In this paper, a coded aperture optimization approach based on sparse principal component analysis (SPCA) is proposed to maximize the information sensed by a set of cone-beam projections. The variables in the CT system matrix correspond to observations of the attenuation characteristics of X-ray projections. An adjusted joint variance is used to update the variables and thus the overlapping information of the kth principal component is constrained by the previous k-1 principal components. Since the coded aperture matrix is diagonal and binary, an efficient algorithm is proposed to reduce the complexity by one order of magnitude. Simulations using simulated datasets, 3D Shepp-Logan phantom, show significant gains up to 23.5dB compared with that attained by random coded apertures. Singular value decomposition (SVD) of the optimized coded apertures is used to analyze the performance of the proposed coded aperture optimization method based on SPCA.
This manuscript explores a new approach for spectral X-ray tomography that uses K-edge filtering structures to attain spectral and spatially coded illumination which enables the acquisition of compressive measurements for the reconstruction of energy-binned images. The system is coined compressive spectral X-ray imaging (CSXI). A multi-stage algorithm is proposed to solve the non-linear ill-posed problem using sparse and low-rank regularization constraints to exploit the structure of the spectral data cube. The proposed algorithm can reconstruct both the energy binned images as well as the material decomposition of the object given a set of basis materials.
The CT system structure matrix in the coded aperture compressive X-ray tomography (CACXT) is highly structured and thus the random coded apertures are not optimal. A fast approach based on minimal information loss is proposed. The peak signal to noise ratios (PSNR) of the reconstructed images with optimized coded apertures exhibit significant gains and the design execution time is reduced by orders of magnitude. Simulations results for optimized coded apertures are shown, and their performance is compared to the use of random coded apertures.
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