Exploiting rank deficiency and transform domain sparsity for MR image reconstruction

The reconstruction of magnetic resonance (MR) images from the partial samples of their k-space data using compressed sensing (CS)-based methods has generated a lot of interest in recent years. To reconstruct the MR images, these techniques exploit the sparsity of the image in a transform domain (wavelets, total variation, etc.). In a recent work, it has been shown that it is also possible to reconstruct MR images by exploiting their rank deficiency. In this work, it will be shown that, instead of exploiting the sparsity of the image or rank deficiency alone, better reconstruction results can be achieved by combining transform domain sparsity with rank deficiency.To reconstruct an MR image using its transform domain sparsity and its rank deficiency, this work proposes a combined l₁-norm (of the transform coefficients) and nuclear norm (of the MR image matrix) minimization problem. Since such an optimization problem has not been encountered before, this work proposes and derives a first-order algorithm to solve it.The reconstruction results show that the proposed approach yields significant improvements, in terms of both visual quality as well as the signal to noise ratio, over previous works that reconstruct MR images either by exploiting rank deficiency or by the standard CS-based technique popularly known as the ‘Sparse MRI.’     

Adaptive fixed-point iterative shrinkage/thresholding algorithm for MR imaging reconstruction using compressed sensing

Recently compressed sensing (CS) has been applied to under-sampling MR image reconstruction for significantly reducing signal acquisition time. To guarantee the accuracy and efficiency of the CS-based MR image reconstruction, it necessitates determining several regularization and algorithm-introduced parameters properly in practical implementations. The regularization parameter is used to control the trade-off between the sparsity of MR image and the fidelity measures of k-space data, and thus has an important effect on the reconstructed image quality. The algorithm-introduced parameters determine the global convergence rate of the algorithm itself. These parameters make CS-based MR image reconstruction a more difficult scheme than traditional Fourier-based method while implemented on a clinical MR scanner. In this paper, we propose a new approach that reveals that the regularization parameter can be taken as a threshold in a fixed-point iterative shrinkage/thresholding algorithm (FPIST) and chosen by employing minimax threshold selection method. No extra parameter is introduced by FPIST. The simulation results on synthetic and real complex-valued MRI data show that the proposed method can adaptively choose the regularization parameter and effectively achieve high reconstruction quality. The proposed method should prove very useful for practical CS-based MRI applications.     

Pulse sequence optimization for T2-weighted MR imaging of the brain

The authors implemented bipolar velocity compensated pulse techniques for T2-weighted MR imaging of the brain. Signal-to-noise (S/N) and image quality was compared for pulse sequences with standard and optimized RF pulses, low and regular bandwidth versions and cardiac triggering. Images from bipolar velocity compensated sequences allowed better visualization of vessels and basilar cisterns and improved image quality relative to standard sequences without velocity compensation. The implementation of optimized RF pulses with bipolar sequences resulted in further improvement in image quality. Single echo sequences consistently had improved image quality and signal-to-noise relative to the second echo of a double echo sequence. Low bandwidth bipolar sequences with extended sampling period had 30% higher S/N, but at the cost of slight loss in edge definition. The highest image quality was obtained with the bipolar, optimized RF, single echo sequence. Using this technique contiguous high quality image slices could be obtained with velocity compensation. The addition of cardiac triggering to bipolar sequences resulted in slight improvement in image quality, but this difference was marginal and probably rarely necessary for MR imaging of the brain.     

3.0 T MR investigation of CLIPPERS: Role of susceptibility weighted and perfusion weighted imaging

For the first time we describe and interpret Susceptibility Weighted Imaging (SWI) and Perfusion Weighted Imaging (PWI) findings in a case of Chronic Lymphocytic Inflammation with Perivascular Pontine Enhancement Responsive to Steroids (CLIPPERS). The diagnosis of the disease was formulated on the basis of typical Magnetic Resonance (MR) findings and its responsiveness to steroids in a 40-year-old man with acute onset of dizziness, ataxia and diplopia. The patient underwent a 3 tesla (T) MR examination including SWI and PWI sequences. SWI revealed prominent veins and multiple hypointense lesions of different size widely distributed in brainstem and cerebellum, which could be expression of iron deposition or cellular infiltrates. PWI demonstrated global infratentorial hypoperfusion. SWI and PWI provide new information on CLIPPERS that might be helpful to understand the physiopathology of the disease. Further observations are needed to evaluate if these findings are peculiar for CLIPPERS and if they might have a role in a non-invasive diagnosis of the disease.     

Non-convex algorithm for sparse and low-rank recovery: Application to dynamic MRI reconstruction

In this work we exploit two assumed properties of dynamic MRI in order to reconstruct the images from under-sampled K-space samples. The first property assumes the signal is sparse in the x-f space and the second property assumes the signal is rank-deficient in the x-t space. These assumptions lead to an optimization problem that requires minimizing a combined l_p-norm and Schatten-p norm. We propose a novel FOCUSS based approach to solve the optimization problem. Our proposed method is compared with state-of-the-art techniques in dynamic MRI reconstruction. Experimental evaluation carried out on three real datasets shows that for all these datasets, our method yields better reconstruction both in quantitative and qualitative evaluation.     

Central neurocytoma: proton MR spectroscopy and diffusion weighted MR imaging findings

Purpose

To present proton magnetic resonance spectroscopy and diffusion-weighted imaging (DWI) findings of central neurocytoma (CN).

Methods and Materials

Imaging findings of seven patients with the histopathological diagnosis of CN (five male and two female; age range, 21–28 years of age) were evaluated retrospectively. In addition to conventional magnetic resonance imaging features, we also assessed the metabolite ratios and tumor normalized apparent diffusion coefficient (NADC), which was calculated by dividing the tumor apparent diffusion coefficient (ADC) values by normal ADC. Approval from our institutional review board was obtained for this review.

Results

The tumor choline/creatine ratios were 5.17±2.38, while N-acetyl aspartate/choline and N-acetyl aspartate/creatine ratios were 0.33±0.15 and 1.84±1.38, respectively. On DWI, tumors had heterogeneous hyperintense appearances when compared with the contralateral parietal lobe white matter and tumor NADC values were 0.63±0.05.

Conclusion

Significantly increased choline/creatine and decreased N-acetyl aspartate/choline ratios with lower NADC values in CN resemble high-grade gliomas and complicate the diagnosis. Familarity its physiologic features would help to presurgical diagnosis of ventricular and exraventricular CNs.     

Effect of Gd-EOB-DTPA on hepatic fat quantification using high-speed T2-corrected multi-echo acquisition in H MR spectroscopy

Purpose

To determine whether gadolinium ethoxybenzyldiethylenetriaminepentaacetic acid (Gd-EOB-DTPA) administration affects hepatic fat quantification by magnetic resonance spectroscopy (MRS) using the fast breath-hold high-speed T2-corrected multiecho (HISTO) technique.

Materials and Methods

Seventy-six patients underwent Gd-EOB-DTPA-enhanced liver MR and 15 sec breath-hold HISTO MRS (4 times), twice before and twice after Gd-EOB-DTPA administration. Two consecutive MRSs were performed immediately before the dynamic study. Post-contrast MRS was performed twice continuously, approximately 15 min after contrast injection, prior to obtaining 20-min hepatobiliary phase images. We used paired t-test and intraclass correlation coefficient (ICC) to evaluate the variability of the mean fat fraction (FF) on pre-contrast MRS and post-contrast MRS and the effect of the contrast agent on the mean FF.

Results

The mean FFs were not significantly different between pre-contrast MRS and post-contrast MRS (6.50% ± 6.54 versus 6.70% ± 6.61, P = 0.15). The ICC of FF calculation between pre- and post-contrast MRS was 0.984. The ICCs for the FF magnitude between pre- and post-contrast MRS were 0.452, 0.771, and 0.995 for FF < 5%, FF 5–10%, and FF ≥ 10%, respectively.

Conclusion

Gd-EOB-DTPA does not appear to influence hepatic fat quantification, especially for patients with hepatic steatosis.     

Use of continuous optimization methods to find carbon links in 2D INADEQUATE spectra

The 2-D INADEQUATE experiment is a useful experiment for determining carbon structures of organic molecules, which is known for having low signal-to-noise ratios. A non-linear optimization method for solving low-signal spectra resulting from this experiment is introduced to compensate. The method relies on the peak locations defined by the INADEQUATE experiment to create boxes around these areas and measure the signal in each. By measuring pairs of these boxes and applying penalty functions that represent a priori information, we are able to quickly and reliably solve spectra with an acquisition time approximately a quarter of that required by traditional methods. Examples are shown using the spectrum of sucrose.     

Short T2 contrast with three-dimensional ultrashort echo time imaging

There is increasing interest in imaging short T2 species which show little or no signal with conventional magnetic resonance (MR) pulse sequences. In this paper, we describe the use of three-dimensional ultrashort echo time (3D UTE) sequences with TEs down to 8 μs for imaging of these species. Image contrast was generated with acquisitions using dual echo 3D UTE with echo subtraction, dual echo 3D UTE with rescaled subtraction, long T2 saturation 3D UTE, long T2 saturation dual echo 3D UTE with echo subtraction, single adiabatic inversion recovery 3D UTE, single adiabatic inversion recovery dual echo 3D UTE with echo subtraction and dual adiabatic inversion recovery 3D UTE. The feasibility of using these approaches was demonstrated in in vitro and in vivo imaging of calcified cartilage, aponeuroses, menisci, tendons, ligaments and cortical bone with a 3-T clinical MR scanner. Signal-to-noise ratios and contrast-to-noise ratios were used to compare the techniques.     

Compressed sensing and the reconstruction of ultrafast 2D NMR data: Principles and biomolecular applications

A topic of active investigation in 2D NMR relates to the minimum number of scans required for acquiring this kind of spectra, particularly when these are dictated by sampling rather than by sensitivity considerations. Reductions in this minimum number of scans have been achieved by departing from the regular sampling used to monitor the indirect domain, and relying instead on non-uniform sampling and iterative reconstruction algorithms. Alternatively, so-called "ultrafast" methods can compress the minimum number of scans involved in 2D NMR all the way to a minimum number of one, by spatially encoding the indirect domain information and subsequently recovering it via oscillating field gradients. Given ultrafast NMR's simultaneous recording of the indirect- and direct-domain data, this experiment couples the spectral constraints of these orthogonal domains - often calling for the use of strong acquisition gradients and large filter widths to fulfill the desired bandwidth and resolution demands along all spectral dimensions. This study discusses a way to alleviate these demands, and thereby enhance the method's performance and applicability, by combining spatial encoding with iterative reconstruction approaches. Examples of these new principles are given based on the compressed-sensed reconstruction of biomolecular 2D HSQC ultrafast NMR data, an approach that we show enables a decrease of the gradient strengths demanded in this type of experiments by up to 80%.     

The use of T2*-weighted multi-echo GRE imaging as a novel method to diagnose hepatocellular carcinoma compared with gadolinium-enhanced MRI: a feasibility study

Background

The goal of the study was to assess a T2*-weighted MRI sequence for the ability to identify hepatocellular carcinoma (HCC).

Methods

Hepatic iron deposition, which is common in chronic liver disease (CLD), may increase the conspicuity of HCC on GRE imaging due to increased T2* signal decay in liver parenchyma. In this study, a breath-hold T2*-weighted MRI sequence was evaluated by a blinded observer for HCC and the results compared to a reference standard of gadolinium-enhanced MRI in these same patients. Forty-one patients (mean age 56.2 years; 17 females) were included in this approved, retrospective study.

Results

By the reference standard, 14 of 41 patients had a total of 25 HCCs. The sensitivity of the T2*-weighted MR sequence for identifying HCC, per lesion, was 60%, while the specificity was 100%. There was a significantly lower T2* value of liver parenchyma in patients with HCC identified by the T2*-weighted sequence than in those with HCCs which were not identified by the T2*-weighted sequence (27.8±2.2 vs. 21.9±2.1 ms; P=.02).

Conclusions

A T2*-weighted MRI sequence can identify HCC in patients with CLD. This technique may be beneficial for imaging of patients contraindicated for gadolinium.     

Parallel imaging with 3D TPI trajectory: SNR and acceleration benefits

Three-dimensional (3D) twisted projection imaging (TPI) trajectory has a unique advantage in sodium (²³Na) imaging on clinical MRI scanners at 1.5 or 3 T, generating a high signal-to-noise ratio (SNR) with a short acquisition time (∼10 min). Parallel imaging with an array of coil elements transits SNR benefits from small coil elements to acquisition efficiency by sampling partial k-space. This study investigates the feasibility of parallel sodium imaging with emphases on SNR and acceleration benefits provided by the 3D TPI trajectory. Computer simulations were used to find available acceleration factors and noise amplification. Human head studies were performed on clinical 1.5/3-T scanners with four-element coil arrays to verify simulation outcomes. In in vivo studies, proton (¹H) data, however, were acquired for concept–proof purpose. The sensitivity encoding (SENSE) method with the conjugate gradient algorithm was used to reconstruct images from accelerated TPI-SENSE data sets. Self-calibration was employed to estimate coil sensitivities. Noise amplification in TPI-SENSE was evaluated using multiple noise trials. It was found that the acceleration factor was as high as 5.53 (corresponding to acceleration number 2×3, ring-by-rotation), with a small image error of 6.9% when TPI projections were reduced in both polar (ring) and azimuthal (rotation) directions. The average noise amplification was as low as 98.7%, or 27% lower than Cartesian SENSE at that acceleration factor. The 3D nature of both TPI trajectory and coil sensitivities might be responsible for the high acceleration and low noise amplification. Consequently, TPI-SENSE may have potential advantages for parallel sodium imaging.     

BRAHMA: Population specific T1, T2, and FLAIR weighted brain templates and their impact in structural and functional imaging studies

Differences in brain morphology across population groups necessitate creation of population-specific Magnetic Resonance Imaging (MRI) brain templates for interpretation of neuroimaging data. Variations in the neuroanatomy in a genetically heterogeneous population make the development of a population-specific brain template for the Indian subcontinent imperative. A dataset of high-resolution 3D T1, T2-weighted, and FLAIR images acquired from a group of 113 volunteers (M/F - 56/57, mean age-28.96 ± 7.80 years) are used to construct T1, T2-weighted, and FLAIR templates, collectively referred to as Indian Brain Template, “BRAHMA”. A processing pipeline is developed and implemented in a MATLAB based toolbox for template construction and generation of tissue probability maps and segmentation atlases, with additional labels for deep brain regions such as the Substantia Nigra generated from the T2-weighted and FLAIR templates. The use of BRAHMA template for analysis of structural and functional neuroimaging data obtained from Indian participants, provides improved accuracy with statistically significant results over that obtained using the ICBM-152 (International Consortium for Brain Mapping) template. Our results indicate that segmentations generated on structural images are closer in volume to those obtained from registration to the BRAHMA template than to the ICBM-152. Furthermore, functional MRI data obtained for Working Memory and Finger Tapping paradigms processed using the BRAHMA template show a significantly higher percentage of the activation area than ICBM-152 in relevant brain regions, i.e. the left middle frontal gyrus, and the left and right precentral gyri, respectively. The availability of different image contrasts, tissue maps, and segmentation atlases makes the BRAHMA template a comprehensive tool for multi-modal image analysis in laboratory and clinical settings.     

Fast T2-weighted MR imaging: impact of variation in pulse sequence parameters on image quality and artifacts

The purpose of this study was to quantitatively evaluate in a phantom model the practical impact of alteration of key imaging parameters on image quality and artifacts for the most commonly used fast T(2)-weighted MR sequences. These include fast spin-echo (FSE), single shot fast spin-echo (SSFSE), and spin-echo echo-planar imaging (EPI) pulse sequences. We developed a composite phantom with different T1 and T2 values, which was evaluated while stationary as well as during periodic motion. Experiments involved controlled variations in key parameters including effective TE, TR, echo spacing (ESP), receive bandwidth (BW), echo train length (ETL), and shot number (SN). Quantitative analysis consisted of signal-to-noise ratio (SNR), image nonuniformity, full-width-at-half-maximum (i.e., blurring or geometric distortion) and ghosting ratio. Among the fast T(2)-weighted sequences, EPI was most sensitive to alterations in imaging parameters. Among imaging parameters that we tested, effective TE, ETL, and shot number most prominently affected image quality and artifacts. Short T(2) objects were more sensitive to alterations in imaging parameters in terms of image quality and artifacts. Optimal clinical application of these fast T(2)-weighted imaging pulse sequences requires careful attention to selection of imaging parameters.     

Short TE in vivo (1)H MR spectroscopic imaging at 1.5 T: acquisition and automated spectral analysis

Spectral analysis of short TE in vivo proton magnetic resonance spectroscopic imaging (MRSI) data are complicated by the presence of spectral overlap, low signal to noise and uncharacterized signal contributions. In this study, it is shown that an automated data analysis method can be used to generate metabolite images from MRSI data obtained from human brain at TE = 25 ms and 1.5 T when optimized pulse sequences and a priori metabolite knowledge are used. The analysis approach made use of computer simulation methods to obtain a priori spectral information of the metabolites of interest and utilized a combination of parametric spectral modeling and non-parametric signal characterization for baseline fitting. This approach was applied to data from optimized PRESS-SI and multi-slice spin-echo SI acquisitions, for which sample spectra and metabolite images are shown.     

CO_2/NH_3复叠系统热力分析与冷凝蒸发器冷凝温度的优化

对CO2/NH3复叠制冷系统进行合理的假设,并将与压比有关的压缩机等熵效率拟合公式引用到计算中,其结果与实验数据吻合的比较好。通过热力分析,可知系统各主要部件由不可逆而多消耗的附加功在不同的Tcas_c下对系统的影响程度是不同的。对数据进行分析并应用多元线性回归法拟合出以Te、Tc和ΔT为自变量的最优Tcas_c及相应COPmax数学表达式。     

Cardiac T2 measurements in patients with iron overload: a comparison of imaging parameters and analysis techniques

Measurement of cardiac T2 has emerged as an important tool to noninvasively quantify cardiac iron concentration in order to detect preclinical evidence of toxic levels and titrate chelation therapy. However, there exists variation among practitioners in cardiac T2 measurement methods. This study examines the impact of different imaging parameters and data analysis techniques on the calculated cardiac R2 (1/T2) in patients at risk for cardiac siderosis. The study group consisted of 36 patients with thalassemia syndromes who had undergone clinical magnetic resonance imaging assessment of cardiac siderosis using a standardized protocol and who were selected to yield a broad range of cardiac R2 values. Cardiac R2 measurements were performed on a 1.5-T scanner using an electrocardiogram-gated, segmented, multiecho gradient echo sequence obtained in a single breath-hold. R2 was calculated from the signal intensity versus echo time data in the ventricular septum on a single midventricular short-axis slice. There was good agreement between R2 measured with a blood suppression prepulse (black blood technique) and without (mean difference 6.0 ± 10.7 Hz). The black blood technique had superior within-study reproducibility (R2 mean difference 1.6 ± 8.6 Hz versus 2.7 ± 14.6 Hz) and better interobserver agreement (R2 mean difference 3.4 ± 8.2 Hz versus 8.3 ± 16.5 Hz). With the same minimum echo time, the use of small (1.0 ms) versus large (2.2 ms) echo spacing had minimal impact on cardiac R2 (mean difference 0.3 ± 8.7 Hz). The application of a region-of-interest-based versus a pixel-based data analysis also had little effect on cardiac R2 calculation (mean difference 8.4 ± 6.9 Hz). With black blood images, fitting the signal curve to a monoexponential decay or to a monoexponential decay with a constant offset yielded similar R2 values (mean difference 3.4 ± 8.1 Hz). In conclusion, the addition of a blood suppression prepulse for cardiac R2 measurement yields similar R2 values and improves reproducibility and interobserver agreement. The findings regarding other variations may be helpful in establishing a broadly accepted imaging and analysis technique for cardiac R2 calculation.     

Quantification of low fat contents: a comparison of MR imaging and spectroscopy methods at 1.5 and 3 T

Magnetic resonance spectroscopy (MRS) has long been considered the golden standard for non-invasive measurement of tissue fat content. With improved techniques for fat/water separation, imaging has become an alternative to MRS for fat quantification. Several imaging models have been proposed, but their performance relative to MRS at very low fat contents is yet not fully established. In this work, imaging and spectroscopy were compared at 1.5 T and 3 T in phantoms with 0-3% fat fraction (FF). We propose a multispectral model with individual a priori R₂ relaxation rates for water and fat, and a common unknown R₂′ relaxation. Magnitude and complex image reconstructions were also compared. Best accuracy was obtained with the imaging method at 1.5 T. At 3 T, the FFs were underestimated due to larger fat-water phase shifts. Agreement between measured and true FF was excellent for the imaging method at 1.5 T (imaging: FF_meas= 0.98 FF_true− 0.01%, spectroscopy: FF_meas= 0.77 FF_true+ 0.08%), and fair at 3 T (imaging: FF_meas= 0.91 FF_true− 0.19%, spectroscopy: FF_meas= 0.79 FF_true+ 0.02%). The imaging method was able to quantify FFs down to approx. 0.5%. We conclude that the suggested imaging model is capable of fat quantification with accuracy and precision similar to or better than spectroscopy and offers an improvement vs. a model with a common R₂* relaxation only.     

On- and off-resonance spin-lock MR imaging of normal human brain at 0.1 T: possibilities to modify image contrast

The aim of the present investigation was to determine spin lock (SL) relaxation parameters for the normal brain tissues and thus, to provide basis for optimizing the imaging contrast at 0.1 T. 68 healthy volunteers were included. On-resonance spin lock relaxation time (T_1ρ) and off-resonance spin lock relaxation parameters (T_1ρ^off, M_e/M_o), MT parameters (T_1sat, M_s/M_o), and T₁, T₂ were determined for the cortical gray matter, and for the frontal and parietal white matters. The T_1ρ for the frontal and parietal white matters ranged from 110 to 133 ms and from 122 to 155 ms with locking field strengths from 50 μT to 250 μT, respectively. Accordingly, the values for the gray matter ranged from 127 to 155 ms. With a locking field strength of 50 μT, T_1ρ^off for the frontal and parietal white matters were from 114 to 217 ms and from 126 to 219 ms, and for the gray matter from 136 to 267 ms with the angle between the effective magnetic field (B_eff) and the z-axis (θ) ranging from 60° to 15°, respectively. The T_1ρ of the white and gray matters increased significantly with increasing locking field amplitude (p < 0.001). The T_1ρ^off decreased significantly with increasing θ (p < 0.001). T_1ρ and T_1ρ^off with θ ≥ 30° were statistically significantly shorter in the frontal than in the parietal white matters (p < 0.05). The duration, amplitude and θ of the locking pulse provide additional parameters to optimize contrast in brain SL imaging.     

Conventional high resolution versus fast T(2)-weighted MR imaging of the heart: assessment of reperfusion induced myocardial injury in an animal model

Cardiac image quality in terms of spatial resolution and signal contrast was assessed for conventional and newly developed T(2)-weighted fast spin-echo imaging with high k-space segmentation. The capability in revealing regional myocardial edema and cellular damage was examined by a porcine model using histopathologic correlation. Twelve porcine hearts were excised from slaughtered animals and instantly perfused with 1000 mL cold cardioplegic solution. After 4 h of cold ischemia the hearts were reperfused for one hour using a "Langendorff" perfusion model followed by MR imaging at 1.5 Tesla. Three additional pig hearts served as controls and were studied by MR directly after harvesting. Histopathological analysis of regional tissue changes was performed macro- and microscopically. Short axis T(2)-weighted (3000/45 and 90) high quality fast spin-echo (FSE) images were recorded without cardiac action and signal intensity was correlated with histology. These images also served as gold standard for evaluation of newly developed faster sequences allowing measuring times shorter than 20 s. Fast T(2)-weighted imaging comprised single-slice fast spin echo (moderate echo train length of 23 echoes, FSE(m)), and multi-slice single-shot half-Fourier fast spin-echo (71 echoes, FSE(HASTE)) sequences, supplemented by versions with inversion recovery preparation (FSE(m)IR and FSE(HASTE)IR). Systolic function after reperfusion was restored in 10 porcine hearts. Tissue alterations included myocardial edema and contraction band necrosis which was found to be most severe in myocardium with maximum T(2) SI. Especially FSE(m) and FSE(m)IR sequences allowed differentiation of all categories of tissue damage on a high level of significance. In contrast, single-shot FSE(HASTE) and FSE(HASTE)IR sequences did not provide sufficient image quality to discriminate moderate and severe myocardial damage (p > 0.05). Different degrees of myocardial injury after ischemia and reperfusion can be staged by MR imaging, especially using conventional high resolution T(2)-weighted FSE sequences. The animal study indicates that fast T(2)-weighted FSE(m) and FSE(m)IR sequences lead to superior image quality and diagnostic accuracy compared to FSE(HASTE) and FSE(HASTE)IR imaging.