An official website of the United States government
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.
more »
« less
A Look-Up Table-Based Ray Integration Framework for 2-D/3-D Forward and Back Projection in X-Ray CT
Iterative algorithms have become increasingly popular in Computed Tomography (CT) image reconstruction since they better deal with the adverse image artifacts arising from low radiation dose image acquisition. But iterative methods remain computationally expensive. The main cost emerges in the projection and backprojection operations where accurate CT system modeling can greatly improve the quality of the reconstructed image. We present a framework that improves upon one particular aspect - the accurate projection of the image basis functions. It differs from current methods in that it substitutes the high computational complexity associated with accurate voxel projection by a small number of memory operations. Coefficients are computed in advance and stored in look-up tables parameterized by the CT system's projection geometry. The look-up tables only require a few kilobytes of storage and can be efficiently accelerated on the GPU. We demonstrate our framework with both numerical and clinical experiments and compare its performance with the current state of the art scheme - the separable footprint method.
more »
« less
- Award ID(s):
- 1650499
- PAR ID:
- 10054447
- Date Published:
- Journal Name:
- IEEE transactions on medical imaging
- Volume:
- 1
- Issue:
- 1
- ISSN:
- 0278-0062
- Page Range / eLocation ID:
- pp. 99
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract PurposeForward and backprojections are the basis of all model‐based iterative reconstruction (MBIR) methods. However, computing these accurately is time‐consuming. In this paper, we present a method for MBIR in parallel X‐ray beam geometry that utilizes a Gram filter to efficiently implement forward and backprojection. MethodsWe propose using voxel‐basis and modeling its footprint in a box spline framework to calculate the Gram filter exactly and improve the performance of backprojection. In the special case of parallel X‐ray beam geometry, the forward and backprojection can be implemented by an estimated Gram filter efficiently if the sinogram signal is bandlimited. In this paper, a specialized sinogram interpolation method is proposed to eliminate the bandlimited prerequisite and thus improve the reconstruction accuracy. We build on this idea by utilizing the continuity of the voxel‐basis' footprint, which provides a more accurate sinogram interpolation and further improves the efficiency and quality of backprojection. In addition, the detector blur effect can be efficiently accounted for in our method to better handle realistic scenarios. ResultsThe proposed method is tested on both phantom and real computed tomography (CT) images under different resolutions, sinogram sampling steps, and noise levels. The proposed method consistently outperforms other state‐of‐the‐art projection models in terms of speed and accuracy for both backprojection and reconstruction. ConclusionsWe proposed a iterative reconstruction methodology for 3D parallel‐beam X‐ray CT reconstruction. Our experimental results demonstrate that the proposed methodology is accurate, fast, and reproducible, and outperforms alternative state‐of‐the‐art projection models on both backprojection and reconstruction results significantly.more » « less
-
The majority of iterative algorithms for CT reconstruction rely on discrete-to-discrete modeling, where both the sinogram measurements and image to be estimated are discrete arrays. However, tomographic projections are ideally modeled as line integrals of a continuous attenuation function, i.e., the true inverse problem is discrete-to-continuous in nature. Recently, coordinate-based neural networks (CBNNs), also known as implicit neural representations, have gained traction as a flexible type of continuous domain image representation in a variety of inverse problems arising in computer vision and computational imaging. Using standard neural network training techniques, a CBNN can be fit to measurements to give a continuous domain estimate of the image. In this study, we empirically investigate the potential of CBNNs to solve the continuous domain inverse problems in CT imaging. In particular, we experiment with reconstructing an analytical phantom from its ideal sparse-view sinogram measurements. Our results illustrate that reconstruction with a CBNN are more accurate than filtered back projection and algebraic reconstruction techniques at a variety of resolutions, and competitive with total variation regularized iterative reconstruction.more » « less
-
Abstract The goal of this study is to develop a new computed tomography (CT) image reconstruction method, aiming at improving the quality of the reconstructed images of existing methods while reducing computational costs. Existing CT reconstruction is modeled by pixel-based piecewise constant approximations of the integral equation that describes the CT projection data acquisition process. Using these approximations imposes a bottleneck model error and results in a discrete system of a large size. We propose to develop a content-adaptive unstructured grid (CAUG) based regularized CT reconstruction method to address these issues. Specifically, we design a CAUG of the image domain to sparsely represent the underlying image, and introduce a CAUG-based piecewise linear approximation of the integral equation by employing a collocation method. We further apply a regularization defined on the CAUG for the resulting ill-posed linear system, which may lead to a sparse linear representation for the underlying solution. The regularized CT reconstruction is formulated as a convex optimization problem, whose objective function consists of a weighted least square norm based fidelity term, a regularization term and a constraint term. Here, the corresponding weighted matrix is derived from the simultaneous algebraic reconstruction technique (SART). We then develop a SART-type preconditioned fixed-point proximity algorithm to solve the optimization problem. Convergence analysis is provided for the resulting iterative algorithm. Numerical experiments demonstrate the superiority of the proposed method over several existing methods in terms of both suppressing noise and reducing computational costs. These methods include the SART without regularization and with the quadratic regularization, the traditional total variation (TV) regularized reconstruction method and the TV superiorized conjugate gradient method on the pixel grid.more » « less
-
null (Ed.)A widely-regarded approach in Printed Circuit Board (PCB) reverse engineering (RE) uses non-destructive Xray computed tomography (CT) to produce three-dimensional volumes with several slices of data corresponding to multi-layered PCBs. The noise sources specific to X-ray CT and variability from designers make it difficult to acquire the features needed for the RE process. Hence, these X-ray CT images require specialized image processing techniques to examine the various features of a single PCB to later be translated to a readable CAD format. Previously, we presented an approach where the Hough Circle Transform was used for initial feature detection, and then an iterative false positive removal process was developed specifically for detecting vias on PCBs. Its performance was compared to an off-the-shelf application of the Mask Region-based Convolutional Network (M-RCNN). M-RCNN is an excellent deep learning approach that is able to localize and classify numerous objects of different scales within a single image. In this paper, we present a version of M-RCNN that is fine-tuned for via detection. Changes include polygon boundary annotations on the single X-ray images of vias for training and transfer learning to leverage the full potential of the network. We discuss the challenges of detecting vias using deep learning, our working solution, and our experimental procedure. Additionally, we provide a qualitative evaluation of our approach and use quantitative metrics to compare the proposed approach with the previous iterative one.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/DOI: 10.1109/TMI.2017.2741781
