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Local sparsity enhanced compressed sensing magnetic resonance imaging in uniform discrete curvelet domain.

Yang B, Yuan M, Ma Y, Zhang J, Zhan K - BMC Med Imaging (2015)

Bottom Line: Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data.It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l 1 sparse regularization and constraining k-space measurements fidelity.It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm.

View Article: PubMed Central - PubMed

Affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. 18919849359@163.com.

ABSTRACT

Background: Compressed sensing(CS) has been well applied to speed up imaging by exploring image sparsity over predefined basis functions or learnt dictionary. Firstly, the sparse representation is generally obtained in a single transform domain by using wavelet-like methods, which cannot produce optimal sparsity considering sparsity, data adaptivity and computational complexity. Secondly, most state-of-the-art reconstruction models seldom consider composite regularization upon the various structural features of images and transform coefficients sub-bands. Therefore, these two points lead to high sampling rates for reconstructing high-quality images.

Methods: In this paper, an efficient composite sparsity structure is proposed. It learns adaptive dictionary from lowpass uniform discrete curvelet transform sub-band coefficients patches. Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data. It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l 1 sparse regularization and constraining k-space measurements fidelity. A new augmented Lagrangian method is then introduced to optimize the reconstruction model. It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm.

Results: Experimental results on in vivo data show that the proposed method obtains high-quality reconstructed images. The reconstructed images exhibit the least aliasing artifacts and reconstruction error among current CS MRI methods.

Conclusions: The proposed sparsity structure can fit and provide hierarchical sparsity for magnetic resonance images simultaneously, bridging the gap between predefined sparse representation methods and explicit dictionary. The new augmented Lagrangian method provides solutions fully complying to the composite regularization reconstruction model with fast convergence speed.

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Reconstructed MBA_T2_slice006 under Cartesian undersampling scheme at 0.35 sampling rate. (a)–(e) Reconstructed images from DLMRI, MRSFLCT based CS MRI, LORAKS, PANO and LSECSMRI, (f)–(j) difference images between fully sampled MR image and images in (a)–(e) with gray scale of [0,0.25], respectively. PSNRs of them are 30.95dB, 30.25dB, 28.33dB, 35.21dB and 35.80dB. TEIs are 0.5806, 0.5872, 0.5218, 0.7513, and 0.7765. RLNEs are 0.1152, 0.1249, 0.1558, 0.0705 and 0.0659 separately. And computational time is 62.7+90.5sec, 30.5sec, 711.3sec, 291.2sec and 52.7+514.6sec separately
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Fig7: Reconstructed MBA_T2_slice006 under Cartesian undersampling scheme at 0.35 sampling rate. (a)–(e) Reconstructed images from DLMRI, MRSFLCT based CS MRI, LORAKS, PANO and LSECSMRI, (f)–(j) difference images between fully sampled MR image and images in (a)–(e) with gray scale of [0,0.25], respectively. PSNRs of them are 30.95dB, 30.25dB, 28.33dB, 35.21dB and 35.80dB. TEIs are 0.5806, 0.5872, 0.5218, 0.7513, and 0.7765. RLNEs are 0.1152, 0.1249, 0.1558, 0.0705 and 0.0659 separately. And computational time is 62.7+90.5sec, 30.5sec, 711.3sec, 291.2sec and 52.7+514.6sec separately

Mentions: Figure 7(a)-(e) exhibit reconstructed results from DLMRI, MRSFLCT based CS MRI, LORAKS, PANO and LSECSMRI separately for image in Fig. 4(b) under Cartesian undersampling scheme at 0.35 sampling rate. The difference images in Fig. 7(f)-(j) show that LSECSMRI reconstructed image possesses the least artifacts and reconstructed error among the compared methods. PSNR of LSECSMRI reconstructed image is 35.80dB, separately 4.85, 5.55, 7.47 and 0.59dB higher than that of DLMRI, MRSFLCT based CS MRI, LORAKS and PANO reconstructed images. RLNE of LSECSMRI reconstructed image is 0.0659, separately 0.0493, 0.0590, 0.0899 and 0.0046 lower than that of DLMRI, MRSFLCT based CS MRI, LORAKS and PANO reconstructed images. These indicate that LSECSMRI can obtain preeminent reconstruction performance among state-of-the-art methods.Fig. 7


Local sparsity enhanced compressed sensing magnetic resonance imaging in uniform discrete curvelet domain.

Yang B, Yuan M, Ma Y, Zhang J, Zhan K - BMC Med Imaging (2015)

Reconstructed MBA_T2_slice006 under Cartesian undersampling scheme at 0.35 sampling rate. (a)–(e) Reconstructed images from DLMRI, MRSFLCT based CS MRI, LORAKS, PANO and LSECSMRI, (f)–(j) difference images between fully sampled MR image and images in (a)–(e) with gray scale of [0,0.25], respectively. PSNRs of them are 30.95dB, 30.25dB, 28.33dB, 35.21dB and 35.80dB. TEIs are 0.5806, 0.5872, 0.5218, 0.7513, and 0.7765. RLNEs are 0.1152, 0.1249, 0.1558, 0.0705 and 0.0659 separately. And computational time is 62.7+90.5sec, 30.5sec, 711.3sec, 291.2sec and 52.7+514.6sec separately
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC4528851&req=5

Fig7: Reconstructed MBA_T2_slice006 under Cartesian undersampling scheme at 0.35 sampling rate. (a)–(e) Reconstructed images from DLMRI, MRSFLCT based CS MRI, LORAKS, PANO and LSECSMRI, (f)–(j) difference images between fully sampled MR image and images in (a)–(e) with gray scale of [0,0.25], respectively. PSNRs of them are 30.95dB, 30.25dB, 28.33dB, 35.21dB and 35.80dB. TEIs are 0.5806, 0.5872, 0.5218, 0.7513, and 0.7765. RLNEs are 0.1152, 0.1249, 0.1558, 0.0705 and 0.0659 separately. And computational time is 62.7+90.5sec, 30.5sec, 711.3sec, 291.2sec and 52.7+514.6sec separately
Mentions: Figure 7(a)-(e) exhibit reconstructed results from DLMRI, MRSFLCT based CS MRI, LORAKS, PANO and LSECSMRI separately for image in Fig. 4(b) under Cartesian undersampling scheme at 0.35 sampling rate. The difference images in Fig. 7(f)-(j) show that LSECSMRI reconstructed image possesses the least artifacts and reconstructed error among the compared methods. PSNR of LSECSMRI reconstructed image is 35.80dB, separately 4.85, 5.55, 7.47 and 0.59dB higher than that of DLMRI, MRSFLCT based CS MRI, LORAKS and PANO reconstructed images. RLNE of LSECSMRI reconstructed image is 0.0659, separately 0.0493, 0.0590, 0.0899 and 0.0046 lower than that of DLMRI, MRSFLCT based CS MRI, LORAKS and PANO reconstructed images. These indicate that LSECSMRI can obtain preeminent reconstruction performance among state-of-the-art methods.Fig. 7

Bottom Line: Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data.It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l 1 sparse regularization and constraining k-space measurements fidelity.It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm.

View Article: PubMed Central - PubMed

Affiliation: School of Information Science & Engineering, Lanzhou University, Tianshui South Road No.222, Lanzhou, 730000, China. 18919849359@163.com.

ABSTRACT

Background: Compressed sensing(CS) has been well applied to speed up imaging by exploring image sparsity over predefined basis functions or learnt dictionary. Firstly, the sparse representation is generally obtained in a single transform domain by using wavelet-like methods, which cannot produce optimal sparsity considering sparsity, data adaptivity and computational complexity. Secondly, most state-of-the-art reconstruction models seldom consider composite regularization upon the various structural features of images and transform coefficients sub-bands. Therefore, these two points lead to high sampling rates for reconstructing high-quality images.

Methods: In this paper, an efficient composite sparsity structure is proposed. It learns adaptive dictionary from lowpass uniform discrete curvelet transform sub-band coefficients patches. Consistent with the sparsity structure, a novel composite regularization reconstruction model is developed to improve reconstruction results from highly undersampled k-space data. It is established via minimizing spatial image and lowpass sub-band coefficients total variation regularization, transform sub-bands coefficients l 1 sparse regularization and constraining k-space measurements fidelity. A new augmented Lagrangian method is then introduced to optimize the reconstruction model. It updates representation coefficients of lowpass sub-band coefficients over dictionary, transform sub-bands coefficients and k-space measurements upon the ideas of constrained split augmented Lagrangian shrinkage algorithm.

Results: Experimental results on in vivo data show that the proposed method obtains high-quality reconstructed images. The reconstructed images exhibit the least aliasing artifacts and reconstruction error among current CS MRI methods.

Conclusions: The proposed sparsity structure can fit and provide hierarchical sparsity for magnetic resonance images simultaneously, bridging the gap between predefined sparse representation methods and explicit dictionary. The new augmented Lagrangian method provides solutions fully complying to the composite regularization reconstruction model with fast convergence speed.

Show MeSH