimal complementary BCMs should obey the blue noise distribution in the sense of mathematical expectation. In addition, the benefits of the blue noise coding strategy are assessed by a set of simulations, where better reconstruction quality is observed compared to the random BCMs and other complementary BCMs.

Compressive x-ray tomosynthesis (CXT) uses a set of encoded projection measurements from different incident angles to reconstruct the object under inspection. We consider the variable motion of objects on a conveyor mechanism and establish an imaging model based on the sensing geometry of a dynamic CXT system. Then, a numerical algorithm is proposed to optimize the structured illumination series to improve reconstruction accuracy with reduced radiation dose. Compared with the state-of-the-art method, the proposed strategy increases the degrees of optimization freedom by jointly optimizing the coding mask patterns, locations of x-ray sources, and exposure moments in the CXT system, thus obtaining better reconstruction performance. A genetic algorithm is applied to achieve the optimization results. It shows that the proposed method outperforms the traditional CXT approach by further improving reconstruction performance under comparable radiation dose.

Coded aperture X-ray CT (CAXCT) is a new low-dose imaging technology that promises far-reaching benefits in industrial and clinical applications. It places various coded apertures (CA) at a time in front of the X-ray source to partially block the radiation. The ill-posed inverse reconstruction problem is then solved using l1-norm-based iterative reconstruction methods. Unfortunately, to attain high-quality reconstructions, the CA patterns must change in concert with the view-angles making the implementation impractical. This paper proposes a simple yet radically different approach to CAXCT, which is coined StaticCodeCT, that uses a single-static CA in the CT gantry, thus making the imaging system amenable for practical implementations. Rather than using conventional compressed sensing algorithms for recovery, we introduce a new reconstruction framework for StaticCodeCT. Namely, we synthesize the missing measurements using low-rank tensor completion principles that exploit the multi-dimensional data correlation and low-rank nature of a 3-way tensor formed by stacking the 2D coded CT projections. Then, we use the FDK algorithm to recover the 3D object. Computational experiments using experimental projection measurements exhibit up to 10% gains in the normalized root mean square distance of the reconstruction using the proposed method compared with those attained by alternative low-dose systems.

Dynamic coded x-ray tomosynthesis (CXT) uses a set of encoded x-ray sources to interrogate objects lying on a moving conveyor mechanism. The object is reconstructed from the encoded measurements received by the uniform linear array detectors. We propose a multi-objective optimization (MO) method for structured illuminations to balance the reconstruction quality and radiation dose in a dynamic CXT system. The MO framework is established based on a dynamic sensing geometry with binary coding masks. The Strength Pareto Evolutionary Algorithm 2 is used to solve the MO problem by jointly optimizing the coding masks, locations of x-ray sources, and exposure moments. Computational experiments are implemented to assess the proposed MO method. They show that the proposed strategy can obtain a set of Pareto optimal solutions with different levels of radiation dose and better reconstruction quality than the initial setting.

Static coded aperture x-ray tomography was introduced recently where a static illumination pattern is used to interrogate an object with a low radiation dose, from which an accurate 3D reconstruction of the object can be attained computationally. Rather than continuously switching the pattern of illumination with each view angle, as traditionally done, static code computed tomography (CT) places a single pattern for all views. The advantages are many, including the feasibility of practical implementation. This paper generalizes this powerful framework to develop single-scan dual-energy coded aperture spectral tomography that enables material characterization at a significantly reduced exposure level. Two sensing strategies are explored: rapid kV switching with a single-static block/unblock coded aperture, and coded apertures with non-uniform thickness. Both systems rely on coded illumination with a plurality of x-ray spectra created by kV switching or 3D coded apertures. The structured x-ray illumination is projected through the objects of interest and measured with standard x-ray energy integrating detectors. Then, based on the tensor representation of projection data, we develop an algorithm to estimate a full set of synthesized measurements that can be used with standard reconstruction algorithms to accurately recover the object in each energy channel. Simulation and experimental results demonstrate the effectiveness of the proposed cost-effective solution to attain material characterization in low-dose dual-energy CT.