SPECT reconstruction using DCT-induced tight framelet regularization

Jiahan Zhang; Si Li; Yuesheng Xu; C. R. Schmidtlein; Edward D. Lipson; David H. Feiglin; Andrzej Krol

doi:10.1117/12.2082118

SPECT reconstruction using DCT-induced tight framelet regularization

Jiahan Zhang, Si Li, Yuesheng Xu, C. R. Schmidtlein, Edward D. Lipson, David H. Feiglin, Andrzej Krol

Department of Physics

Research output: Chapter in Book/Entry/Poem › Conference contribution

2 Scopus citations

Abstract

Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the 1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the 1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the 1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.

Original language	English (US)
Title of host publication	Medical Imaging 2015
Subtitle of host publication	Physics of Medical Imaging
Editors	Christoph Hoeschen, Despina Kontos, Christoph Hoeschen
Publisher	SPIE
ISBN (Electronic)	9781628415025
DOIs	https://doi.org/10.1117/12.2082118
State	Published - 2015
Event	Medical Imaging 2015: Physics of Medical Imaging - Orlando, United States Duration: Feb 22 2015 → Feb 25 2015

Publication series

Name	Progress in Biomedical Optics and Imaging - Proceedings of SPIE
Volume	9412
ISSN (Print)	1605-7422

Other

Other	Medical Imaging 2015: Physics of Medical Imaging
Country/Territory	United States
City	Orlando
Period	2/22/15 → 2/25/15

Keywords

DCT
Framelet
Image reconstruction
Noise reduction
Re gularization

ASJC Scopus subject areas

Electronic, Optical and Magnetic Materials
Atomic and Molecular Physics, and Optics
Radiology Nuclear Medicine and imaging
Biomaterials

Access to Document

10.1117/12.2082118

Cite this

Zhang, J., Li, S., Xu, Y., Schmidtlein, C. R., Lipson, E. D., Feiglin, D. H., & Krol, A. (2015). SPECT reconstruction using DCT-induced tight framelet regularization. In C. Hoeschen, D. Kontos, & C. Hoeschen (Eds.), Medical Imaging 2015: Physics of Medical Imaging Article 94123H (Progress in Biomedical Optics and Imaging - Proceedings of SPIE; Vol. 9412). SPIE. https://doi.org/10.1117/12.2082118

SPECT reconstruction using DCT-induced tight framelet regularization. / Zhang, Jiahan; Li, Si; Xu, Yuesheng et al.
Medical Imaging 2015: Physics of Medical Imaging. ed. / Christoph Hoeschen; Despina Kontos; Christoph Hoeschen. SPIE, 2015. 94123H (Progress in Biomedical Optics and Imaging - Proceedings of SPIE; Vol. 9412).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Zhang, J, Li, S, Xu, Y, Schmidtlein, CR, Lipson, ED, Feiglin, DH & Krol, A 2015, SPECT reconstruction using DCT-induced tight framelet regularization. in C Hoeschen, D Kontos & C Hoeschen (eds), Medical Imaging 2015: Physics of Medical Imaging., 94123H, Progress in Biomedical Optics and Imaging - Proceedings of SPIE, vol. 9412, SPIE, Medical Imaging 2015: Physics of Medical Imaging, Orlando, United States, 2/22/15. https://doi.org/10.1117/12.2082118

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title = "SPECT reconstruction using DCT-induced tight framelet regularization",

abstract = "Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the 1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the 1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the 1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.",

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AU - Lipson, Edward D.

AU - Feiglin, David H.

AU - Krol, Andrzej

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N2 - Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the 1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the 1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the 1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.

AB - Wavelet transforms have been successfully applied in many fields of image processing. Yet, to our knowledge, they have never been directly incorporated to the objective function in Emission Computed Tomography (ECT) image reconstruction. Our aim has been to investigate if the 1-norm of non-decimated discrete cosine transform (DCT) coefficients of the estimated radiotracer distribution could be effectively used as the regularization term for the penalized-likelihood (PL) reconstruction, where a regularizer is used to enforce the image smoothness in the reconstruction. In this study, the 1-norm of 2D DCT wavelet decomposition was used as a regularization term. The Preconditioned Alternating Projection Algorithm (PAPA), which we proposed in earlier work to solve penalized likelihood (PL) reconstruction with non-differentiable regularizers, was used to solve this optimization problem. The DCT wavelet decompositions were performed on the transaxial reconstructed images. We reconstructed Monte Carlo simulated SPECT data obtained for a numerical phantom with Gaussian blobs as hot lesions and with a warm random lumpy background. Reconstructed images using the proposed method exhibited better noise suppression and improved lesion conspicuity, compared with images reconstructed using expectation maximization (EM) algorithm with Gaussian post filter (GPF). Also, the mean square error (MSE) was smaller, compared with EM-GPF. A critical and challenging aspect of this method was selection of optimal parameters. In summary, our numerical experiments demonstrated that the 1-norm of discrete cosine transform (DCT) wavelet frame transform DCT regularizer shows promise for SPECT image reconstruction using PAPA method.

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ER -

SPECT reconstruction using DCT-induced tight framelet regularization

Abstract

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Keywords

ASJC Scopus subject areas

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