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Compressed Sensing in MRI
Novel MRI encoding and sampling techniques
We have proposed and developed a non-Fourier, random encoding technique for MRI to satisfy the incoherence condition of compressed sensing. In contrast to Fourier encoding, the technique allows uniform sampling. The Toeplitz structure of the encoding matrix makes the image reconstruction efficient.
· F. Sebert, Y. M. Zou, L. Ying, “Compressed sensing MRI with random B1 field”, International Society of Magnetic Resonance in Medicine Scientific Meeting, p. 3151, 2008.
· H. Wang, D. Liang, K. King, L. Ying “Toeplitz Random Encoding for Reduced Acquisition Using Compressed Sensing”, Proceedings of International Society of Magnetic Resonance in Medicine Scientific Meeting, p. 2669, 2009.
· H. Wang, D. Liang, L. Ying, “Pseudo 2D Random Sampling for Compressed Sensing MRI”, Proceedings of IEEE Engineering in Medicine and Biology Conference, pp. 2672-2675, 2009.
· D. Liang, G. Xu, H. Wang, K. F.
King, D. Xu, L. Ying, “Toeplitz random encoded MR imaging using
compressed sensing”, International Symposium on Biomedical Imaging,
pp. 270-273, 2009.
Figure: Reconstructions from actual scanned data using Non-Fourier encoding.
Integration with parallel imaging
We have systematically studied how to combine parallel imaging and compressed sensing for further reduction and propose two methods for the Cartesian case. The straightforward method, named SparseSENSE, reconstructs image from the multi-channel data using the same nonlinear convex program as that of SparseMRI, except that the Fourier encoding is replaced by the sensitivity encoding. The alternative method, named CS-SENSE, sequentially carries out SparseMRI for reconstructing the aliased image in each channel and then SENSE for the final image. Our results show that both SparseSENSE and CS-SENSE can achieve a reduction factor higher than those achieved by SparseMRI and SENSE individually.
· D. Liang, K. King, B. Liu, L. Ying, “Accelerating SENSE using distributed compressed sensing”, Proceedings of International Society of Magnetic Resonance in Medicine Scientific Meeting, p. 377, 2009.
Figure: Axial images reconstructed using CS-SENSE (A), SparseSENSE (B), SparseMRI followed by Sum-of-Square (C), and SENSE (D) from a set of eight-channel scanned data with different net reduction factors show on the top right corner of each image.
Efficient sparse representations for MR images
We have investigated various sparsifying transformations for compressed sensing. We are currently investigating redundant basis for sparse representations. We improve the image reconstruction quality through redundant translational-invariant sparsifying transforms. Cycle spinning is used with the wavelet transform and overlapping patches are used with the discrete cosine transform to achieve translational invariance. Experimental results show significant improvement in artifact reduction when contrasted with non-translational invariant transforms.
Figure: Original (left) and reconstructions using wavelet (middle) and translational-invariant wavelet by cycle spinning (right) as the sparsifying transform.
k-t ISD for dynamic cardiac imaging
Compressed sensing (CS) has been used in dynamic cardiac MRI to reduce the data acquisition time. The sparseness of the dynamic image series in the spatial and temporal-frequency (y-f) domain has been exploited in existing work. In this paper, we propose a new k-t Iterative Support Detection (k-t ISD) method to improve the CS reconstruction for dynamic cardiac MRI by incorporating additional information on the support of the dynamic image in y-f space. The proposed method uses an iterative procedure for alternating image reconstruction and support detection in y-f space. At each iteration, a truncated L1 minimization is applied to obtain the reconstructed image in y-f space using support information from the previous iteration. Subsequently, by thresholding the reconstruction, we update the support information to be used in the next iteration. Experimental results demonstrate that the proposed k-t ISD method improves the reconstruction quality of dynamic cardiac MRI over the basic CS method in which support information is not exploited.
· D. Liang, E. V. R. DiBella, R.-R. Chen, and L. Ying “k-t ISD: dynamic cardiac MR imaging using compressed sensing with iterative support detection”, preprint.
· D. Liang and L. Ying, “Compressed-sensing dynamic MR imaging using partially known support”, Proceedings of IEEE Engineering in Medicine and Biology Conference, 2010.
Figure:
Comparison of proposed k-t ISD with k-t FOCUSS and OMP in reconstruction (left)
and error image (right).
Blind
Iterative Parallel Imaging Reconstruction Using Compressed Sensing (Sparse
BLIP)
We
propose a new approach to jointly reconstruct the image and sensitivity
functions from undersampled, multichannel k-space
data. The proposed method integrates JSENSE with compressed sensing where total
variation (TV) is used to regularize both image and coil sensitivities. Both
phantom and in vivo experiment results demonstrate the proposed method can the
reconstruction quality of SparseSENSE and L1 SPIRiT.
