Compressed sensing parallel magnetic resonance imaging

High-resolution MRI of spinal cords by compressive sensing parallel imaging

Spinal Cord Injury (SCI) is a common injury due to diseases or accidents. Noninvasive imaging methods play a critical role in diagnosing SCI and monitoring the response to therapy. Magnetic Resonance Imaging (MRI), by the virtue of providing excellent soft tissue contrast, is the most promising imaging method for this application. However, spinal cord has a very small cross-section, which needs high-resolution images for better visualization and diagnosis. Acquiring high-resolution spinal cord MRI images requires long acquisition time due to the physical and physiological constraints. Moreover, long acquisition time makes MRI more susceptible to motion artifacts. In this paper, we studied the application of compressive sensing (CS) and parallel imaging to achieve high-resolution imaging from sparsely sampled and reduced k-space data acquired by parallel receive arrays. In particular, the studies are limited to the effects of 2D Cartesian sampling with different subsampling schemes and reduction factors. The results show that compressive sensing parallel MRI has the potential to provide high-resolution images of the spinal cord in 1/3 of the acquisition time required by the conventional methods.

Multichannel compressive sensing MRI using noiselet encoding

The incoherence between measurement and sparsifying transform matrices and the restricted isometry property (RIP) of measurement matrix are two of the key factors in determining the performance of compressive sensing (CS). In CS-MRI, the randomly under-sampled Fourier matrix is used as the measurement matrix and the wavelet transform is usually used as sparsifying transform matrix. However, the incoherence between the randomly under-sampled Fourier matrix and the wavelet matrix is not optimal, which can deteriorate the performance of CS-MRI. Using the mathematical result that noiselets are maximally incoherent with wavelets, this paper introduces the noiselet unitary bases as the measurement matrix to improve the incoherence and RIP in CS-MRI. Based on an empirical RIP analysis that compares the multichannel noiselet and multichannel Fourier measurement matrices in CS-MRI, we propose a multichannel compressive sensing (MCS) framework to take the advantage of multichannel data acquisition used in MRI scanners. Simulations are presented in the MCS framework to compare the performance of noiselet encoding reconstructions and Fourier encoding reconstructions at different acceleration factors. The comparisons indicate that multichannel noiselet measurement matrix has better RIP than that of its Fourier counterpart, and that noiselet encoded MCS-MRI outperforms Fourier encoded MCS-MRI in preserving image resolution and can achieve higher acceleration factors. To demonstrate the feasibility of the proposed noiselet encoding scheme, a pulse sequences with tailored spatially selective RF excitation pulses was designed and implemented on a 3T scanner to acquire the data in the noiselet domain from a phantom and a human brain. The results indicate that noislet encoding preserves image resolution better than Fouirer encoding.

Enhancement of the low resolution image quality using randomly sampled data for multi-slice MR imaging

Low resolution images are often acquired in in vivo MR applications involving in large field-of-view (FOV) and high speed imaging, such as, whole-body MRI screening and functional MRI applications. In this work, we investigate a multi-slice imaging strategy for acquiring low resolution images by using compressed sensing (CS) MRI to enhance the image quality without increasing the acquisition time. In this strategy, low resolution images of all the slices are acquired using multiple-slice imaging sequence. In addition, extra randomly sampled data in one center slice are acquired by using the CS strategy. These additional randomly sampled data are multiplied by the weighting functions generated from low resolution full k-space images of the two slices, and then interpolated into the k-space of other slices. In vivo MR images of human brain were employed to investigate the feasibility and the performance of the proposed method. Quantitative comparison between the conventional low resolution images and those from the proposed method was also performed to demonstrate the advantage of the method.

Sparse parallel transmission on randomly perturbed spiral k-space trajectory

Combination of parallel transmission and sparse pulse is able to shorten the excitation by using both the coil sensitivity and sparse k-space, showing improved fast excitation capability over the use of parallel transmission alone. However, to design an optimal k-space trajectory for sparse parallel transmission is a challenging task. In this work, a randomly perturbed sparse k-space trajectory is designed by modifying the path of a spiral trajectory along the sparse k-space data, and the sparse parallel transmission RF pulses are subsequently designed based on this optimal trajectory. This method combines the parallel transmission and sparse spiral k-space trajectory, potentially to further reduce the RF transmission time. Bloch simulation of 90° excitation by using a four channel coil array is performed to demonstrate its feasibility. Excitation performance of the sparse parallel transmission technique at different reduction factors of 1, 2, and 4 is evaluated. For comparison, parallel excitation using regular spiral trajectory is performed. The passband errors of the excitation profiles of each transmission are calculated for quantitative assessment of the proposed excitation method.

High-frequency subband compressed sensing MRI using quadruplet sampling

PURPOSE

To present and validate a new method that formalizes a direct link between k-space and wavelet domains to apply separate undersampling and reconstruction for high- and low-spatial-frequency k-space data.

THEORY AND METHODS

High- and low-spatial-frequency regions are defined in k-space based on the separation of wavelet subbands, and the conventional compressed sensing problem is transformed into one of localized k-space estimation. To better exploit wavelet-domain sparsity, compressed sensing can be used for high-spatial-frequency regions, whereas parallel imaging can be used for low-spatial-frequency regions. Fourier undersampling is also customized to better accommodate each reconstruction method: random undersampling for compressed sensing and regular undersampling for parallel imaging.

RESULTS

Examples using the proposed method demonstrate successful reconstruction of both low-spatial-frequency content and fine structures in high-resolution three-dimensional breast imaging with a net acceleration of 11-12.

CONCLUSION

The proposed method improves the reconstruction accuracy of high-spatial-frequency signal content and avoids incoherent artifacts in low-spatial-frequency regions. This new formulation also reduces the reconstruction time due to the smaller problem size.

Interpolated compressed sensing for 2D multiple slice fast MR imaging

Sparse MRI has been introduced to reduce the acquisition time and raw data size by undersampling the k-space data. However, the image quality, particularly the contrast to noise ratio (CNR), decreases with the undersampling rate. In this work, we proposed an interpolated Compressed Sensing (iCS) method to further enhance the imaging speed or reduce data size without significant sacrifice of image quality and CNR for multi-slice two-dimensional sparse MR imaging in humans. This method utilizes the k-space data of the neighboring slice in the multi-slice acquisition. The missing k-space data of a highly undersampled slice are estimated by using the raw data of its neighboring slice multiplied by a weighting function generated from low resolution full k-space reference images. In-vivo MR imaging in human feet has been used to investigate the feasibility and the performance of the proposed iCS method. The results show that by using the proposed iCS reconstruction method, the average image error can be reduced and the average CNR can be improved, compared with the conventional sparse MRI reconstruction at the same undersampling rate.

A simple application of compressed sensing to further accelerate partially parallel imaging

Compressed sensing (CS) and partially parallel imaging (PPI) enable fast magnetic resonance (MR) imaging by reducing the amount of k-space data required for reconstruction. Past attempts to combine these two have been limited by the incoherent sampling requirement of CS since PPI routines typically sample on a regular (coherent) grid. Here, we developed a new method, "CS+GRAPPA," to overcome this limitation. We decomposed sets of equidistant samples into multiple random subsets. Then, we reconstructed each subset using CS and averaged the results to get a final CS k-space reconstruction. We used both a standard CS and an edge- and joint-sparsity-guided CS reconstruction. We tested these intermediate results on both synthetic and real MR phantom data and performed a human observer experiment to determine the effectiveness of decomposition and to optimize the number of subsets. We then used these CS reconstructions to calibrate the generalized autocalibrating partially parallel acquisitions (GRAPPA) complex coil weights. In vivo parallel MR brain and heart data sets were used. An objective image quality evaluation metric, Case-PDM, was used to quantify image quality. Coherent aliasing and noise artifacts were significantly reduced using two decompositions. More decompositions further reduced coherent aliasing and noise artifacts but introduced blurring. However, the blurring was effectively minimized using our new edge- and joint-sparsity-guided CS using two decompositions. Numerical results on parallel data demonstrated that the combined method greatly improved image quality as compared to standard GRAPPA, on average halving Case-PDM scores across a range of sampling rates. The proposed technique allowed the same Case-PDM scores as standard GRAPPA using about half the number of samples. We conclude that the new method augments GRAPPA by combining it with CS, allowing CS to work even when the k-space sampling pattern is equidistant.

Edge-enhanced spatiotemporal constrained reconstruction of undersampled dynamic contrast-enhanced radial MRI

Dynamic contrast-enhanced magnetic resonance imaging (MRI) is a technique used to study and track contrast kinetics in an area of interest in the body over time. Reconstruction of images with high contrast and sharp edges from undersampled data is a challenge. While good results have been reported using a radial acquisition and a spatiotemporal constrained reconstruction (STCR) method, we propose improvements from using spatially adaptive weighting and an additional edge-based constraint. The new method uses intensity gradients from a sliding window reference image to improve the sharpness of edges in the reconstructed image. The method was tested on eight radial cardiac perfusion data sets with 24 rays and compared to the STCR method. The reconstructions showed that the new method, termed edge-enhanced spatiotemporal constrained reconstruction, was able to reconstruct images with sharper edges, and there were a 36%±13.7% increase in contrast-to-noise ratio and a 24%±11% increase in contrast near the edges when compared to STCR. The novelty of this paper is the combination of spatially adaptive weighting for spatial total variation (TV) constraint along with a gradient matching term to improve the sharpness of edges. The edge map from a reference image allows the reconstruction to trade-off between TV and edge enhancement, depending on the spatially varying weighting provided by the edge map.

Fast cardiac T1 mapping in mice using a model-based compressed sensing method

Direct measurement of the longitudinal relaxation time T1 provides objective and quantitative diagnostic information. However, current T1 mapping methods are generally time consuming without the aid of fast imaging. This study used a model-based compressed sensing method for fast cardiac T1 mapping in small animals. Based on the physics of magnetization recovery, the aliasing artifact associated with under-sampling was removed by exploiting the sparsity of the signals in the T1 recovery direction. Simulation study was performed to evaluate the reconstruction accuracy under various experimental conditions. Several approaches that accounted for phase variations were compared for optimized reconstruction in the phantom study. In vivo validation was performed on a cardiac manganese-enhanced MRI study using mice. Accurate reconstruction of the under-sampled images and the resulting T1 maps were achieved in both simulation and MRI studies on phantom and in vivo mice. These results suggest that the current compressed sensing method allows fast (<80 s) T1 mapping of the mouse heart at high spatial resolution (234×469 μm2).

Feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory

PURPOSE

To investigate the feasibility of high temporal resolution breast DCE-MRI using compressed sensing theory.

METHODS

Two experiments were designed to investigate the feasibility of using reference image based compressed sensing (RICS) technique in DCE-MRI of the breast. The first experiment examined the capability of RICS to faithfully reconstruct uptake curves using undersampled data sets extracted from fully sampled clinical breast DCE-MRI data. An average approach and an approach using motion estimation and motion compensation (ME/MC) were implemented to obtain reference images and to evaluate their efficacy in reducing motion related effects. The second experiment, an in vitro phantom study, tested the feasibility of RICS for improving temporal resolution without degrading the spatial resolution.

RESULTS

For the uptake-curve reconstruction experiment, there was a high correlation between uptake curves reconstructed from fully sampled data by Fourier transform and from undersampled data by RICS, indicating high similarity between them. The mean Pearson correlation coefficients for RICS with the ME/MC approach and RICS with the average approach were 0.977 +/- 0.023 and 0.953 +/- 0.031, respectively. The comparisons of final reconstruction results between RICS with the average approach and RICS with the ME/MC approach suggested that the latter was superior to the former in reducing motion related effects. For the in vitro experiment, compared to the fully sampled method, RICS improved the temporal resolution by an acceleration factor of 10 without degrading the spatial resolution.

CONCLUSIONS

The preliminary study demonstrates the feasibility of RICS for faithfully reconstructing uptake curves and improving temporal resolution of breast DCE-MRI without degrading the spatial resolution.