Quantitative study of undersampled recoverability for sparse images in computed tomography

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Quantitative study of undersampled recoverability for sparse images in computed tomography. / Jørgensen, Jakob Heide; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan.

In: arXiv, 2012, p. 1-20.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

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Jørgensen, Jakob Heide; Sidky, Emil Y.; Hansen, Per Christian; Pan, Xiaochuan / Quantitative study of undersampled recoverability for sparse images in computed tomography.

In: arXiv, 2012, p. 1-20.

Publication: Research - peer-reviewJournal article – Annual report year: 2012

Bibtex

@article{bec25de535b9428ba33c61360c844f3e,
title = "Quantitative study of undersampled recoverability for sparse images in computed tomography",
keywords = "Computed Tomography, Image Reconstruction, Sparse approximation, Compressed Sensing, Recoverability, Inverse Problems",
publisher = "Cornell-University",
author = "Jørgensen, {Jakob Heide} and Sidky, {Emil Y.} and Hansen, {Per Christian} and Xiaochuan Pan",
year = "2012",
pages = "1--20",
journal = "arXiv",

}

RIS

TY - JOUR

T1 - Quantitative study of undersampled recoverability for sparse images in computed tomography

AU - Jørgensen,Jakob Heide

AU - Sidky,Emil Y.

AU - Hansen,Per Christian

AU - Pan,Xiaochuan

PB - Cornell-University

PY - 2012

Y1 - 2012

N2 - Image reconstruction methods based on exploiting image sparsity, motivated by compressed sensing (CS), allow reconstruction from a significantly reduced number of projections in X-ray computed tomography (CT). However, CS provides neither theoretical guarantees of accurate CT reconstruction, nor any relation between sparsity and a sufficient number of measurements for recovery. In this paper, we demonstrate empirically through computer simulations that minimization of the image 1-norm allows for recovery of sparse images from fewer measurements than unknown pixels, without relying on artificial random sampling patterns. We establish quantitatively an average-case relation between image sparsity and sufficient number of measurements for recovery, and we show that the transition from non-recovery to recovery is sharp within well-defined classes of simple and semi-realistic test images. The specific behavior depends on the type of image, but the same quantitative relation holds independently of image size.

AB - Image reconstruction methods based on exploiting image sparsity, motivated by compressed sensing (CS), allow reconstruction from a significantly reduced number of projections in X-ray computed tomography (CT). However, CS provides neither theoretical guarantees of accurate CT reconstruction, nor any relation between sparsity and a sufficient number of measurements for recovery. In this paper, we demonstrate empirically through computer simulations that minimization of the image 1-norm allows for recovery of sparse images from fewer measurements than unknown pixels, without relying on artificial random sampling patterns. We establish quantitatively an average-case relation between image sparsity and sufficient number of measurements for recovery, and we show that the transition from non-recovery to recovery is sharp within well-defined classes of simple and semi-realistic test images. The specific behavior depends on the type of image, but the same quantitative relation holds independently of image size.

KW - Computed Tomography

KW - Image Reconstruction

KW - Sparse approximation

KW - Compressed Sensing

KW - Recoverability

KW - Inverse Problems

JO - arXiv

JF - arXiv

SP - 1

EP - 20

ER -