Nonconvex prior image constrained compressed sensing (NCPICCS): Theory and simulations on perfusion CT

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Abstract

Purpose: To present and evaluate a new image reconstruction method for dynamic CT based on a nonconvex prior image constrained compressed sensing (NCPICCS) algorithm. The authors systematically compared the undersampling potential, functional information recovery, and solution convergence speed of four compressed sensing (CS) based image reconstruction methods using perfusion CT data: Standard ℓ 1 -based CS, nonconvex CS (NCCS), and ℓ 1 -based and nonconvex CS, including an additional constraint based on a prior image (PICCS and NCPICCS, respectively). Methods: The Shepp-Logan phantom was modified such that its uppermost ellipses changed attenuation through time, simulating both an arterial input function (AIF) and a homogeneous tissue perfusion region. Data were simulated with and without Poisson noise added to the projection data and subsequently reconstructed with all four CS-based methods at four levels of undersampling: 20, 12, 6, and 4 projections. Root mean squared (RMS) error of reconstructed images and recovered time attenuation curves (TACs) were assessed as well as convergence speed. The performance of both PICCS and NCPICCS methods were also evaluated using a kidney perfusion animal experiment data set. Results: All four CS-based methods were able to reconstruct the phantoms with 20 projections, with similar results on the RMS error of the recovered TACs. NCCS allowed accurate reconstructions with as few as 12 projections, PICCS with as few as six projections, and NCPICCS with as few as four projections. These results were consistent for noise-free and noisy data. NCPICCS required the fewest iterations to converge across all simulation conditions, followed by PICCS, NCCS, and then CS. On animal data, at the lowest level of undersampling tested (16 projections), the image quality of NCPICCS was better than PICCS with fewer streaking artifacts, while the TAC accuracy on the selected region of interest was comparable. Conclusions: The authors have presented a novel method for image reconstruction using highly undersampled dynamic CT data. The NCPICCS method takes advantage of the information provided by a prior image, as in PICCS, but employs a more general nonconvex sparsity measure [such as the ℓ p -norm (0<p≤1)] rather than the conventional convex ℓ 1-norm. Despite the lack of guarantees of a globally optimal solution, the proposed nonconvex extension of PICCS consistently allowed for image reconstruction from fewer samples than the analogous ℓ 1-based PICCS method. Both nonconvex sparsity measures as well as prior image information (when available) significantly reduced the number of iterations required for convergence, potentially providing computational advantages for practical implementation of CS-based image reconstruction techniques.

Original languageEnglish (US)
Pages (from-to)2157-2167
Number of pages11
JournalMedical Physics
Volume38
Issue number4
DOIs
StatePublished - Apr 2011

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Perfusion
Computer-Assisted Image Processing
Noise
Artifacts
Kidney

Keywords

  • compressed sensing
  • dynamic CT
  • image reconstruction
  • perfusion CT
  • radiation dose reduction

ASJC Scopus subject areas

  • Biophysics
  • Radiology Nuclear Medicine and imaging

Cite this

@article{ee0ca2ee24244f06b9c2999312a01c58,
title = "Nonconvex prior image constrained compressed sensing (NCPICCS): Theory and simulations on perfusion CT",
abstract = "Purpose: To present and evaluate a new image reconstruction method for dynamic CT based on a nonconvex prior image constrained compressed sensing (NCPICCS) algorithm. The authors systematically compared the undersampling potential, functional information recovery, and solution convergence speed of four compressed sensing (CS) based image reconstruction methods using perfusion CT data: Standard ℓ 1 -based CS, nonconvex CS (NCCS), and ℓ 1 -based and nonconvex CS, including an additional constraint based on a prior image (PICCS and NCPICCS, respectively). Methods: The Shepp-Logan phantom was modified such that its uppermost ellipses changed attenuation through time, simulating both an arterial input function (AIF) and a homogeneous tissue perfusion region. Data were simulated with and without Poisson noise added to the projection data and subsequently reconstructed with all four CS-based methods at four levels of undersampling: 20, 12, 6, and 4 projections. Root mean squared (RMS) error of reconstructed images and recovered time attenuation curves (TACs) were assessed as well as convergence speed. The performance of both PICCS and NCPICCS methods were also evaluated using a kidney perfusion animal experiment data set. Results: All four CS-based methods were able to reconstruct the phantoms with 20 projections, with similar results on the RMS error of the recovered TACs. NCCS allowed accurate reconstructions with as few as 12 projections, PICCS with as few as six projections, and NCPICCS with as few as four projections. These results were consistent for noise-free and noisy data. NCPICCS required the fewest iterations to converge across all simulation conditions, followed by PICCS, NCCS, and then CS. On animal data, at the lowest level of undersampling tested (16 projections), the image quality of NCPICCS was better than PICCS with fewer streaking artifacts, while the TAC accuracy on the selected region of interest was comparable. Conclusions: The authors have presented a novel method for image reconstruction using highly undersampled dynamic CT data. The NCPICCS method takes advantage of the information provided by a prior image, as in PICCS, but employs a more general nonconvex sparsity measure [such as the ℓ p -norm (01-norm. Despite the lack of guarantees of a globally optimal solution, the proposed nonconvex extension of PICCS consistently allowed for image reconstruction from fewer samples than the analogous ℓ 1-based PICCS method. Both nonconvex sparsity measures as well as prior image information (when available) significantly reduced the number of iterations required for convergence, potentially providing computational advantages for practical implementation of CS-based image reconstruction techniques.",
keywords = "compressed sensing, dynamic CT, image reconstruction, perfusion CT, radiation dose reduction",
author = "Ramirez-Giraldo, {J. C.} and Trazasko, {Joshua D} and Shuai Leng and Lifeng Yu and Armando Manduca and McCollough, {Cynthia H}",
year = "2011",
month = "4",
doi = "10.1118/1.3560878",
language = "English (US)",
volume = "38",
pages = "2157--2167",
journal = "Medical Physics",
issn = "0094-2405",
publisher = "AAPM - American Association of Physicists in Medicine",
number = "4",

}

TY - JOUR

T1 - Nonconvex prior image constrained compressed sensing (NCPICCS)

T2 - Theory and simulations on perfusion CT

AU - Ramirez-Giraldo, J. C.

AU - Trazasko, Joshua D

AU - Leng, Shuai

AU - Yu, Lifeng

AU - Manduca, Armando

AU - McCollough, Cynthia H

PY - 2011/4

Y1 - 2011/4

N2 - Purpose: To present and evaluate a new image reconstruction method for dynamic CT based on a nonconvex prior image constrained compressed sensing (NCPICCS) algorithm. The authors systematically compared the undersampling potential, functional information recovery, and solution convergence speed of four compressed sensing (CS) based image reconstruction methods using perfusion CT data: Standard ℓ 1 -based CS, nonconvex CS (NCCS), and ℓ 1 -based and nonconvex CS, including an additional constraint based on a prior image (PICCS and NCPICCS, respectively). Methods: The Shepp-Logan phantom was modified such that its uppermost ellipses changed attenuation through time, simulating both an arterial input function (AIF) and a homogeneous tissue perfusion region. Data were simulated with and without Poisson noise added to the projection data and subsequently reconstructed with all four CS-based methods at four levels of undersampling: 20, 12, 6, and 4 projections. Root mean squared (RMS) error of reconstructed images and recovered time attenuation curves (TACs) were assessed as well as convergence speed. The performance of both PICCS and NCPICCS methods were also evaluated using a kidney perfusion animal experiment data set. Results: All four CS-based methods were able to reconstruct the phantoms with 20 projections, with similar results on the RMS error of the recovered TACs. NCCS allowed accurate reconstructions with as few as 12 projections, PICCS with as few as six projections, and NCPICCS with as few as four projections. These results were consistent for noise-free and noisy data. NCPICCS required the fewest iterations to converge across all simulation conditions, followed by PICCS, NCCS, and then CS. On animal data, at the lowest level of undersampling tested (16 projections), the image quality of NCPICCS was better than PICCS with fewer streaking artifacts, while the TAC accuracy on the selected region of interest was comparable. Conclusions: The authors have presented a novel method for image reconstruction using highly undersampled dynamic CT data. The NCPICCS method takes advantage of the information provided by a prior image, as in PICCS, but employs a more general nonconvex sparsity measure [such as the ℓ p -norm (01-norm. Despite the lack of guarantees of a globally optimal solution, the proposed nonconvex extension of PICCS consistently allowed for image reconstruction from fewer samples than the analogous ℓ 1-based PICCS method. Both nonconvex sparsity measures as well as prior image information (when available) significantly reduced the number of iterations required for convergence, potentially providing computational advantages for practical implementation of CS-based image reconstruction techniques.

AB - Purpose: To present and evaluate a new image reconstruction method for dynamic CT based on a nonconvex prior image constrained compressed sensing (NCPICCS) algorithm. The authors systematically compared the undersampling potential, functional information recovery, and solution convergence speed of four compressed sensing (CS) based image reconstruction methods using perfusion CT data: Standard ℓ 1 -based CS, nonconvex CS (NCCS), and ℓ 1 -based and nonconvex CS, including an additional constraint based on a prior image (PICCS and NCPICCS, respectively). Methods: The Shepp-Logan phantom was modified such that its uppermost ellipses changed attenuation through time, simulating both an arterial input function (AIF) and a homogeneous tissue perfusion region. Data were simulated with and without Poisson noise added to the projection data and subsequently reconstructed with all four CS-based methods at four levels of undersampling: 20, 12, 6, and 4 projections. Root mean squared (RMS) error of reconstructed images and recovered time attenuation curves (TACs) were assessed as well as convergence speed. The performance of both PICCS and NCPICCS methods were also evaluated using a kidney perfusion animal experiment data set. Results: All four CS-based methods were able to reconstruct the phantoms with 20 projections, with similar results on the RMS error of the recovered TACs. NCCS allowed accurate reconstructions with as few as 12 projections, PICCS with as few as six projections, and NCPICCS with as few as four projections. These results were consistent for noise-free and noisy data. NCPICCS required the fewest iterations to converge across all simulation conditions, followed by PICCS, NCCS, and then CS. On animal data, at the lowest level of undersampling tested (16 projections), the image quality of NCPICCS was better than PICCS with fewer streaking artifacts, while the TAC accuracy on the selected region of interest was comparable. Conclusions: The authors have presented a novel method for image reconstruction using highly undersampled dynamic CT data. The NCPICCS method takes advantage of the information provided by a prior image, as in PICCS, but employs a more general nonconvex sparsity measure [such as the ℓ p -norm (01-norm. Despite the lack of guarantees of a globally optimal solution, the proposed nonconvex extension of PICCS consistently allowed for image reconstruction from fewer samples than the analogous ℓ 1-based PICCS method. Both nonconvex sparsity measures as well as prior image information (when available) significantly reduced the number of iterations required for convergence, potentially providing computational advantages for practical implementation of CS-based image reconstruction techniques.

KW - compressed sensing

KW - dynamic CT

KW - image reconstruction

KW - perfusion CT

KW - radiation dose reduction

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