Spread spectrum magnetic resonance imaging

Non-Cartesian 3D-SPARKLING vs Cartesian 3D-EPI encoding schemes for functional Magnetic Resonance Imaging at 7 Tesla

The quest for higher spatial and/or temporal resolution in functional MRI (fMRI) while preserving a sufficient temporal signal-to-noise ratio (tSNR) has generated a tremendous amount of methodological contributions in the last decade ranging from Cartesian vs. non-Cartesian readouts, 2D vs. 3D acquisition strategies, parallel imaging and/or compressed sensing (CS) accelerations and simultaneous multi-slice acquisitions to cite a few. In this paper, we investigate the use of a finely tuned version of 3D-SPARKLING. This is a non-Cartesian CS-based acquisition technique for high spatial resolution whole-brain fMRI. We compare it to state-of-the-art Cartesian 3D-EPI during both a retinotopic mapping paradigm and resting-state acquisitions at 1mm3 (isotropic spatial resolution). This study involves six healthy volunteers and both acquisition sequences were run on each individual in a randomly-balanced order across subjects. The performances of both acquisition techniques are compared to each other in regards to tSNR, sensitivity to the BOLD effect and spatial specificity. Our findings reveal that 3D-SPARKLING has a higher tSNR than 3D-EPI, an improved sensitivity to detect the BOLD contrast in the gray matter, and an improved spatial specificity. Compared to 3D-EPI, 3D-SPARKLING yields, on average, 7% more activated voxels in the gray matter relative to the total number of activated voxels.

Improved gradient-echo 3D magnetic resonance imaging using compressed sensing and Toeplitz encoding with phase-scrambled RF excitation

PURPOSE

To develop a novel three-dimensional (3D) hybrid-encoding framework using compressed sensing (CS) and Toeplitz encoding with variable phase-scrambled radio-frequency (RF) excitation, which has the following advantages: low power deposition of RF pulses, reduction of the signal dynamic range, no additional hardware requirement, and signal-to-noise ratio (SNR) improvement.

METHODS

In light of the actual imaging framework of magnetic resonance imaging (MRI) scanners, we applied specially tailored RF pulses with phase-scrambled RF excitation to implement a 3D hybrid Fourier-Toeplitz encoding method based on 3D gradient-recalled echo pulse (GRASS) sequence. This method exploits Toeplitz encoding along the phase encoding direction, while keeping Fourier encoding along the readout and slice encoding directions. Phantom experiments were conducted to optimize the amplitude of specially tailored RF pulses in the 3D GRASS sequence. In vivo experiments were conducted to validate the feasibility of the proposed method, and simulations were conducted to compare the 3D hybrid-encoding method with Fourier encoding and other non-Fourier encoding methods.

RESULTS

An optimized low RF amplitude was obtained in the phantom experiments. Using the optimized specially tailored RF pulses, both the watermelon and knee experiments demonstrated that the proposed method was able to preserve more image details than the conventional 3D Fourier-encoded methods at acceleration factors of 3.1 and 2.0. Additionally, SNR was improved because of no additional gradients and 3D volume encoding, when compared with single-slice scanning without 3D encoding. Simulation results demonstrated that the proposed scheme was superior to the conventional Fourier encoding method, and obtained comparative performance with other non-Fourier encoding methods in preserving details.

CONCLUSIONS

We developed a practical hybrid-encoding method for 3D MRI with specially tailored RF pulses of phase-scrambled RF excitation. The proposed method improves image SNR and detail preservation compared with the conventional Fourier encoding methods. Furthermore, our proposed method exhibits superior performance in terms of detail preservation, compared with the conventional Fourier encoding method.

Compressed sensing MRI: a review from signal processing perspective

Magnetic resonance imaging (MRI) is an inherently slow imaging modality, since it acquires multi-dimensional k-space data through 1-D free induction decay or echo signals. This often limits the use of MRI, especially for high resolution or dynamic imaging. Accordingly, many investigators has developed various acceleration techniques to allow fast MR imaging. For the last two decades, one of the most important breakthroughs in this direction is the introduction of compressed sensing (CS) that allows accurate reconstruction from sparsely sampled k-space data. The recent FDA approval of compressed sensing products for clinical scans clearly reflect the maturity of this technology. Therefore, this paper reviews the basic idea of CS and how this technology have been evolved for various MR imaging problems.

An empirical study of the maximum degree of undersampling in compressed sensing for T2*-weighted MRI

Magnetic Resonance Imaging (MRI) is one of the most dynamic and safe imaging modalities used in clinical routine today. Yet, one major limitation to this technique resides in its long acquisition times. Over the last decade, Compressed Sensing (CS) has been increasingly used to address this issue and offers to shorten MR scans by reconstructing images from undersampled Fourier data. Nevertheless, a quantitative guide on the degree of acceleration applicable to a given acquisition scenario is still lacking today, leading in practice to a trial-and-error approach in the selection of the appropriate undersampling factor. In this study, we shortly point out the existing theoretical sampling results in CS and their limitations which motivate the focus of this work: an empirical and quantitative analysis of the maximum degree of undersampling allowed by CS in the specific context of T₂^*-weighted MRI. We make use of a generic method based on retrospective undersampling to quantitatively deduce the maximum acceleration factor R_max which preserves a desired image quality as a function of the image resolution and the available signal-to-noise ratio (SNR). Our results quantify how larger acceleration factors can be applied to higher resolution images as long as a minimum SNR is guaranteed. In practice however, the maximum acceleration factor for a given resolution appears to be constrained by the available SNR inherent to the considered acquisition. Our analysis enables to take this a priori knowledge into account, allowing to derive a sequence-specific maximum acceleration factor adapted to the intrinsic SNR of any MR pipeline. These results obtained on an analytical T₂^*-weighted phantom image were corroborated by prospective experiments performed on MR data collected with radial trajectories on a 7 T scanner with the same contrast. The proposed framework allows to study other sequence weightings and therefore better optimize sequences when accelerated using CS.

A Sparse Reconstruction Framework for Fourier-Based Plane-Wave Imaging

Ultrafast imaging based on plane-wave (PW) insonification is an active area of research due to its capability of reaching high frame rates. Among PW imaging methods, Fourier-based approaches have demonstrated to be competitive compared with traditional delay and sum methods. Motivated by the success of compressed sensing techniques in other Fourier imaging modalities, like magnetic resonance imaging, we propose a new sparse regularization framework to reconstruct highquality ultrasound (US) images. The framework takes advantage of both the ability to formulate the imaging inverse problem in the Fourier domain and the sparsity of US images in a sparsifying domain. We show, by means of simulations, in vitro and in vivo data, that the proposed framework significantly reduces image artifacts, i.e., measurement noise and sidelobes, compared with classical methods, leading to an increase of the image quality.

Ultrafast multi-slice spatiotemporally encoded MRI with slice-selective dimension segmented

As a recently emerging method, spatiotemporally encoded (SPEN) magnetic resonance imaging (MRI) has a high robustness to field inhomogeneity and chemical shift effect. It has been broadened from single-slice scanning to multi-slice scanning. In this paper, a novel multi-slice SPEN MRI method was proposed. In this method, the slice-selective dimension was segmented to lower the specific absorption rate (SAR) and improve the image quality. This segmented method, dubbed SeSPEN method, was theoretically analyzed and demonstrated with phantom, lemon and in vivo rat brain experiments. The experimental results were compared with the results obtained from the spin-echo EPI, spin-echo SPEN method and multi-slice global SPEN method proposed by Frydman and coauthors (abbr. GlSPEN method). All the SPEN images were super-resolved reconstructed using deconvolution method. The results indicate that the SeSPEN method retains the advantage of SPEN MRI with respect to resistance to field inhomogeneity and can provide better signal-to-noise ratio than multi-slice GlSPEN MRI technique. The SeSPEN method has comparable SAR to the GlSPEN method while the T1 signal attenuation effect is alleviated. The proposed method will facilitate the multi-slice SPEN MRI to scan more slices within one scan with better image quality.

Analysis of generalized rosette trajectory for compressed sensing MRI

PURPOSE

The application of compressed sensing (CS) technology in magnetic resonance imaging (MRI) is to accelerate the MRI scan speed by incoherent undersampling of k-space data and nonlinear iterative reconstruction of MRI images. This paper generalizes the existing rosette trajectories to configure the sampling patterns for undersampled k-space data acquisition in MRI scans. The arch and curvature characteristics of the generalized rosette trajectories are analyzed to explore their feasibility and advantages for CS reconstruction of MRI images.

METHODS

Two key properties crucial to the CS MRI application, the scan speed and sampling incoherence of the generalized rosette trajectories, are analyzed. The analysis on the scan speed of generalized rosette trajectories is based on the transversal time derived from the curvature of the trajectories, and the sampling incoherence is based on the evaluation of the point spread function for the measurement matrix. The results of analysis are supported by extensive simulations where the performances of rosette, spiral, and radial sampling patterns at different acceleration factors are compared.

RESULTS

It is shown that compared with spiral trajectories, the arch and curvature characteristics of the generalized rosette trajectories are more feasible to meet the physical requirements of undersampled k-space data acquisition in terms of time shortness and scan area. It is further shown that the sampling pattern of the rosette trajectory has higher incoherence than that of the other trajectories and can thus achieve higher reconstruction performance. Reconstruction performances illustrate that the rosette trajectory can achieve about 10% higher peak signal-to-noise ratio than radial and spiral trajectories under the high acceleration factor R = 10.

CONCLUSIONS

The generalized rosette trajectories can be a desirable candidate for CS reconstruction of MRI.

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.

Pseudo-random center placement O-space imaging for improved incoherence compressed sensing parallel MRI

PURPOSE

Nonlinear spatial encoding magnetic (SEM) field strategies such as O-space imaging have previously reported dispersed artifacts during accelerated scans. Compressed sensing (CS) has shown a sparsity-promoting convex program allows image reconstruction from a reduced data set when using the appropriate sampling. The development of a pseudo-random center placement (CP) O-space CS approach optimizes incoherence through SEM field modulation to reconstruct an image with reduced error.

THEORY AND METHODS

The incoherence parameter determines the sparsity levels for which CS is valid and the related transform point spread function measures the maximum interference for a single point. The O-space acquisition is optimized for CS by perturbing the Z(2) strength within 30% of the nominal value and demonstrated on a human 3T scanner.

RESULTS

Pseudo-random CP O-space imaging is shown to improve incoherence between the sensing and sparse domains. Images indicate pseudo-random CP O-space has reduced mean squared error compared with a typical linear SEM field acquisition method.

CONCLUSION

Pseudo-random CP O-space imaging, with a nonlinear SEM field designed for CS, is shown to reduce mean squared error of images at high acceleration over linear encoding methods for a 2D slice when using an eight channel circumferential receiver array for parallel imaging.

Sparse regularization for fiber ODF reconstruction: from the suboptimality of ℓ2 and ℓ1 priors to ℓ0

Diffusion MRI is a well established imaging modality providing a powerful way to probe the structure of the white matter non-invasively. Despite its potential, the intrinsic long scan times of these sequences have hampered their use in clinical practice. For this reason, a large variety of methods have been recently proposed to shorten the acquisition times. Among them, spherical deconvolution approaches have gained a lot of interest for their ability to reliably recover the intra-voxel fiber configuration with a relatively small number of data samples. To overcome the intrinsic instabilities of deconvolution, these methods use regularization schemes generally based on the assumption that the fiber orientation distribution (FOD) to be recovered in each voxel is sparse. The well known Constrained Spherical Deconvolution (CSD) approach resorts to Tikhonov regularization, based on an ℓ(2)-norm prior, which promotes a weak version of sparsity. Also, in the last few years compressed sensing has been advocated to further accelerate the acquisitions and ℓ(1)-norm minimization is generally employed as a means to promote sparsity in the recovered FODs. In this paper, we provide evidence that the use of an ℓ(1)-norm prior to regularize this class of problems is somewhat inconsistent with the fact that the fiber compartments all sum up to unity. To overcome this ℓ(1) inconsistency while simultaneously exploiting sparsity more optimally than through an ℓ(2) prior, we reformulate the reconstruction problem as a constrained formulation between a data term and a sparsity prior consisting in an explicit bound on the ℓ(0)norm of the FOD, i.e. on the number of fibers. The method has been tested both on synthetic and real data. Experimental results show that the proposed ℓ(0) formulation significantly reduces modeling errors compared to the state-of-the-art ℓ(2) and ℓ(1) regularization approaches.

Stable and Robust Sampling Strategies for Compressive Imaging

In many signal processing applications, one wishes to acquire images that are sparse in transform domains such as spatial finite differences or wavelets using frequency domain samples. For such applications, overwhelming empirical evidence suggests that superior image reconstruction can be obtained through variable density sampling strategies that concentrate on lower frequencies. The wavelet and Fourier transform domains are not incoherent because low-order wavelets and low-order frequencies are correlated, so compressive sensing theory does not immediately imply sampling strategies and reconstruction guarantees. In this paper, we turn to a more refined notion of coherence-the so-called local coherence-measuring for each sensing vector separately how correlated it is to the sparsity basis. For Fourier measurements and Haar wavelet sparsity, the local coherence can be controlled and bounded explicitly, so for matrices comprised of frequencies sampled from a suitable inverse square power-law density, we can prove the restricted isometry property with near-optimal embedding dimensions. Consequently, the variable-density sampling strategy we provide allows for image reconstructions that are stable to sparsity defects and robust to measurement noise. Our results cover both reconstruction by ℓ1-minimization and total variation minimization. The local coherence framework developed in this paper should be of independent interest, as it implies that for optimal sparse recovery results, it suffices to have bounded average coherence from sensing basis to sparsity basis-as opposed to bounded maximal coherence-as long as the sampling strategy is adapted accordingly.

An aliasing artifacts reducing approach with random undersampling for spatiotemporally encoded single-shot MRI

Compared to the echo planar imaging (EPI), spatiotemporally encoded (SPEN) single-shot MRI holds better immunity to the field inhomogeneity, while retaining comparable spatial and temporal resolutions after the super-resolved reconstruction. Though various reconstruction methods have been proposed, the reconstructed SPEN images usually contain aliasing artifacts because of vast undersampling. A hybrid scheme based on random sampling, singular value decomposition (SVD) and compressed sensing (CS) was introduced to reduce these aliasing artifacts and improve the image quality. The efficiency of this hybrid scheme was demonstrated by numerical simulations and experiments on water phantom and in vivo rat brain. The hybrid scheme provided herein would benefit the SPEN approach in vast undersampling situation.

An efficient de-convolution reconstruction method for spatiotemporal-encoding single-scan 2D MRI

Spatiotemporal-encoding single-scan MRI method is relatively insensitive to field inhomogeneity compared to EPI method. Conjugate gradient (CG) method has been used to reconstruct super-resolved images from the original blurred ones based on coarse magnitude-calculation. In this article, a new de-convolution reconstruction method is proposed. Through removing the quadratic phase modulation from the signal acquired with spatiotemporal-encoding MRI, the signal can be described as a convolution of desired super-resolved image and a point spread function. The de-convolution method proposed herein not only is simpler than the CG method, but also provides super-resolved images with better quality. This new reconstruction method may make the spatiotemporal-encoding 2D MRI technique more valuable for clinic applications.

The Role of Nonlinear Gradients in Parallel Imaging: A k-Space Based Analysis

Sequences that encode the spatial information of an object using nonlinear gradient fields are a new frontier in MRI, with potential to provide lower peripheral nerve stimulation, windowed fields of view, tailored spatially-varying resolution, curved slices that mirror physiological geometry, and, most importantly, very fast parallel imaging with multichannel coils. The acceleration for multichannel images is generally explained by the fact that curvilinear gradient isocontours better complement the azimuthal spatial encoding provided by typical receiver arrays. However, the details of this complementarity have been more difficult to specify. We present a simple and intuitive framework for describing the mechanics of image formation with nonlinear gradients, and we use this framework to review some the main classes of nonlinear encoding schemes.

Enhanced SWIFT acquisition with chaotic compressed sensing by designing the measurement matrix with hyperbolic-secant signals

Sweep imaging Fourier transform (SWIFT) is an efficient (fast and quiet) specialized magnetic resonance imaging (MRI) method for imaging tissues or organs that give only short-lived signals due to fast spin-spin relaxation rates. Based on the idea of compressed sensing, this paper proposes a novel method for further enhancing SWIFT using chaotic compressed sensing (CCS-SWIFT). With reduced number of measurements, CCS-SWIFT effectively faster than SWIFT. In comparison with a recently proposed chaotic compressed sensing method for standard MRI (CCS-MRI), simulation results showed that CCS-SWIFT outperforms CCS-MRI in terms of the normalized relative error in the image reconstruction and the probability of exact reconstruction.