Directional-TV algorithm for image reconstruction from limited-angular-range data

Zheng, Zhang; Chen, Buxin; Xia, Dan; Sidky, Emil Y.; Pan, Xiaochuan

doi:10.1016/j.media.2021.102030

Cited by 61 publications

(52 citation statements)

References 29 publications

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“…We then perform visual inspection of the images reconstructed. Additionally, we also perform a quantitative evaluation of image reconstructed from data collected with two‐orthogonal‐arc configurations by using the normalized root‐mean‐square‐error (nRMSE) metric

\begin{equation} {\rm nRMSE}(\mathbf {f}^{\rm [recon]}) = ||\mathbf {f}^{\rm [recon]}-\mathbf {f}^{\rm [truth]}||_2/||\mathbf {f}^{\rm [truth]}||_2, \end{equation}

and the Pearson‐correlation‐coefficient (PCC) metric 8,20

\begin{eqnarray} \hspace{-42.67912pt} {\rm PCC}(\mathbf {f}^{\rm [recon]}) & = & \frac{\vert \rm Cov(\mathbf {f}^{\rm [recon]}, \mathbf {f}^{\rm [truth]})\vert }{\sigma (\mathbf {f}^{\rm [recon]}) \, \sigma (\mathbf {f}^{\rm [truth]})}, \end{eqnarray}

where

\mathbf {f}^{\rm [recon]}

and

\mathbf {f}^{\rm [truth]}

denote the reconstructed and truth images within a selected ROI,

Cov false(f^{false[recon false]}, f<...>

…”

Section: Methodsmentioning

confidence: 99%

Image reconstruction from data over two orthogonal arcs of limited‐angular ranges

et al. 2022

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Purpose Computed tomography (CT) scanning over limited‐angular ranges (LARs) is of practical interest in possible reduction of imaging dose and time and in design of nonstandard scans. This work aims to investigate image reconstruction for two nonoverlapping arcs of LARs, and to demonstrate that they may allow more accurate image reconstruction than may a single arc of LAR. Methods We consider a configuration with two nonoverlapping arcs of LARs α1$\alpha _1$ and α2$\alpha _2$, whose centers are separated by 90∘$90^\circ$, and refer to it as a two‐orthogonal‐arc configuration. Data are generated from a chest phantom with two‐orthogonal‐arc configurations over total angular coverage ατ=α1+α2$\alpha _\tau =\alpha _1+\alpha _2$ ranging from 18∘$18^\circ$ to 180∘$180^\circ$, and images are reconstructed subsequently by use of the directional‐total‐variation (DTV) algorithm. For comparison, we also consider image reconstruction for a single‐arc configuration of angular range ατ$\alpha _\tau$. Quantitative metrics such as the normalized root‐mean‐square‐error (nRMSE) are used for evaluation of image reconstruction accuracy. Results Visual inspection and quantitative analysis of images reconstructed reveal that a two‐orthogonal‐arc configuration generally yields more accurate image reconstruction than does its single‐arc counterpart. As total angular range ατ$\alpha _\tau$ increases, the DTV algorithm yields image reconstruction with enhanced accuracy, as expected. Also, if ατ$\alpha _\tau$ remains constant, the two‐orthogonal‐arc configuration with α1=α2$\alpha _1 = \alpha _2$ generally leads to image reconstruction more accurate than those of two‐orthogonal‐arc configurations with α1≠α2$\alpha _1 \ne \alpha _2$, as the nRMSE of the former can be lower than that of the latter for up to more than one order of magnitude. Conclusions Appropriately designed two‐orthogonal‐arc configurations may be exploited for improving image‐reconstruction accuracy in CT imaging with reduced angular coverage. This study may yield insights into the design of innovative CT scans for lowering scan time and radiation dose, and/or for avoiding scan collision in, for example, C‐arm CT.

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\begin{equation} {\rm nRMSE}(\mathbf {f}^{\rm [recon]}) = ||\mathbf {f}^{\rm [recon]}-\mathbf {f}^{\rm [truth]}||_2/||\mathbf {f}^{\rm [truth]}||_2, \end{equation}

and the Pearson‐correlation‐coefficient (PCC) metric 8,20

\begin{eqnarray} \hspace{-42.67912pt} {\rm PCC}(\mathbf {f}^{\rm [recon]}) & = & \frac{\vert \rm Cov(\mathbf {f}^{\rm [recon]}, \mathbf {f}^{\rm [truth]})\vert }{\sigma (\mathbf {f}^{\rm [recon]}) \, \sigma (\mathbf {f}^{\rm [truth]})}, \end{eqnarray}

where

\mathbf {f}^{\rm [recon]}

and

\mathbf {f}^{\rm [truth]}

denote the reconstructed and truth images within a selected ROI,

Cov false(f^{false[recon false]}, f<...>

…”

Section: Methodsmentioning

confidence: 99%

Image reconstruction from data over two orthogonal arcs of limited‐angular ranges

et al. 2022

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“…We formulate the reconstruction problem from either low-or high-kVp data over an arc of LAR as a convex optimization problem [10] given by:…”

Section: Image Reconstructionmentioning

confidence: 99%

“…As the detailed derivation of the DTV algorithm can be found in Appendix A of Ref. [10], we list below only the pseudo-code of the DTV algorithm.…”

Section: Image Reconstructionmentioning

confidence: 99%

“…We first perform visual inspection of the monochromatic images obtained at energy levels of interest to assess LAR artifacts. In addition to visual inspection, we compute two quantitative metrics, Pearson correlation coefficient (PCC) and normalized mutual information (nMI) [10,[23][24][25], for evaluating the visual correlation between a monochromatic image obtained from the LAR data and its corresponding reference image. Specifically, the maximum values of PCC and nMI are 1, and the higher the PCC and nMI values, the better the visual correlation between an image and its reference image.…”

Section: Visual Inspection and Quantitative Analysis Of Monochromatic...mentioning

confidence: 99%

“…In this work, we investigate image reconstructions in LAR DECT by exploiting the directional-total-variation (DTV) algorithm [10] recently developed for image reconstruction in conventional CT with LAR data [10][11][12][13]. In the investigation, for each of the low-and high-kVp data sets collected over LARs in DECT, we first formulate image reconstruction as a convex optimization problem designed in which data-2 is minimized under image's DTV constraints along orthogonal axes, and then use the DTV algorithm developed recently to solve the optimization problem for achieving image reconstructions.…”

Section: Introductionmentioning

confidence: 99%

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Dual-energy CT imaging with limited-angular-range data

Chen,

Zhang,

Xia

et al. 2021

Preprint

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In dual-energy computed tomography (DECT), low-and high-kVp data are collected often over a full-angular range (FAR) of 360 • . While there exists strong interest in DECT with low-and high-kVp data acquired over limited-angular ranges (LARs), there remains little investigation of image reconstruction in DECT with LAR data. Objective: We investigate image reconstruction with minimized LAR artifacts from low-and high-kVp data over LARs of ≤ 180 • by using a directional-total-variation (DTV) algorithm. Methods: Image reconstruction from LAR data is formulated as a convex optimization problem in which data-2 is minimized with constraints on image's DTVs along orthogonal axes. We then achieve image reconstruction by applying the DTV algorithm to solve the optimization problem. We conduct numerical studies from data generated over arcs of LARs, ranging from 14 • to 180 • , and perform visual inspection and quantitative analysis of images reconstructed. Results: Monochromatic images of interest obtained with the DTV algorithm from LAR data show substantially reduced artifacts that are observed often in images obtained with existing algorithms. The improved image quality also leads to accurate estimation of physical quantities of interest, such as effective atomic number and iodine-contrast concentration. Conclusion: Our study reveals that from LAR data of low-and high-kVp, monochromatic images can be obtained that are visually, and physical quantities can be estimated that are quantitatively, comparable to those obtained in FAR DECT. Significance: As LAR DECT is of high practical application interest, the results acquired in the work may engender insights into the design of DECT with LAR scanning configurations of practical application significance.

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Hybrid regularization inspired by total variation and deep denoiser prior for image restoration

Liang,

Zhang,

Wei

et al. 2024

Complex Intell. Syst.

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Image restoration is a fundamental problem in computer vision, with the goal of restoring high-quality images from degraded low-quality observation images. However, the ill-posedness of restoration problem often leads to artifacts in the results. It inspires us to study the combination of prior, effectively restrict the solution space and improving the quality of the restored image. In this paper, a novel hybrid regularization method for image restoration is proposed, which adopts both internal and external image priors into a unified framework. Specifically, a new hybrid regularization model is designed. The TV model and a deep image denoiser are inserted into the restoration model using the plug-and-play framework, protecting image details while implicitly using external information for deep denoising. Moreover, in order to make the proposed hybrid regularization operable, an adaptive parameter method is proposed to adaptively balance the TV model and learned model in iteration. Experiments show that the proposed method surpasses the performance of existing image restoration techniques.

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Directional-TV algorithm for image reconstruction from limited-angular-range data

Cited by 61 publications

References 29 publications

Image reconstruction from data over two orthogonal arcs of limited‐angular ranges

Image reconstruction from data over two orthogonal arcs of limited‐angular ranges

Dual-energy CT imaging with limited-angular-range data

Hybrid regularization inspired by total variation and deep denoiser prior for image restoration

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