Non-local total bounded variation scheme for multiple-coil magnetic resonance image restoration

In this paper, we design a variational model for restoring multiple-coil magnetic resonance images (MRI) corrupted by non-central Chi distributed noise. The energy functional corresponding to the restoration problem is derived using the maximum a posteriori (MAP) estimator. Optimizing this functional yields the solution, which corresponds to the restored version of the image. The non-local total bounded variation prior is being used as the regularization term in the functional derived using the MAP estimation process. Further, the split-Bregman iteration scheme is being followed for fast numerical computation of the model. The results are compared with the state of the art MRI restoration models using visual representations and statistical measures.     

MR susceptibility misregistration correction

The authors present a new in vivo method to correct the nonlinear, object-shape-dependent and material-dependent spatial distortion in magnetic resonance (MR) images caused by magnetic susceptibility variations. This distortion across the air/tissue interface before and after the correction is quantified using a phantom. The results are compared to the distortion-free computed tomography (CT) images of the same phantom by fusing CT and MR images using fiducials, with a registration accuracy of better than a millimeter. The distortion at the bone/tissue boundary is negligible compared to the typical MRI (MR imaging) resolution of 1 mm, while that at the air/tissue boundary creates displacements of about 2 mm (for G(x) 3.13 mT/m). This is a significant value if MRI is to provide highly accurate geometric measurements, as in the case of target localization for stereotaxic surgery. The correction scheme provides MR images with accuracy similar to that of CT: 1 mm. A new method to estimate the magnetic susceptibility of materials from MR images is presented. The magnetic susceptibility of cortical bone is measured using a SQUID magnetometer, and is found to be -8.86 ppm (with respect to air), which is quite similar to that of tissue (-9 ppm).     

Nonlinear Stochastic Regularization to Characterize Tissue Residue Function in Bolus-Tracking MRI: Assessment and Comparison With SVD, Block-Circulant SVD, and Tikhonov

An accurate characterization of tissue residue function $R$($t$) in bolus-tracking magnetic resonance imaging is of crucial importance to quantify cerebral hemodynamics. $R$($t$) estimation requires to solve a deconvolution problem. The most popular deconvolution method is singular value decomposition (SVD). However, SVD is known to bear some limitations, e.g., $R$($t$) profiles exhibit nonphysiological oscillations and take on negative values. In addition, SVD estimates are biased in presence of bolus delay and dispersion. Recently, other deconvolution methods have been proposed, in particular block-circulant SVD (cSVD) and Tikhonov regularization (TIKH). Here we propose a new method based on nonlinear stochastic regularization (NSR). NSR is tested on simulated data and compared with SVD, cSVD, and TIKH in presence and absence of bolus dispersion. A clinical case in one patient has also been considered. NSR is shown to perform better than SVD, cSVD, and TIKH in reconstructing both the peak and the residue function, in particular when bolus dispersion is considered. In addition, differently from SVD, cSVD, and TIKH, NSR always provides positive and smooth $R$($t$).      

Quantitative Analysis of Dynamic Contrast-Enhanced MR Images Based on Bayesian P-Splines

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is an important tool for detecting subtle kinetic changes in cancerous tissue. Quantitative analysis of DCE-MRI typically involves the convolution of an arterial input function (AIF) with a nonlinear pharmacokinetic model of the contrast agent concentration. Parameters of the kinetic model are biologically meaningful, but the optimization of the nonlinear model has significant computational issues. In practice, convergence of the optimization algorithm is not guaranteed and the accuracy of the model fitting may be compromised. To overcome these problems, this paper proposes a semi-parametric penalized spline smoothing approach, where the AIF is convolved with a set of B-splines to produce a design matrix using locally adaptive smoothing parameters based on Bayesian penalized spline models (P-splines). It has been shown that kinetic parameter estimation can be obtained from the resulting deconvolved response function, which also includes the onset of contrast enhancement. Detailed validation of the method, both with simulated and in vivo data, is provided.      

Narrowband Magnetic Particle Imaging

The magnetic particle imaging (MPI) method directly images the magnetization of super-paramagnetic iron oxide (SPIO) nanoparticles, which are contrast agents commonly used in magnetic resonance imaging (MRI). MPI, as originally envisioned, requires a high-bandwidth receiver coil and preamplifier, which are difficult to optimally noise match. This paper introduces Narrowband MPI, which dramatically reduces bandwidth requirements and increases the signal-to-noise ratio for a fixed specific absorption rate. We employ a two-tone excitation (called intermodulation) that can be tailored for a high-Q, narrowband receiver coil. We then demonstrate a new MPI instrument capable of full 3-D tomographic imaging of SPIO particles by imaging acrylic and tissue phantoms.      

Superparamagnetic Nanostructures for Off‐Resonance Magnetic Resonance Spectroscopic Imaging

This study proposes a new method to generate positive contrast in magnetic resonance imaging (MRI) using superparamagnetic contrast agents. Superparamagnetic nanostructures consisting of octahedron manganese ferrite nanoparticles embedded in spherical nanogels are fabricated using a bottom‐up approach. The composite nanoparticles are strongly magnetized in an external magnetic field and produce a unique NMR frequency shift in water protons, which can be demonstrated in MR spectroscopy and imaging to be different from the bulk pool. Moreover, the particles exhibit excellent colloidal stability in aqueous media and good cell biocompatibility. Hence, these particles are potentially useful as biomarkers by taking advantage of the positive contrast effects produced in MRI.     

Local Harmonic $B_z$ Algorithm With Domain Decomposition in MREIT: Computer Simulation Study

Magnetic resonance electrical impedance tomography (MREIT) attempts to provide conductivity images of an electrically conducting object with a high spatial resolution. When we inject current into the object, it produces internal distributions of current density ${bf J}$ and magnetic flux density ${bf B}=(B_x,B_y,B_z)$. By using a magnetic resonance imaging (MRI) scanner, we can measure $B_z$ data where $z$ is the direction of the main magnetic field of the scanner. Conductivity images are reconstructed based on the relation between the injection current and $B_z$ data. The harmonic $B_z$ algorithm was the first constructive MREIT imaging method and it has been quite successful in previous numerical and experimental studies. Its performance is, however, degraded when the imaging object contains low-conductivity regions such as bones and lungs. To overcome this difficulty, we carefully analyzed the structure of a current density distribution near such problematic regions and proposed a new technique, called the local harmonic $B_z$ algorithm. We first reconstruct conductivity values in local regions with a low conductivity contrast, separated from those problematic regions. Then, the method of characteristics is employed to find conductivity values in the problematic regions. One of the most interesting observations of the new algorithm is that it can provide a scaled conductivity image in a local region without knowing conductivity values outside the region. We present the performance of the new algorithm by using computer simulation methods.      

Real-Time Reconstruction of Sensitivity Encoded Radial Magnetic Resonance Imaging Using a Graphics Processing Unit

A barrier to the adoption of non-Cartesian parallel magnetic resonance imaging for real-time applications has been the times required for the image reconstructions. These times have exceeded the underlying acquisition time thus preventing real-time display of the acquired images. We present a reconstruction algorithm for commodity graphics hardware (GPUs) to enable real time reconstruction of sensitivity encoded radial imaging (radial SENSE). We demonstrate that a radial profile order based on the golden ratio facilitates reconstruction from an arbitrary number of profiles. This allows the temporal resolution to be adjusted on the fly. A user adaptable regularization term is also included and, particularly for highly undersampled data, used to interactively improve the reconstruction quality. Each reconstruction is fully self-contained from the profile stream, i.e., the required coil sensitivity profiles, sampling density compensation weights, regularization terms, and noise estimates are computed in real-time from the acquisition data itself. The reconstruction implementation is verified using a steady state free precession (SSFP) pulse sequence and quantitatively evaluated. Three applications are demonstrated; real-time imaging with real-time SENSE 1) or $k$-$t$ SENSE 2) reconstructions, and 3) offline reconstruction with interactive adjustment of reconstruction settings.      

Data Specific Spatially Varying Regularization for Multimodal Fluorescence Molecular Tomography

Fluorescence molecular tomography (FMT) allows in vivo localization and quantification of fluorescence biodistributions in whole animals. The ill-posed nature of the tomographic reconstruction problem, however, limits the attainable resolution. Improvements in resolution and overall imaging performance can be achieved by forming image priors from geometric information obtained by a secondary anatomical or functional high-resolution imaging modality such as X-ray computed tomography or magnetic resonance imaging. A particular challenge in using image priors is to avoid the use of assumptions that may bias the solution and reduced the accuracy of the inverse problem. This is particularly relevant in FMT inversions where there is not an evident link between secondary geometric information and the underlying fluorescence biodistribution. We present here a new, two step approach to incorporating structural priors into the FMT inverse problem. By using the anatomic information to define a low dimensional inverse problem, we obtain a solution which we then use to determine the parameters defining a spatially varying regularization matrix for the full resolution problem. The regularization term is thus customized for each data set and is guided by the data rather than depending only on user defined a priori assumptions. Results are presented for both simulated and experimental data sets, and show significant improvements in image quality as compared to traditional regularization techniques.      

An Adaptable Nanoplatform for Integrating Anatomic and Functional Magnetic Resonance Imaging under a 3.0 T Magnetic Field

It is well known that acidic tumor microenvironment (TME) is very important for tumor' growth, metastasis, and drug resistance. In addition, accurate diagnosis of the solid tumors' acidic microenviroment based on the precise location of their site is especially essential for the further treatment and prognostic evaluation of cancer. Although magnetic resonance imaging (MRI) is widely used for clinical cancer diagnosis, there are still enormous challenges left for developing MRI agents which integrate anatomic imaging for tumor site location with functional imaging for pH evaluation, especially for medium or high magnetic field machines. Herein, an innovative strategy is proposed to incorporate anatomic imaging (T₁‐weighted imaging, T₁WI) with functional imaging (susceptibility weighted imaging, SWI) using one 3.0 T MRI scanner on an adaptable nanoplatform namely, NaGdF₄@polydopamine@polyethylene glycol (PEG), which can self‐aggregate under the specific low pH in TME to realize regulatory susceptibility. Moreover, the nanoplatform performs well in tumor accurately location as well as pH sensitively perception. Most importantly, the strategy not only fuses two MRI models on one nanoplatform using one 3.0 T machine to extend the application range but also provides a new insight for the design of other novel imaging agents.     

A fast wavelet-based reconstruction method for magnetic resonance imaging

In this work, we exploit the fact that wavelets can represent magnetic resonance images well, with relatively few coefficients. We use this property to improve magnetic resonance imaging (MRI) reconstructions from undersampled data with arbitrary k-space trajectories. Reconstruction is posed as an optimization problem that could be solved with the iterative shrinkage/thresholding algorithm (ISTA) which, unfortunately, converges slowly. To make the approach more practical, we propose a variant that combines recent improvements in convex optimization and that can be tuned to a given specific k-space trajectory. We present a mathematical analysis that explains the performance of the algorithms. Using simulated and in vivo data, we show that our nonlinear method is fast, as it accelerates ISTA by almost two orders of magnitude. We also show that it remains competitive with TV regularization in terms of image quality.     

一种基于全变分正则化低秩稀疏分解的动态MRI重建方法

针对应用迭代软阈值(IST)算法对基于低秩稀疏矩 阵(L＋S,low rank and sparse)分解模型的动态磁共振成像(MRI)图像 进行重建存在重建精度一般和重建速度慢的问题,提出在矩阵L＋S分解模 型的基础上引入全变分(TV)正则项,达到进一步去噪声和去伪影,提高重建精度目的;利用 非精确增广拉 格朗日算法(IALM)达到快速重建的目的。通过对心脏灌注动态MRI成像和心电影MRI成 像的仿真实 验表明:对于L＋S低秩稀疏矩阵分解模型的重建,IALM比IS T算法速度更快,精度更高;模型引入TV正则项 后再利用IALM重建,重建速度虽然比之前的IALM有所降低,但依然优于IST算法, 并且重建精 度高于之前的IALM。在L＋S分解模型中引入TV正则项 提高了MRI重建精度,运用IALM进行求解加快了重建速度,结合TV正则项和IALM达到了 快速、高精度重建的目的。     

$$\ell _{1/2,1}$$ group sparse regularization for compressive sensing

Recently, the design of group sparse regularization has drawn much attention in group sparse signal recovery problem. Two of the most popular group sparsity-inducing regularization models are \(\ell _{1,2}\) and \(\ell _{1,\infty }\) regularization. Nevertheless, they do not promote the intra-group sparsity. For example, Huang and Zhang (Ann Stat 38:1978–2004, 2010) claimed that the \(\ell _{1,2}\) regularization is superior to the \(\ell _1\) regularization only for strongly group sparse signals. This means the sparsity of intra-group is useless for \(\ell _{1,2}\) regularization. Our experiments show that recovering signals with intra-group sparse needs more measurements than those without, by the \(\ell _{1,\infty }\) regularization. In this paper, we propose a novel group sparsity-inducing regularization defined as a mixture of the \(\ell _{1/2}\) norm and the \(\ell _{1}\) norm, referred to as \(\ell _{1/2,1}\) regularization, which can overcome these shortcomings of \(\ell _{1,2}\) and \(\ell _{1,\infty }\) regularization. We define a new null space property for \(\ell _{1/2,1}\) regularization and apply it to establish a recoverability theory for both intra-group and inter-group sparse signals. In addition, we introduce an iteratively reweighted algorithm to solve this model and analyze its convergence. Comprehensive experiments on simulated data show that the proposed \(\ell _{1/2,1}\) regularization is superior to \(\ell _{1,2}\) and \(\ell _{1,\infty }\) regularization.     

A Spectral-Scanning Nuclear Magnetic Resonance Imaging (MRI) Transceiver

An integrated spectral-scanning nuclear magnetic resonance imaging (MRI) transceiver is implemented in a 0.12$ mu$m SiGe BiCMOS process. The MRI transmitter and receiver circuitry is designed specifically for small-scale surface MRI diagnostics applications where creating low (below 1 T) and inhomogeneous magnetic field is more practical. The operation frequency for magnetic resonance detection and analysis is tunable from 1 kHz to 37 MHz, corresponding to 0–0.9 T magnetization for $^{1}$ H (Hydrogen). The concurrent measurement bandwidth is approximately one frequency octave. The chip can also be used for conventional narrowband nuclear magnetic resonance (NMR) spectroscopy from 1 kHz up to 250 MHz. This integrated transceiver consists of both the magnetic resonance transmitter which generates the required excitation pulses for the magnetic dipole excitation, and the receiver which recovers the responses of the dipoles.      

An inverse design of an open,head/neck RF coil for MRI

Radio-frequency (RF) coils are a necessary component of magnetic resonance imaging (MRI) systems. When used in transmit operation, they act to generate a homogeneous RF magnetic field within a volume of interest and when in receive operation, they act to receive the nuclear magnetic resonance signal from the RF-excited specimen. This paper outlines a procedure for the design of open RF coils using the time-harmonic inverse method. This method entails the calculation of an ideal current density on a multipaned planar surface that would generate a specified magnetic field within the volume of interest. Because of the averaging effect of the regularization technique in the matrix solution, the specified magnetic field is shaped within an iterative procedure until the generated magnetic field matches the desired magnetic field. The stream-function technique is used to ascertain conductor positions and a method of moments package is then used to finalize the design. An open head/neck coil was designed to operate in a clinical 2T MRI system and the presented results prove the efficacy of this design methodology.     

Magnetic nanostructures and nanodevices with a semiconductor or dielectric spacer

Magnetic properties of nanoscale magnetic-layer systems using FeNi, Co, FeMn, Al₂O₃, and SiC layers are studied experimentally. The dependence of magnetic behavior on the system geometry and parameters is addressed. Ferromagnet-semiconductor exchange coupling subject to the amplitude of an applied magnetic field is revealed. It is found that the magnetic behavior of the nanostructures varies in a nonlinear manner with applied magnetic field. Spin-tunneling magnetoresistance is observed in magnetic-layer junctions containing an Al₂O₃ spacer. In-plane-conduction magnetic-field sensors using an Al₂O₃ or a SiC spacer are fabricated and tested.Translated from Mikroelektronika, Vol. 34, No. 1, 2005, pp. 56–64.Original Russian Text Copyright © 2005 by Kasatkin, Muravjev, Plotnikova, Pudonin, Azhaeva, Sergeeva, Khodzhaev.     

Parallel MR image reconstruction using augmented Lagrangian methods

Magnetic resonance image (MRI) reconstruction using SENSitivity Encoding (SENSE) requires regularization to suppress noise and aliasing effects. Edge-preserving and sparsity-based regularization criteria can improve image quality, but they demand computation-intensive nonlinear optimization. In this paper, we present novel methods for regularized MRI reconstruction from undersampled sensitivity encoded data--SENSE-reconstruction--using the augmented Lagrangian (AL) framework for solving large-scale constrained optimization problems. We first formulate regularized SENSE-reconstruction as an unconstrained optimization task and then convert it to a set of (equivalent) constrained problems using variable splitting. We then attack these constrained versions in an AL framework using an alternating minimization method, leading to algorithms that can be implemented easily. The proposed methods are applicable to a general class of regularizers that includes popular edge-preserving (e.g., total-variation) and sparsity-promoting (e.g., l(1)-norm of wavelet coefficients) criteria and combinations thereof. Numerical experiments with synthetic and in vivo human data illustrate that the proposed AL algorithms converge faster than both general-purpose optimization algorithms such as nonlinear conjugate gradient (NCG) and state-of-the-art MFISTA.     

Imaging the distribution of magnetic nanoparticles with ultrasound

Magnetic nanoparticles can be caused to oscillate under the influence of an incident ultrasonic wave. If the particles are momentarily aligned with a magnetizing pulse creating a macroscopic magnetization, this oscillation will result in a time-varying magnetic moment which should be detectable as an induced voltage in a nearby pickup coil. In this way, focused ultrasound can be used to map, or image, the spatial distribution of the magnetic particles after these particles have been introduced into the body. The magnetic particles could be antibody-labeled to target tumor cells or used as a cardiovascular contrast agent, among other applications. The magnitude of the induced signal is estimated for one micron particles with a Fe/tissue volume fraction of 10(-6), which is about the limit of detectability for MRI superparamagnetic contrast agents consisting of single domain iron-oxide particles. One advantage of this method compared to conventional MRI is potentially greater sensitivity due to the absence of a large background signal.     

Improved Time Series Reconstruction for Dynamic Magnetic Resonance Imaging

Time series of in vivo magnetic resonance images exhibit high levels of temporal correlation. Higher temporal resolution reconstructions are obtained by acquiring data at a fraction of the Nyquist rate and resolving the resulting aliasing using the correlation information. The dynamic imaging experiment is modeled as a linear dynamical system. A Kalman filter based unaliasing reconstruction is described for accelerated dynamic magnetic resonance imaging (MRI). The algorithm handles arbitrary readout trajectories naturally. The reconstruction is causal and very fast, making it applicable to real-time imaging. In vivo results are presented for cardiac MRI of healthy volunteers.      

Numerical Study of the Shielding Properties of Macroscopic Hybrid Ferromagnetic/Superconductor Hollow Cylinders

We study the magnetic shielding properties of hybrid ferromagnetic/superconductor (F/S) structures consisting of two coaxial cylinders, with one of each material. We use an axisymmetric finite-element model in which the electrical properties of the superconducting tube are modeled by a nonlinear $E$ -$J$ power law with a magnetic-field-dependent critical current density whereas the magnetic properties of the ferromagnetic material take saturation into account. We study and compare the penetration of a uniform axial magnetic field in two cases: 1) a ferromagnetic tube placed inside a larger superconducting tube (Ferro-In configuration) and 2) a ferromagnetic tube placed outside the superconducting one (Ferro-Out configuration). In both cases, we assess how the ferromagnetic tube improves the shielding properties of the sole superconducting tube. The influence of the geometrical parameters of the ferromagnetic tube is also studied: It is shown that, upon an optimal choice of the geometrical parameters, the range of magnetic fields that are efficiently shielded by the high-temperature superconductor tube alone can be increased by a factor of up to 7 (2) in a Ferro-Out (Ferro-In) configuration. The optimal configuration uses a 1020 carbon steel with a thickness of 2 mm and a height that is half that of the superconducting cylinder (80 mm).