• Title/Summary/Keyword: total variation regularization

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Sparse-View CT Image Recovery Using Two-Step Iterative Shrinkage-Thresholding Algorithm

  • Chae, Byung Gyu;Lee, Sooyeul
    • ETRI Journal
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    • v.37 no.6
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    • pp.1251-1258
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    • 2015
  • We investigate an image recovery method for sparse-view computed tomography (CT) using an iterative shrinkage algorithm based on a second-order approach. The two-step iterative shrinkage-thresholding (TwIST) algorithm including a total variation regularization technique is elucidated to be more robust than other first-order methods; it enables a perfect restoration of an original image even if given only a few projection views of a parallel-beam geometry. We find that the incoherency of a projection system matrix in CT geometry sufficiently satisfies the exact reconstruction principle even when the matrix itself has a large condition number. Image reconstruction from fan-beam CT can be well carried out, but the retrieval performance is very low when compared to a parallel-beam geometry. This is considered to be due to the matrix complexity of the projection geometry. We also evaluate the image retrieval performance of the TwIST algorithm -sing measured projection data.

MULTIGRID METHOD FOR TOTAL VARIATION IMAGE DENOISING

  • HAN, MUN S.;LEE, JUN S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.2
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    • pp.9-24
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    • 2002
  • Total Variation(TV) regularization method is effective for reconstructing "blocky", discontinuous images from contaminated image with noise. But TV is represented by highly nonlinear integro-differential equation that is hard to solve. There have been much effort to obtain stable and fast methods. C. Vogel introduced "the Fixed Point Lagged Diffusivity Iteration", which solves the nonlinear equation by linearizing. In this paper, we apply multigrid(MG) method for cell centered finite difference (CCFD) to solve system arise at each step of this fixed point iteration. In numerical simulation, we test various images varying noises and regularization parameter $\alpha$ and smoothness $\beta$ which appear in TV method. Numerical tests show that the parameter ${\beta}$ does not affect the solution if it is sufficiently small. We compute optimal $\alpha$ that minimizes the error with respect to $L^2$ norm and $H^1$ norm and compare reconstructed images.

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Performance Comparison of Regularization Methods in Electrical Resistance Tomography (전기 저항 단층촬영법에서의 조정기법 성능비교)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.20 no.3
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    • pp.226-234
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    • 2016
  • Electrical resistance tomography (ERT) is an imaging technique where the internal resistivity distribution inside an object is reconstructed. The ERT image reconstruction is a highly nonlinear ill-posed problem, so regularization methods are used to achieve desired image. The reconstruction outcome is dependent on the type of regularization method employed such as l2-norm, l1-norm, and total variation regularization method. That is, use of an appropriate regularization method considering the flow characteristics is necessary to attain good reconstruction performance. Therefore, in this paper, regularization methods are tested through numerical simulations with different flow conditions and the performance is compared.

Resistivity Image Reconstruction Using Interacting Dual-Mode Regularization (상호작용 이중-모드 조정방법을 이용한 저항률 영상 복원)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.20 no.2
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    • pp.152-162
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    • 2016
  • Electrical resistivity tomography (ERT) is a technique to reconstruct the internal resistivity distribution using the measured voltages on the surface electrodes. ERT inverse problem suffers from ill-posedness nature, so regularization methods are used to mitigate ill-posedness. The reconstruction performance varies depending on the type of regularization method. In this paper, an interacting dual-mode regularization method is proposed with two different regularization methods, L1-norm regularization and total variation (TV) regularization, to achieve robust reconstruction performance. The interacting dual-mode regularization method selects the suitable regularization method and combines the regularization methods based on computed mode probabilities depending on the actual conditions. The proposed method is tested with numerical simulations and the results demonstrate an improved reconstruction performance.

Mathematical Model for Acousto-Optical Tomography and Its Numerical Simulation (음향광학 단층촬영(Acousto-Optical Tomography)의 수학적 모델과 수치해석적 시뮬레이션)

  • Nam, Hae-Won;Hur, Jang-Yong;Kim, So-Young;Lee, Re-Na
    • Progress in Medical Physics
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    • v.23 no.1
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    • pp.42-47
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    • 2012
  • In this paper, Acousto-Optical tomography is modeled by a linear integral equation and an inverse problem involving a diffusion equation in n-spatial dimensions. We make two-step mathematical model. First, we solve a linear integral equation. Assuming the optical energy fluence rate has been recovered from the previous equation, the absorption coefficient ${\mu}$ is then reconstructed by solving an inverse problem. Numerical experiments are presented for the case n=2. The traditional gradient descent method is used for the numerical simulations. The result of the gradient descent method produces the blurring effect. To get rid of the blurring effect, we suggest the total variation regularization for the minimization problem.

Compressed-sensing (CS)-based Image Deblurring Scheme with a Total Variation Regularization Penalty for Improving Image Characteristics in Digital Tomosynthesis (DTS) (디지털 단층합성 X-선 영상의 화질개선을 위한 TV-압축센싱 기반 영상복원기법 연구)

  • Je, Uikyu;Kim, Kyuseok;Cho, Hyosung;Kim, Guna;Park, Soyoung;Lim, Hyunwoo;Park, Chulkyu;Park, Yeonok
    • Progress in Medical Physics
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    • v.27 no.1
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    • pp.1-7
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    • 2016
  • In this work, we considered a compressed-sensing (CS)-based image deblurring scheme with a total-variation (TV) regularization penalty for improving image characteristics in digital tomosynthesis (DTS). We implemented the proposed image deblurring algorithm and performed a systematic simulation to demonstrate its viability. We also performed an experiment by using a table-top setup which consists of an x-ray tube operated at $90kV_p$, 6 mAs and a CMOS-type flat-panel detector having a $198-{\mu}m$ pixel resolution. In the both simulation and experiment, 51 projection images were taken with a tomographic angle range of ${\theta}=60^{\circ}$ and an angle step of ${\Delta}{\theta}=1.2^{\circ}$ and then deblurred by using the proposed deblurring algorithm before performing the common filtered-backprojection (FBP)-based DTS reconstruction. According to our results, the image sharpness of the recovered x-ray images and the reconstructed DTS images were significantly improved and the cross-plane spatial resolution in DTS was also improved by a factor of about 1.4. Thus the proposed deblurring scheme appears to be effective for the blurring problems in both conventional radiography and DTS and is applicable to improve the present image characteristics.