High-Quality Parallel-Ray x-Ray CT Back Projection Using Optimized Interpolation

We propose a new, cost-efficient method for computing back projections in parallel-ray X-ray CT. Forward and back projections are the basis of almost all X-ray CT reconstruction methods, but computing these accurately is costly. In the special case of parallel-ray geometry, it turns out that reconstruction requires back projection only. One approach to accelerate the back projection is through interpolation: fit a continuous representation to samples of the desired signal, then sample it at the required locations. Instead, we propose applying a prefilter that has the effect of orthogonally projecting the underlying signal onto the space spanned by the interpolator, which can significantly improve the quality of the interpolation. We then build on this idea by using oblique projection, which simplifies the computation while giving effectively the same improvement in quality. Our experiments on analytical phantoms show that this refinement can improve the reconstruction quality for both filtered back projection and iterative reconstruction in the high-quality regime, i.e., with low noise and many measurements

Gram filtering and sinogram interpolation for pixel-basis in parallel-beam X-ray CT reconstruction

The key aspect of parallel-beam X-ray CT is forward and back projection, but its computational burden continues to be an obstacle for applications. We propose a method to improve the performance of related algorithms by calculating the Gram filter exactly and interpolating the sinogram signal optimally. In addition, the detector blur effect can be included in our model efficiently. The improvements in speed and quality for back projection and iterative reconstruction are shown in our experiments on both analytical phantoms and real CT images

Deep Radon Prior: A Fully Unsupervised Framework for Sparse-View CT Reconstruction

Although sparse-view computed tomography (CT) has significantly reduced radiation dose, it also introduces severe artifacts which degrade the image quality. In recent years, deep learning-based methods for inverse problems have made remarkable progress and have become increasingly popular in CT reconstruction. However, most of these methods suffer several limitations: dependence on high-quality training data, weak interpretability, etc. In this study, we propose a fully unsupervised framework called Deep Radon Prior (DRP), inspired by Deep Image Prior (DIP), to address the aforementioned limitations. DRP introduces a neural network as an implicit prior into the iterative method, thereby realizing cross-domain gradient feedback. During the reconstruction process, the neural network is progressively optimized in multiple stages to narrow the solution space in radon domain for the under-constrained imaging protocol, and the convergence of the proposed method has been discussed in this work. Compared with the popular pre-trained method, the proposed framework requires no dataset and exhibits superior interpretability and generalization ability. The experimental results demonstrate that the proposed method can generate detailed images while effectively suppressing image artifacts.Meanwhile, DRP achieves comparable or better performance than the supervised methods.Comment: 11 pages, 12 figures, Journal pape