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Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme.
Magn Reson Imaging. 2013 Oct; 31(8):1399-411.MR

Abstract

PURPOSE

Compressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l1 norm while approaching an l0 norm.

MATERIALS AND METHODS

The CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l1-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect.

RESULTS

It was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l1-based counterpart.

CONCLUSION

The SCAD regularization improves the performance of l1-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI.

Authors+Show Affiliations

Division of Nuclear Medicine and Molecular Imaging, Geneva University Hospital, CH-1211 Geneva, Switzerland.No affiliation info availableNo affiliation info availableNo affiliation info availableNo affiliation info available

Pub Type(s)

Journal Article
Research Support, Non-U.S. Gov't

Language

eng

PubMed ID

23891179

Citation

Mehranian, Abolfazl, et al. "Smoothly Clipped Absolute Deviation (SCAD) Regularization for Compressed Sensing MRI Using an Augmented Lagrangian Scheme." Magnetic Resonance Imaging, vol. 31, no. 8, 2013, pp. 1399-411.
Mehranian A, Rad HS, Rahmim A, et al. Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme. Magn Reson Imaging. 2013;31(8):1399-411.
Mehranian, A., Rad, H. S., Rahmim, A., Ay, M. R., & Zaidi, H. (2013). Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme. Magnetic Resonance Imaging, 31(8), 1399-411. https://doi.org/10.1016/j.mri.2013.05.010
Mehranian A, et al. Smoothly Clipped Absolute Deviation (SCAD) Regularization for Compressed Sensing MRI Using an Augmented Lagrangian Scheme. Magn Reson Imaging. 2013;31(8):1399-411. PubMed PMID: 23891179.
* Article titles in AMA citation format should be in sentence-case
TY - JOUR T1 - Smoothly clipped absolute deviation (SCAD) regularization for compressed sensing MRI using an augmented Lagrangian scheme. AU - Mehranian,Abolfazl, AU - Rad,Hamidreza Saligheh, AU - Rahmim,Arman, AU - Ay,Mohammad Reza, AU - Zaidi,Habib, Y1 - 2013/07/24/ PY - 2013/02/15/received PY - 2013/05/28/revised PY - 2013/05/30/accepted PY - 2013/7/30/entrez PY - 2013/7/31/pubmed PY - 2014/4/4/medline KW - Augmented Lagrangian KW - Compressed sensing KW - Smoothly Clipped Absolute Deviation (SCAD) KW - Total variation SP - 1399 EP - 411 JF - Magnetic resonance imaging JO - Magn Reson Imaging VL - 31 IS - 8 N2 - PURPOSE: Compressed sensing (CS) provides a promising framework for MR image reconstruction from highly undersampled data, thus reducing data acquisition time. In this context, sparsity-promoting regularization techniques exploit the prior knowledge that MR images are sparse or compressible in a given transform domain. In this work, a new regularization technique was introduced by iterative linearization of the non-convex smoothly clipped absolute deviation (SCAD) norm with the aim of reducing the sampling rate even lower than it is required by the conventional l1 norm while approaching an l0 norm. MATERIALS AND METHODS: The CS-MR image reconstruction was formulated as an equality-constrained optimization problem using a variable splitting technique and solved using an augmented Lagrangian (AL) method developed to accelerate the optimization of constrained problems. The performance of the resulting SCAD-based algorithm was evaluated for discrete gradients and wavelet sparsifying transforms and compared with its l1-based counterpart using phantom and clinical studies. The k-spaces of the datasets were retrospectively undersampled using different sampling trajectories. In the AL framework, the CS-MRI problem was decomposed into two simpler sub-problems, wherein the linearization of the SCAD norm resulted in an adaptively weighted soft thresholding rule with a sparsity enhancing effect. RESULTS: It was demonstrated that the proposed regularization technique adaptively assigns lower weights on the thresholding of gradient fields and wavelet coefficients, and as such, is more efficient in reducing aliasing artifacts arising from k-space undersampling, when compared to its l1-based counterpart. CONCLUSION: The SCAD regularization improves the performance of l1-based regularization technique, especially at reduced sampling rates, and thus might be a good candidate for some applications in CS-MRI. SN - 1873-5894 UR - https://www.unboundmedicine.com/medline/citation/23891179/Smoothly_clipped_absolute_deviation__SCAD__regularization_for_compressed_sensing_MRI_using_an_augmented_Lagrangian_scheme_ L2 - https://linkinghub.elsevier.com/retrieve/pii/S0730-725X(13)00209-9 DB - PRIME DP - Unbound Medicine ER -