Accounting for signal loss due to dephasing in the correction of distortions in gradient-echo EPI via nonrigid registration

Gradient-echo (GE) echo planar imaging (EPI) is susceptible to both geometric distortions and signal loss. This paper presents a retrospective correction approach based on nonrigid image registration. A new physics-based intensity correction factor derived to compensate for intravoxel dephasing in GE EPI images is incorporated into a previously reported nonrigid registration algorithm. Intravoxel dephasing causes signal loss and thus intensity attenuation in the images. The new rephasing factor we introduce, which changes the intensity of a voxel in images during the registration, is used to improve the accuracy of the intensity-based nonrigid registration method and mitigate the intensity attenuation effect. Simulation-based experiments are first used to evaluate the method. A magnetic resonance (MR) simulator and a real field map are used to generate a realistic GE EPI image. The geometric distortion computed from the field map is used as the ground truth to which the estimated nonrigid deformation is compared. We then apply the algorithm to a set of real human brain images. The results show that, after registration, alignment between EPI and multi-shot, spin-echo images, which have relatively long acquisition times but negligible distortion, is improved and that signal loss caused by dephasing can be recovered.     

An inverse problem approach to the correction of distortion in EPI images

Magnetic resonance imaging using the echo planar imaging (EPI) technique is particularly sensitive to main (B0) field inhomogeneities. The primary effect is geometrical distortion in the phase encoding direction. In this paper, we present a method based on the conjugate gradient algorithm to correct for this geometrical distortion, by solving the EPI imaging equation. Two versions are presented: one that attempts to solve the full four-dimensional (4-D) imaging equation, and one that independently solves for each profile along the blip encoding direction. Results are presented for both phantom and in vivo brain EPI images and compared with other proposed correction methods.     

Conjugate phase MRI reconstruction with spatially variant sample density correction

A new image reconstruction method to correct for the effects of magnetic field inhomogeneity in non-Cartesian sampled magnetic resonance imaging (MRI) is proposed. The conjugate phase reconstruction method, which corrects for phase accumulation due to applied gradients and magnetic field inhomogeneity, has been commonly used for this case. This can lead to incomplete correction, in part, due to the presence of gradients in the field inhomogeneity function. Based on local distortions to the k-space trajectory from these gradients, a spatially variant sample density compensation function is introduced as part of the conjugate phase reconstruction. This method was applied to both simulated and experimental spiral imaging data and shown to produce more accurate image reconstructions. Two approaches for fast implementation that allow the use of fast Fourier transforms are also described. The proposed method is shown to produce fast and accurate image reconstructions for spiral sampled MRI.     

A method of generalized projections (MGP) ghost correction algorithm for interleaved EPI

Investigations into the method of generalized projections (MGP) as a ghost correction method for interleaved EPI are described. The technique is image-based and does not require additional reference scans. The algorithm was found to be more effective if a priori knowledge was incorporated to reduce the degrees of freedom, by modeling the ghosting as arising from a small number of phase offsets. In simulations with phase variation between consecutive shots for n-interleaved echo planar imaging (EPI), ghost reduction was achieved for n = 2 only. With no phase variation between shots, ghost reduction was obtained with n up to 16. Incorporating a relaxation parameter was found to improve convergence. Dependence of convergence on the region of support was also investigated. A fully automatic version of the method was developed, using results from the simulations. When tested on in vivo 2-, 16-, and 32-interleaved spin-echo EPI data, the method achieved deghosting and image restoration close to that obtained by both reference scan and odd/even filter correction, although some residual artifacts remained.     

A New Distortion Model for Strong Inhomogeneity Problems in Echo-Planar MRI

This paper proposes a new distortion model for strong inhomogeneity problems in echo planar imaging (EPI). Fast imaging sequences in magnetic resonance imaging (MRI), such as EPI, are very important in applications where temporal resolution or short total acquisition time is essential. Unfortunately, fast imaging sequences are very sensitive to variations in the homogeneity of the main magnetic field. The inhomogeneity leads to geometrical distortions and intensity changes in the image reconstructed via fast Fourier transform. Also, under strong inhomogeneity, the accelerated intravoxel dephase may overly attenuate signals coming from regions with higher inhomogeneity variations. Moreover, coarse discretization schemes for the inhomogeneity are not able to cope with this problem, producing discretization artifacts when large inhomogeneity variations occur. Most of the existing models do not attempt to solve this problem. In this paper, we propose a modification of the discrete distortion model to incorporate the effects of the intravoxel inhomogeneity and to minimize the discretization artifacts. As a result, these problems are significantly reduced. Extensive experiments are shown to demonstrate the achieved improvements. Also, the performance of the new model is evaluated for conjugate phase, least squares method (minimized iteratively using conjugated gradients), and regularized methods (using a total variation penalty).      

Iterative Off-Resonance and Signal Decay Estimation and Correction for Multi-Echo MRI

Signal dephasing due to field inhomogeneity and signal decay due to transverse relaxation lead to perturbations of the Fourier encoding commonly applied in magnetic resonance imaging. Hence, images acquired with long readouts suffer from artifacts such as blurring, distortion, and intensity variation. These artifacts can be removed in reconstruction, usually based on separately collected information in form of field and relaxation maps. In this work, a recently proposed gridding-based algorithm for off-resonance correction is extended to also address signal decay. It is integrated into a new fixed-point iteration, which permits the joint estimation of an image and field and relaxation maps from multi-echo acquisitions. This approach is then applied in simulations and in vivo experiments and demonstrated to improve both images and maps. The rapid convergence of the fixed-point iteration in combination with the efficient gridding-based correction promises to render the running time of such a joint estimation acceptable.      

一种改进的EPI伪影校正算法

EPI是功能磁共振成像(fMRI)广泛采用的一种扫描技术。成像物体的磁敏感性、化学位移、静磁场不均匀性以及系统硬件性能的不完善等因素导致EPI图像在相位编码方向存明显的ghost伪影,严重破坏了图像的质量。研究基于图像的后处理方法校正EPI伪影具有明显的实际临床应用价值。首先分析了现行相位校正算法和相位恢复算法的不足之处,然后提出了一种改进的EPI伪影校正算法。改进的算法充分利用两种方法的优点,并克服了各自的缺点,较好地实现了伪影校正。通过对实际的phantom图像处理,阐明了改进算法的稳定性及可靠性。     

Simultaneous correction of ghost and geometric distortion artifactsin EPI using a multiecho reference scan

A computationally efficient technique is described for the simultaneous removal of ghosting and geometrical distortion artifacts in echo-planar imaging (EPI) utilizing a multiecho, gradient-echo reference scan. Nyquist ghosts occur in EPI reconstructions because odd and even lines of k-space are acquired with opposite polarity, and experimental imperfections such as gradient eddy currents, imperfect pulse sequence timing, B0 field inhomogeneity, susceptibility, and chemical shift result in the even and odd lines of k-space being offset by different amounts relative to the true center of the acquisition window. Geometrical distortion occurs due to the limited bandwidth of the EPI images in the phase-encode direction. This distortion can be problematic when attempting to overlay an activation map from a functional magnetic resonance imaging experiment generated from EPI data on a high-resolution anatomical image. The method described here corrects for geometrical distortion related to B0 inhomogeneity, gradient eddy currents, radio-frequency pulse frequency offset, and chemical shift effect. The algorithm for removing ghost artifacts utilizes phase information in two dimensions and is, thus, more robust than conventional one-dimensional methods. An additional reference scan is required which takes approximately 2 min for a matrix size of 64 X 64 and a repetition time of 2 s. Results from a water phantom and a human brain at 3 T demonstrate the effectiveness of the method for removing ghosts and geometric distortion artifacts.     

Reconstruction by weighted correlation for MRI with time-varying gradients

A general reconstruction algorithm for magnetic resonance imaging (MRI) with gradients having arbitrary time dependence is presented. This method estimates spin density by calculating the weighted correlation of the observed free induction decay signal and the phase modulation function at each point. A theorem which states that this method can be derived from the conditions of linearity and shift invariance is presented. Since these conditions are general, most of the MRI reconstruction algorithms proposed so far are equivalent to the weighted correlation method. An explicit representation of the point spread function (PSF) in the weighted correlation method is given. By using this representation, a method to control the PSF and the static field inhomogeneity effects is studied. A correction method for the inhomogeneity is proposed, and a limitation is clarified. Some simulation results are presented.     

The computation of MR image distortions caused by tissue susceptibility using the boundary element method

Static field inhomogeneity in magnetic resonance (MR) imaging produces geometrical distortions which restrict the clinical applicability of MR images, e.g., for planning of precision radiotherapy. The authors describe a method to compute distortions which are caused by the difference in magnetic susceptibility between the scanned object and the surrounding air. Such a method is useful for understanding how the distortions depend on the object geometry, and for correcting for geometrical distortions, and thereby improving MR/CT registration algorithms. The geometric distortions in MR can be directly computed from the magnetic field inhomogeneity and the applied gradients. The boundary value problem of computing the magnetic field inhomogeneity caused by susceptibility differences is analyzed. It is shown that the boundary element method (BEM) has several advantages over previously applied methods to compute the magnetic field. Starting from the BEM and the assumption that the susceptibilities are very small (typically O(10(-5)) or less), a formula is derived to compute the magnetic field directly, without the need to solve a large system of equations. The method is computationally very efficient when the magnetic field is needed at a limited number of points, e.g., to compute geometrical distortions of a set of markers or a single surface. In addition to its computational advantage the method proves to be efficient to correct for the lack of data outside the scan which normally causes large artifacts in the computed magnetic field. These artifacts can be reduced by assuming that at the scan boundary the object extends to infinity in the form of a generalized cylinder. With the adaptation of the BEM this assumption is equivalent to simply omitting the scan boundary from the computations. To the authors' knowledge, no such simple correction method exists for other computation methods. The accuracy of the algorithm was tested by comparing the BEM solution with the analytical solution for a sphere. When the applied homogeneous field is 1.5 T the agreement between both methods was within 0.11.10(-6) T. As an example, the method was applied to compute the displacement vector field of the surface of a human head, derived from an MR imaging data set. This example demonstrates that the distortions can be as large as 3 mm for points just outside the head when a gradient strength of 3 mT/m is used. It was also observed that distortion within the head can be described accurately as a linear scaling in the axial direction.     

Joint Estimation and Correction of Geometric Distortions for EPI Functional MRI Using Harmonic Retrieval

Magnetic resonance imaging (MRI) uses applied spatial variations in the magnetic field to encode spatial position. Therefore, nonuniformities in the main magnetic field can cause image distortions. In order to correct the image distortions, it is desirable to simultaneously acquire data with a field map in registration. We propose a joint estimation (JE) framework with a fast, noniterative approach using harmonic retrieval (HR) methods, combined with a multi-echo echo-planar imaging (EPI) acquisition. The connection with HR establishes an elegant framework to solve the JE problem through a sequence of 1-D HR problems in which efficient solutions are available. We also derive the condition on the smoothness of the field map in order for HR techniques to recover the image with high signal-to-noise ratio. Compared to other dynamic field mapping methods, this method is not constrained by the absolute level of the field inhomogeneity over the slice, but relies on a generous pixel-to-pixel smoothness. Moreover, this method can recover image, field map, and T2* map simultaneously.      

Parametric estimate of intensity inhomogeneities applied to MRI

This paper presents a new approach to the correction of intensity inhomogeneities in magnetic resonance imaging (MRI) that significantly improves intensity-based tissue segmentation. The distortion of the image brightness values by a low-frequency bias field impedes visual inspection and segmentation. The new correction method called parametric bias field correction (PABIC) is based on a simplified model of the imaging process, a parametric model of tissue class statistics, and a polynomial model of the inhomogeneity field. We assume that the image is composed of pixels assigned to a small number of categories with a priori known statistics. Further we assume that the image is corrupted by noise and a low-frequency inhomogeneity field. The estimation of the parametric bias field is formulated as a nonlinear energy minimization problem using an evolution strategy (ES). The resulting bias field is independent of the image region configurations and thus overcomes limitations of methods based on homomorphic filtering. Furthermore, PABIC can correct bias distortions much larger than the image contrast. Input parameters are the intensity statistics of the classes and the degree of the polynomial function. The polynomial approach combines bias correction with histogram adjustment, making it well suited for normalizing the intensity histogram of datasets from serial studies. We present simulations and a quantitative validation with phantom and test images. A large number of MR image data acquired with breast, surface, and head coils, both in two dimensions and three dimensions, have been processed and demonstrate the versatility and robustness of this new bias correction scheme.     

Regularized field map estimation in MRI

In fast magnetic resonance (MR) imaging with long readout times, such as echo-planar imaging (EPI) and spiral scans, it is important to correct for the effects of field inhomogeneity to reduce image distortion and blurring. Such corrections require an accurate field map, a map of the off-resonance frequency at each voxel. Standard field map estimation methods yield noisy field maps, particularly in image regions with low spin density. This paper describes regularized methods for field map estimation from two or more MR scans having different echo times. These methods exploit the fact that field maps are generally smooth functions. The methods use algorithms that decrease monotonically a regularized least-squares cost function, even though the problem is highly nonlinear. Results show that the proposed regularized methods significantly improve the quality of field map estimates relative to conventional unregularized methods.      

Correction for Susceptibility-Induced Distortion in Echo-Planar Imaging Using Field Maps and Model-Based Point Spread Function

Susceptibility-induced distortion is one of the major artifacts in echo-planar imaging (EPI), and many solutions have been proposed for the problem, including the Fourier method and the point spread function (PSF) method. In this paper, a framework unifying both methods is presented. Under this framework, a model-based PSF method is proposed in which the PSF of the source object is modeled along with a single field map measured by TE-offset reference scans. EPI images of a phantom and a healthy human subject were acquired, and the results of distortion correction by the Fourier method, linear interpolation method, and the model-based PSF method were compared. The results showed that the model-based PSF method could correct for geometric distortion and signal intensity distortion satisfactorily, avoiding the rippling artifact shown in the Fourier method. In conclusion, the proposed framework gave us an overall picture of how different correction methods work. The model-based PSF method, which required fewer reference scans and less computational load, was more clinically feasible than other methods.      

Multi-layer and Multi-scale feature aggregation for DIBR-Synthesized image quality assessment

Depth-Image-Based Rendering (DIBR) is one of the main fundamental techniques for generating new viewpoints in 3D video applications such as multi-viewpoint video (MVV), free viewpoint video (FVV) and virtual reality (VR). Due to the imperfections of color images, depth maps or texture restoration techniques, several types of distortions occur in synthesized views. However, most of related works evaluated the quality of DIBR-synthesized views by only detecting a specific type of distortion, such as stretching, black holes, blurring, etc., which were unable to accurately evaluate the quality of DIBR-synthesized views. In this paper, a new no-reference image quality assessment method is proposed to evaluate the quality of DIBR-synthesized images by combining multi-layer and multi-scale features of images. To be specific, the distortions introduced by different stages of virtual viewpoint synthesis are first analyzed, and then multi-layer and multi-scale features are extracted to estimate the degree of texture and structure distortions. As a result, individual quality scores associated with two types of distortions (e.g., structural distortion and texture distortion) are aggregated to an overall image quality. Experimental results on two publicly available DIBR datasets show that the method has better performance than the state-of-the-art models.Index Terms: image quality assessment, DIBR-synthesized image, distortion correction, BIQA.     

Automated model-based bias field correction of MR images of the brain

We propose a model-based method for fully automated bias field correction of MR brain images. The MR signal is modeled as a realization of a random process with a parametric probability distribution that is corrupted by a smooth polynomial inhomogeneity or bias field. The method we propose applies an iterative expectation-maximization (EM) strategy that interleaves pixel classification with estimation of class distribution and bias field parameters, improving the likelihood of the model parameters at each iteration. The algorithm, which can handle multichannel data and slice-by-slice constant intensity offsets, is initialized with information from a digital brain atlas about the a priori expected location of tissue classes. This allows full automation of the method without need for user interaction, yielding more objective and reproducible results. We have validated the bias correction algorithm on simulated data and we illustrate its performance on various MR images with important field inhomogeneities. We also relate the proposed algorithm to other bias correction algorithms.     

Improving geometric accuracy in the presence of susceptibility difference artifacts produced by metallic implants in magnetic resonance imaging

Geometric and intensity distortions due to the presence of metallic implants in magnetic resonance imaging impede the full exploitation of this advanced imaging modality. The aim of this study is to provide a method for (a) quantifying and (b) reducing the implant distortions in patient images. Initially, a set of reference images (without distortion) was obtained by imaging a custom-designed three-dimensional grid phantom. Corresponding test images (containing the distortion) were acquired with the same imaging parameters, after positioning a specific metallic implant in the grid phantom. After determining: 1) the nonrecoverable; 2) the distorted, but recoverable; and 3) the unaffected areas, a point-based thin-plate spline image registration algorithm was employed to align the reference and test images. The calculated transformation functions utilized to align the image pairs described the implant distortions and could therefore be used to correct any other images containing the same distortions. The results demonstrate successful correction of grid phantom images with a metallic implant. Furthermore, the calculated correction was applied to porcine thigh images bearing the same metallic implant, simulating a patient environment. Qualitative and quantitative assessments of the proposed correction method are included.     

流场测速中基于深度卷积神经网络的光学畸变校正技术

基于光学成像的流场测量技术,如粒子图像测速技术（PIV）,易受到因流体中折射率的不均匀性或晃动的介质边界引起的光学畸变而带来的影响。这些畸变会使得示踪粒子在图像上的位置分布产生误差且严重影响图像清晰度,从而增大流场速度测量的误差。为了提高光学流场速度测量的测量精度,自适应光学系统可以应用于其中去校正光学畸变。基于图像流场测量中的光学像差具有频率高,动态范围大,空间分辨率高等特点,对于这一应用场景,基于波前校正器件的自适应光学系统受到了器件本身性能的影响。基于深度学习的自适应光学技术在流场测量中的应用,建立了一种基于深度神经网络的无波前校正器件自适应光学校正技术,以深度神经网络代替传统的波前校正器件,用于粒子图像测速技术中的光学畸变校正。为了生成神经网络所需要的训练和测试数据集,搭建了可以实现波前测量的粒子图像测速实验平台,分析并建立了光学畸变在粒子图像上的图像退化模型。最后,以校正后PIV图像的校正效果和流场速度测量结果作为评价标准,对所建立神经网络的畸变校正性能进行了分析。     

Joint MAP registration and high-resolution image estimation using asequence of undersampled images

In many imaging systems, the detector array is not sufficiently dense to adequately sample the scene with the desired field of view. This is particularly true for many infrared focal plane arrays. Thus, the resulting images may be severely aliased. This paper examines a technique for estimating a high-resolution image, with reduced aliasing, from a sequence of undersampled frames. Several approaches to this problem have been investigated previously. However, in this paper a maximum a posteriori (MAP) framework for jointly estimating image registration parameters and the high-resolution image is presented. Several previous approaches have relied on knowing the registration parameters a priori or have utilized registration techniques not specifically designed to treat severely aliased images. In the proposed method, the registration parameters are iteratively updated along with the high-resolution image in a cyclic coordinate-descent optimization procedure. Experimental results are provided to illustrate the performance of the proposed MAP algorithm using both visible and infrared images. Quantitative error analysis is provided and several images are shown for subjective evaluation.     

Interplay between intensity standardization and inhomogeneity correction in MR image processing

Image intensity standardization is a postprocessing method designed for correcting acquisition-to-acquisition signal intensity variations (nonstandardness) inherent in magnetic resonance (MR) images. Inhomogeneity correction is a process used to suppress the low frequency background nonuniformities (inhomogeneities) of the image domain that exist in MR images. Both these procedures have important implications in MR image analysis. The effects of these postprocessing operations on improvement of image quality in isolation has been well documented. However, the combined effects of these two processes on MR images and how the processes influence each other have not been studied thus far. In this paper, we evaluate the effect of inhomogeneity correction followed by standardization and vice-versa on MR images in order to determine the best sequence to follow for enhancing image quality. We conducted experiments on several clinical and phantom data sets (nearly 4000 three-dimensional MR images were analyzed) corresponding to four different MRI protocols. Different levels of artificial nonstandardness, and different models and levels of artificial background inhomogeneity were used in these experiments. Our results indicate that improved standardization can be achieved by preceding it with inhomogeneity correction. There is no statistically significant difference in image quality obtained between the results of standardization followed by correction and that of correction followed by standardization from the perspective of inhomogeneity correction. The correction operation is found to bias the effect of standardization. We demonstrate this bias both qualitatively and quantitatively by using two different methods of inhomogeneity correction. We also show that this bias in standardization is independent of the specific inhomogeneity correction method used. The effect of this bias due to correction was also seen in magnetization transfer ratio (MTR) images, which are naturally endowed with the standardness property. Standardization, on the other hand, does not seem to influence the correction operation. It is also found that longer sequences of repeated correction and standardization operations do not considerably improve image quality. These results were found to hold for the clinical and the phantom data sets, for different MRI protocols, for different levels of artificial nonstandardness, for different models and levels of artificial inhomogeneity, for different correction methods, and for images that were endowed with inherent standardness as well as for those that were standardized by using the intensity standardization method. Overall, we conclude that inhomogeneity correction followed by intensity standardization is the best sequence to follow from the perspective of both image quality and computational efficiency.