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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.

A novel reconstruction method for compressive spectral imaging is designed by assuming that the spectral image of interest is sufficiently smooth on a collection of graphs. Since the graphs are not known in advance, we propose to infer them from a panchromatic image using a state-of-the-art graph learning method. Our approach leads to solutions with closed-form that can be found efficiently by solving multiple sparse systems of linear equations in parallel. Extensive simulations and an experimental demonstration show the merits of our method in comparison with traditional methods based on sparsity and total variation and more recent methods based on low-rank minimization and deep-based plug-and-play priors. Our approach may be instrumental in designing efficient methods based on deep neural networks and covariance estimation.

Compressive spectral X-ray imaging (CSXI) introduces a pixelated spectral modulator called K-edge coded aperture (KCA) in front of the X-ray source, which enables both, lower dosage to the subject, as well as the capability of spectral tomography while using low-cost integrating X-ray detectors. CSXI systems generally use hundreds of different spectral modulators, each with a distinct pattern to uniquely modulate the illumination at every view angle. In contrast, this paper introduces the use of a single and static coded aperture placed in a tomosynthesis gantry. The compressive system thus interrogates the subject with a fixed coded illumination pattern on all view angles. The advantages of the system are many including reduced cost and the feasibility of implementation. Given the reduced set of coded measurement and the limited spectral separation ability in the resulting architecture, the nonlinear inverse reconstruction problem results in a highly ill-posed problem. An efficient alternating minimization method with three-dimensional total variation regularization is developed for image reconstruction. Furthermore, rather than simply using a random pattern, the coded aperture is optimized under a uniform sensing criterion that shapes the spatial and spectral pattern of the coded aperture so as to minimize the overall radiation exposure placed on any volumetric area of the patient. This is of particular importance in medical imaging where patients at risk are recommended to have periodical X-ray tomosynthesis screenings. The coded aperture optimization is then posed as a binary programming problem solved by a gradient-based algorithm with equilibrium constraints. Numerical experiments show that spatial and spectral coding used in the proposed system to interrogate the subject not only reduces the radiation dose but it also improves the quality of image reconstruction. Gains close to 5dB in peak signal to noise ratio are observed in simulations. Furthermore, it is shown that the optimization of the KCA can effectively improve the uniformity of X-ray radiation compared to random KCA modulation, thus reducing the radiation dose throughout all volumetric sub-areas of the subject — an objective that is not possible with the use of random KCAs.

As the use of X-ray computed tomography (CT) grows in medical diagnosis, so does the concern for the harm a radiation dose can cause and the biological risks it represents. StaticCodeCT is a new low-dose imaging architecture that uses a single-static coded aperture (CA) in a CT gantry. It exploits the highly correlated data in the projection domain to estimate the unobserved measurements on the detector. We previously analyzed the StaticCodeCT system by emulating the effect of the coded mask on experimental CT data. In contrast, this manuscript presents test-bed reconstructions using an experimental cone-beam X-ray CT system with a CA holder. We analyzed the reconstruction quality using three different techniques to manufacture the CAs: metal additive manufacturing, cold casting, and ceramic additive manufacturing. Furthermore, we propose an optimization method to design the CA pattern based on the algorithm developed for the measurement estimation. The obtained results point to the possibility of the real deployment of StaticCodeCT systems in practice.

Coded aperture X-ray computed tomography is a computational imaging technique capable of reconstructing inner structures of an object from a reduced set of X-ray projection measurements. Coded apertures are placed in front of the X-ray sources from different views and thus significantly reduce the radiation dose. This paper introduces coded aperture X-ray computed tomography for robotic X-ray systems which offer positioning flexibility. While single coded-aperture 3D tomography was recently introduced for standard trajectory CT scanning, it is shown that significant gains in imaging performance can be attained by simple modifications in the CT scanning trajectories enabled by emerging dual robotic CT systems. In particular, the subject is fixed on a plane and the CT system uniformly rotates around ther −axis which is misaligned with the coordinate axes. A single stationary coded aperture is placed on front of the robotic X-ray source above the plane and the corresponding X-ray projections are measured by a two-dimensional detector on the second arm of the robotic system. The compressive measurements with misalignment enable the reconstruction of high-resolution three-dimensional volumetric images from the low-resolution coded projections on the detector at a sub-sampling rate. An efficient algorithm is proposed to generate the rotation matrix with two basic sub-matrices and thus the forward model is formulated. The stationary coded aperture is designed based on the Pearson product-moment correlation coefficient analysis and the direct binary search algorithm is used to obtain the optimized coded aperture. Simulations using simulated datasets show significant gains in reconstruction performance compared to conventional coded aperture CT systems.

Compressive X-ray tomosynthesis uses a few two-dimensional projection measurements modulated by coding masks to reconstruct the three-dimensional object that can be sparsely represented on a predefined basis. However, the coding mask optimization and object reconstruction require significant computing resources. In addition, existing methods fall short to exploits the synergy between the encoding and reconstruction stages to approach the global optimum. This paper proposes a model-driven deep learning (MDL) approach to significantly improve the computational efficiency and accuracy of tomosynthesis reconstruction. A unified framework is developed to jointly optimize the coding masks and the neural network parameters, which effectively increase the degrees of optimization freedom. It shows that the computational efficiency of coding mask optimization and image reconstruction can be improved by more than one order of magnitude. Furthermore, the performance of reconstruction results is significantly improved.

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.

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.

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.

Coded spectral X-ray computed tomography (CT) based on K-edge filtered illumination is a cost-effective approach to acquire both 3-dimensional structure of objects and their material composition. This approach allows sets of incomplete rays from sparse views or sparse rays with both spatial and spectral encoding to effectively reduce the inspection duration or radiation dose, which is of significance in biological imaging and medical diagnostics. However, reconstruction of spectral CT images from compressed measurements is a nonlinear and ill-posed problem. This paper proposes a material-decomposition-based approach to directly solve the reconstruction problem, without estimating the energy-binned sinograms. This approach assumes that the linear attenuation coefficient map of objects can be decomposed into a few basis materials that are separable in the spectral and space domains. The nonlinear problem is then converted to the reconstruction of the mass density maps of the basis materials. The dimensionality of the optimization variables is thus effectively reduced to overcome the ill-posedness. An alternating minimization scheme is used to solve the reconstruction with regularizations of weighted nuclear norm and total variation. Compared to the state-of-the-art reconstruction method for coded spectral CT, the proposed method can significantly improve the reconstruction quality. It is also capable of reconstructing the spectral CT images at two additional energy bins from the same set of measurements, thus providing more spectral information of the object.