Effects of polar sampling in k-space

Magnetic resonance imaging allows numerous k-space sampling schemes such as cartesian, polar, spherical, and other non-rectilinear trajectories. Non-rectilinear MR acquisitions permit fast scan times and can suppress motion artifacts. Still, these sampling schemes may adversely affect the image characteristics due to aliasing. Here, the Fourier aliasing effects of uniform polar sampling, i.e., equally spaced radial and azimuthal samples, are explained from the principal point spread function (PSF). The principal PSF is determined by assuming equally spaced concentric ring samples in k-space. The radial effects such as replication, smearing, truncation artifacts, and sampling requirements, are characterized based on the PSF.     

Iterative Next-Neighbor Regridding (INNG): improved reconstruction from nonuniformly sampled k-space data using rescaled matrices.

The reconstruction of MR images from nonrectilinearly sampled data is complicated by the fact that the inverse 2D Fourier transform (FT) cannot be performed directly on the acquired k-space data set. k-Space gridding is commonly used because it is an efficient reconstruction method. However, conventional gridding requires optimized density compensation functions (DCFs) to avoid profile distortions. Oftentimes, the calculation of optimized DCFs presents an additional challenge in obtaining an accurately gridded reconstruction. Another type of gridding algorithm, the block uniform resampling (BURS) algorithm, often requires singular value decomposition (SVD) regularization to avoid amplification of data imperfections, and under some conditions it is difficult to adjust the regularization parameters. In this work, new reconstruction algorithms for nonuniformly sampled k-space data are presented. In the newly proposed algorithms, high-quality reconstructed images are obtained from an iterative reconstruction that is performed using matrices scaled to sizes greater than that of the target image matrix. A second version partitions the sampled k-space region into several blocks to avoid limitations that could result from performing multiple 2D-FFTs on large data matrices. The newly proposed algorithms are a simple alternative approach to previously proposed optimized gridding algorithms.     

Deconvolution-interpolation gridding (DING): accurate reconstruction for arbitrary k-space trajectories.

A simple iterative algorithm, termed deconvolution-interpolation gridding (DING), is presented to address the problem of reconstructing images from arbitrarily-sampled k-space. The new algorithm solves a sparse system of linear equations that is equivalent to a deconvolution of the k-space with a small window. The deconvolution operation results in increased reconstruction accuracy without grid subsampling, at some cost to computational load. By avoiding grid oversampling, the new solution saves memory, which is critical for 3D trajectories. The DING algorithm does not require the calculation of a sampling density compensation function, which is often problematic. DING's sparse linear system is inverted efficiently using the conjugate gradient (CG) method. The reconstruction of the gridding system matrix is simple and fast, and no regularization is needed. This feature renders DING suitable for situations where the k-space trajectory is changed often or is not known a priori, such as when patient motion occurs during the scan. DING was compared with conventional gridding and an iterative reconstruction method in computer simulations and in vivo spiral MRI experiments. The results demonstrate a stable performance and reduced root mean square (RMS) error for DING in different k-space trajectories.     

MR coronary vessel wall imaging: comparison between radial and spiral k-space sampling

PURPOSE: To compare radial and spiral k-space sampling in navigator-gated ECG-triggered three-dimensional (3D) coronary vessel wall imaging. MATERIALS AND METHODS: The right coronary artery (RCA) vessel walls of eight healthy subjects were imaged using a modified double-inversion prepulse in concert with radial and spiral data acquisition. For data analysis, two investigators blinded to the sequence parameters subjectively assessed image quality in terms of artifacts and vessel wall visualization. Objective measures of the signal-to-noise ratio (SNR), contrast-to-noise ratio (CNR), and vessel wall definition were also determined. RESULTS: Radial k-space sampling demonstrated fewer artifacts and led to improved visualization of the coronary vessel wall compared to spiral imaging (P < 0.05). This finding was also reflected in a better vessel wall definition using radial data acquisition (P < 0.05). SNR and CNR were found to be higher when spiral k-space sampling was used (n.s.). CONCLUSION: Radial k-space sampling in concert with free-breathing navigator-gated cardiac-triggered MRI of the coronary vessel wall resulted in fewer motion artifacts and improved vessel wall definition compared to spiral k-space sampling. The proposed approach therefore appears to be preferable.     

Reconstruction of MR images from data acquired on an arbitrary k-space trajectory using the same-image weight.

A sampling density compensation function denoted "same-image (SI) weight" is proposed to reconstruct MR images from the data acquired on an arbitrary k-space trajectory. An equation for the SI weight is established on the SI criterion and an iterative scheme is developed to find the weight. The SI weight is then used to reconstruct images from the data calculated on a random trajectory in a numerical phantom case and from the data acquired on interleaved spirals in an in vivo experiment, respectively. In addition, Pipe and Menon's weight (MRM 1999;41:179-186) is also used in the reconstructions to make a comparison. The images obtained with the SI weight were found to be slightly more accurate than those obtained with Pipe's weight.     

Partial k-space reconstruction in single-shot diffusion-weighted echo-planar imaging.

Partial k-space sampling is frequently used in single-shot diffusion-weighted echo-planar imaging (DW-EPI) to reduce the TE and thereby improve the SNR. However, it increases the sensitivity of the technique to bulk rotational motion, which introduces a phase gradient across the tissue that shifts the echo in k-space. If the echo is displaced into the high spatial frequencies, conventional homodyne reconstruction fails, causing intensity oscillations across the image. Zero-padding, on the other hand, compromises the image resolution and may cause truncation artifacts. We present an adaptive version of the homodyne algorithm that detects the location of the echo in k-space and adjusts the center and width of the homodyne filters accordingly. The adaptive algorithm produces artifact-free images when the echo is shifted into the high positive k-space range, and reduces to the standard homodyne algorithm in the absence of bulk motion.     

Rapid PROPELLER‐MRI: A combination of iterative reconstruction and under‐sampling

Purpose:

To develop a technique that is able to reduce acquisition time and remove uneven blurring in reconstructed image for PROPELLER MRI. By using under‐sampling and iterative reconstruction, this proposed technique will be less sensitive to subject motion.

Materials and Methods:

Numerical simulations, as well as experiments on a phantom and healthy human subjects were performed to demonstrate advantages of a combination of under‐sampled acquisition and iterative reconstruction. Method of motion correction was modified to increase accuracy of motion correction for the under‐sampled PROPELLER acquisition.

Results:

It was demonstrated that the proposed approach achieved substantial acceleration of PROPELLER acquisition while maintaining its motion correction advantage.

Conclusion:

An effective method for reducing imaging time in PROPELLER was introduced in this study, which minimizes typical under‐sampling artifacts without uneven spatial resolution and maintains the ability of motion correction. J. Magn. Reson. Imaging 2012;36:1241–1247. © 2012 Wiley Periodicals, Inc.     

Parallel magnetic resonance imaging with adaptive radius in k-space (PARS): constrained image reconstruction using k-space locality in radiofrequency coil encoded data.

A parallel image reconstruction algorithm is presented that exploits the k-space locality in radiofrequency (RF) coil encoded data. In RF coil encoding, information relevant to reconstructing an omitted datum rapidly diminishes as a function of k-space separation between the omitted datum and the acquired signal data. The proposed method, parallel magnetic resonance imaging with adaptive radius in k-space (PARS), harnesses this physical property of RF coil encoding via a sliding-kernel approach. Unlike generalized parallel imaging approaches that might typically involve inverting a prohibitively large matrix for arbitrary sampling trajectories, the PARS sliding-kernel approach creates manageable and distributable independent matrices to be inverted, achieving both computational efficiency and numerical stability. An empirical method designed to measure total error power is described, and the total error power of PARS reconstructions is studied over a range of k-space radii and accelerations, revealing "minimal-error" conditions at comparatively modest k-space radii. PARS reconstructions of undersampled in vivo Cartesian and non-Cartesian data sets are shown and are compared selectively with traditional SENSE reconstructions. Various characteristics of the PARS k-space locality constraint (such as the tradeoff between signal-to-noise ratio and artifact power and the relationship with iterative parallel conjugate gradient approaches or nonparallel gridding approaches) are discussed.     

The modulation transfer function and signal-to-noise ratio of different digital filters: a technical approach

Objectives

The aim of this study was to illustrate the influence of digital filters on the signal-to-noise ratio (SNR) and modulation transfer function (MTF) of digital images. The article will address image pre-processing that may be beneficial for the production of clinically useful digital radiographs with lower radiation dose.

Methods

Three filters, an arithmetic mean filter, a median filter and a Gaussian filter (standard deviation (SD) = 0.4), with kernel sizes of 3 × 3 pixels and 5 × 5 pixels were tested. Synthetic images with exactly increasing amounts of Gaussian noise were created to gather linear regression of SNR before and after application of digital filters. Artificial stripe patterns with defined amounts of line pairs per millimetre were used to calculate MTF before and after the application of the digital filters.

Results

The Gaussian filter with a 5 × 5 kernel size caused the highest noise suppression (SNR increased from 2.22, measured in the synthetic image, to 11.31 in the filtered image). The smallest noise reduction was found with the 3 × 3 median filter. The application of the median filters resulted in no changes in MTF at the different resolutions but did result in the deletion of smaller structures. The 5 × 5 Gaussian filter and the 5 × 5 arithmetic mean filter showed the strongest changes of MTF.

Conclusions

The application of digital filters can improve the SNR of a digital sensor; however, MTF can be adversely affected. As such, imaging systems should not be judged solely on their quoted spatial resolutions because pre-processing may influence image quality.     

Performance of sampling density‐weighted and postfiltered density‐adapted projection reconstruction in sodium magnetic resonance imaging

Sampling density‐weighted apodization projection reconstruction sequences are evaluated for three‐dimensional radial imaging. The readout gradients of the sampling density‐weighted apodization sequence are designed such that the locally averaged sampling density matches a Hamming filter function. This technique is compared with density‐adapted projection reconstruction with nonfiltered and postfiltered image reconstruction. Sampling density‐weighted apodization theoretically allows for a 1.28‐fold higher signal‐to‐noise ratio compared with postfiltered density‐adapted projection reconstruction sequences, if T decay is negligible compared with the readout duration T_RO. Simulations of the point‐spread functions are performed for monoexponential and biexponential decay to investigate the effects of T decay on the performance of the different sequences. Postfiltered density‐adapted projection reconstruction performs superior to sampling density‐weighted apodization for large T_RO/T ratios [>1.36 (monoexponential decay); >0.35 (biexponential decay with T/T = 10)], if signal‐to‐noise ratio of point‐like objects is considered. In conclusion, it depends on the readout parameters, the T relaxation times, and the dimensions of the subject which of both sequences is most suitable. Magn Reson Med, 2013. © 2012 Wiley Periodicals, Inc.     

Alternate k-space sampling in EPI: Compensation for T2* and adjustable T2 weighting

In this work, preliminary results are described for a modification of the MBEST sampling scheme such that image resolution can be increased while preserving image contrast. In this new approach, a single spin-echo is used in sampling k-space. The basic idea relies on acquiring a conventional EPI image from the center of k-space and applying a ψ pulse to permit the acquisition of the two outer edges of k-space. Using this new approach, it is possible to obtain an enhancement in EPI image resolution, while reducing the extent of T₂* weighting. As a result, the resulting images possess reduced T₂* contrast and suffer less signal loss from T₂* effects such as spatial variations in susceptibility and field inhomogeneity.     

Radiation Dose Reduction via Sinogram Affirmed Iterative Reconstruction and Automatic Tube Voltage Modulation (CARE kV) in Abdominal CT

Objective

To evaluate the feasibility of sinogram-affirmed iterative reconstruction (SAFIRE) and automated kV modulation (CARE kV) in reducing radiation dose without increasing image noise for abdominal CT examination.

Materials and Methods

This retrospective study included 77 patients who received CT imaging with an application of CARE kV with or without SAFIRE and who had comparable previous CT images obtained without CARE kV or SAFIRE, using the standard dose (i.e., reference mAs of 240) on an identical CT scanner and reconstructed with filtered back projection (FBP) within 1 year. Patients were divided into two groups: group A (33 patients, CT scanned with CARE kV); and group B (44 patients, scanned after reducing the reference mAs from 240 to 170 and applying both CARE kV and SAFIRE). CT number, image noise for four organs and radiation dose were compared among the two groups.

Results

Image noise increased after CARE kV application (p < 0.001) and significantly decreased as SAFIRE strength increased (p < 0.001). Image noise with reduced-mAs scan (170 mAs) in group B became similar to that of standard-dose FBP images after applying CARE kV and SAFIRE strengths of 3 or 4 when measured in the aorta, liver or muscle (p ≥ 0.108). Effective doses decreased by 19.4% and 41.3% for groups A and B, respectively (all, p < 0.001) after application of CARE kV with or without SAFIRE.

Conclusion

Combining CARE kV, reduction of mAs from 240 to 170 mAs and noise reduction by applying SAFIRE strength 3 or 4 reduced the radiation dose by 41.3% without increasing image noise compared with the standard-dose FBP images.     

k-space interpretation of the Rose Model: noise limitation on the detectable resolution in MRI.

Noise limitation on the detected spatial resolution, described by the Rose Model, is well known in X-ray imaging and routinely used in designing X-ray imaging protocols. The purpose of this article is to revisit the Rose Model in the context of MRI where image data are acquired in the spatial frequency domain. A k-space signal-to-noise ratio (kSNR) is introduced to measure the relative signal and noise powers in a circular annulus in k-space. It is found that the kSNR diminishes rapidly with k-space radius. The Rose criterion that the voxel SNR approximately 4 is translated to kSNR cutoff values was tested using theoretical derivation and experimental histogram analysis. Experiments demonstrate that data acquisition beyond this cutoff k-space radius adds little or no information to the image. In order to reduce the noise limit on spatial resolution, the signal strength must be improved through means such as increasing the coil sensitivity, contrast enhancement, and signal averaging. This finding implies that the optimal k-space volume to be sampled or the optimal scan time in MRI should be matched to the relative SNR level.     

Combined Use of Automatic Tube Voltage Selection and Current Modulation with Iterative Reconstruction for CT Evaluation of Small Hypervascular Hepatocellular Carcinomas: Effect on Lesion Conspicuity and Image Quality

Objective

To assess the lesion conspicuity and image quality in CT evaluation of small (≤ 3 cm) hepatocellular carcinomas (HCCs) using automatic tube voltage selection (ATVS) and automatic tube current modulation (ATCM) with or without iterative reconstruction.

Materials and Methods

One hundred and five patients with 123 HCC lesions were included. Fifty-seven patients were scanned using both ATVS and ATCM and images were reconstructed using either filtered back-projection (FBP) (group A1) or sinogram-affirmed iterative reconstruction (SAFIRE) (group A2). Forty-eight patients were imaged using only ATCM, with a fixed tube potential of 120 kVp and FBP reconstruction (group B). Quantitative parameters (image noise in Hounsfield unit and contrast-to-noise ratio of the aorta, the liver, and the hepatic tumors) and qualitative visual parameters (image noise, overall image quality, and lesion conspicuity as graded on a 5-point scale) were compared among the groups.

Results

Group A2 scanned with the automatically chosen 80 kVp and 100 kVp tube voltages ranked the best in lesion conspicuity and subjective and objective image quality (p values ranging from < 0.001 to 0.004) among the three groups, except for overall image quality between group A2 and group B (p = 0.022). Group A1 showed higher image noise (p = 0.005) but similar lesion conspicuity and overall image quality as compared with group B. The radiation dose in group A was 19% lower than that in group B (p = 0.022).

Conclusion

CT scanning with combined use of ATVS and ATCM and image reconstruction with SAFIRE algorithm provides higher lesion conspicuity and better image quality for evaluating small hepatic HCCs with radiation dose reduction.     

Bunched phase encoding (BPE): a new fast data acquisition method in MRI.

A new fast data acquisition method, "Bunched Phase Encoding" (BPE), is presented. In conventional rectilinear data acquisition, only a readout gradient (and no phase encoding gradient) is applied when k-space data are acquired. Reduction of the number of phase encoding lines by increasing the phase encoding step size often leads to aliasing artifacts. Papoulis's generalized sampling theory asserts that in some cases aliasing artifact-free signals can be reconstructed even if the Nyquist criterion is violated in some regions of the Fourier domain. In this study, Papoulis's theoretical construct is exploited to reduce the number of acquired phase encoding lines. To achieve this, k-space data are sampled along a "zigzag" trajectory during each readout; samples are acquired at a sampling frequency higher than that of the normal rectilinear acquisition. The total number of TR cycles and, hence, the total scan time can be reduced. The resultant signal-to-noise ratio (SNR) often varies across the reconstructed image when using the BPE technique, and the image SNR depends on the reconstruction method. This work is comparable to a gradient based version of parallel imaging. Evidence suggests it may serve as the basis for new opportunities for fast data acquisition in MRI.     

64层螺旋CT机架旋转时间对图像质量的影响探讨

目的研究不同机架旋转时间对64层螺旋CT图像质量的影响。方法使用SOMATOM Sensation 64层螺旋CT。把del-ta模体沿Z轴固定于CT机架的中心,使用腹部螺旋扫描模式,进行扫描和重建,然后制作各位置图像序列的层敏感度曲线(SSP),并对各图像序列的SSP进行傅里叶变换得到调制传递函数(MTF)。后用腹部螺旋扫描模式对CT质控模体Catphan500进行扫描和重建,分别记录图像的最大线对数及其能分辨的各级对比度的最小目标的尺寸。结果0.5s组和1s组的MTF曲线几乎重合,5%MTF值分别为11.3LP/cm和11.9LP/cm;其空间分辨率和低对比度分辨率也完全相同。结论机架旋转时间0.5s组和1s组图像质量无差别。为缩短扫描时间,消除呼吸伪影,我们建议在腹部螺旋扫描时,机架旋转时间0.5作为常规应用。