A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Abstract A comparison of experimental imaging results obtained with linearly polarized and circularly polarized radiofrequency excitation and reception is presented. Simulation images in good agreement with the experimental scans are described. The simulations are calculated with a model in which a homogeneous, isotropic cylinder of lossy dielectric material and infinite axial extent is immersed in a uniform rf magnetic field perpendicular to the axis. It is found that with the usual linear polarization, reconstructions of uniform objects have regions of decreased intensity. These artifacts are shown to arise from dielectric standing wave effects and eddy currents. The effects become more severe as the frequency or object size is increased, and depend upon the complex conductivity of the object. Results indicate that a significant reduction in the artifact intensity is achieved when circular polarization is employed for both transmission and reception. The expected benefits of circular polarization over linear polarization in reduction of excitation power (up to 50% reduction) and signal-to-noise advantage (√2) have been realized in practice with cylindrical objects and human subjects. <s> BIB001 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Receiver coil response is a major cause of nonuniformities in magnetic resonance images. The spatial dependence of the sensitivity and phase of single-saddle receiver coils has been investigated quantitatively by calculating the H1 field and comparing the results with measurements of a uniform phantom. Agreement between the measurements and calculations is excellent. A method is developed which corrects for both the nonuniform sensitivity and the phase shifts introduced by receiver coils. <s> BIB002 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Image non-uniformity in magnetic resonance imaging (MRI) is a recognised problem when using surface coils but is rarely mentioned with respect to standard head coils, yet it can be a source of error in clinical interpretation of images. Figure 1 demonstrates the type of artefacts due to image non-uniformity for a large, homogeneous solution of water and copper sulphate. The image was acquired in the coronal section using a standard head coil, and vertical (i.e. read direction) and horizontal (i.e. phase encode direction) pixel intensity profiles through the centre of the image are illustrated. The standard deviation of pixel intensities, expressed as a percentage of the mean value, is greater than ±27% along the 23 cm length of this phantom. Figure 2 demonstrates how these image nonuniformities can affect the sagittal image of a normal volunteer. The display window width and level have been chosen to produce optimum visual contrast at the level of the cerebellum and brain stem but, as a result to image no... <s> BIB003 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Abstract A procedure which incorporates the aspects of both correction matrix and digital filtering to compensate for sensitivity fall-off of the surface coil has been applied to clinical imaging. In this method the surface coil profile is determined using the surface coil image and a crude body coil image. Our results indicate that the corrected surface coil image exhibits the homogeneity of the body coil image while essentially preserving the sensitivity of the surface coil image. <s> BIB004 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> A method has been developed to compensate for sensitivity variation in surface coil images. An algorithm to derive the surface coil profile by acquiring a crude body coil image of the region under study is presented and tested using a homogeneous phantom. Practical application is demonstrated on images of a tomato and rabbit acquired with a 2 T 33-cm bore magnetic resonance imager/spectrometer. <s> BIB005 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> We describe methods for simultaneously acquiring and subsequently combining data from a multitude of closely positioned NMR receiving coils. The approach is conceptually similar to phased array radar and ultrasound and hence we call our techniques the “NMR phased array.” The NMR phased array offers the signal-to-noise ratio (SNR) and resolution of a small surface coil over fields-of-view (FOV) normally associated with body imaging with no increase in imaging time. The NMR phased array can be applied to both imaging and spectroscopy for all pulse sequences. The problematic interactions among nearby surface coils is eliminated (a) by overlapping adjacent coils to give zero mutual inductance, hence zero interaction, and (b) by attaching low input impedance preamplifiers to all coils, thus eliminating interference among next nearest and more distant neighbors. We derive an algorithm for combining the data from the phased array elements to yield an image with optimum SNR. Other techniques which are easier to implement at the cost of lower SNR are explored. Phased array imaging is demonstrated with high resolution (512 × 512, 48-cm FOV, and 32-cm FOV) spin-echo images of the thoracic and lumbar spine. Data were acquired from four-element linear spine arrays, the first made of 12-cm square coils and the second made of 8-cm square coils. When compared with images from a single 15 × 30-cm rectangular coil and identical imaging parameters, the phased array yields a 2X and 3X higher SNR at the depth of the spine ( ∼ 7 cm). © 1990 Academic Press, Inc. <s> BIB006 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> When time-varying gradients are used for imaging, the off-resonance behavior does not just cause geometric distortion as is the case with spin-warp imaging, but changes the shape of the impulse response and causes blurring. This effect is well known for projection reconstruction and spiral k-space scanning sequences. The authors introduce a reconstruction and homogeneity correction method to correct for the zeroth order effects of inhomogeneity using prior knowledge of the inhomogeneity. In this method, the data are segmented according to collection time, reconstructed using some fast, linear algorithm, correlated for inhomogeneity, and then superimposed to yield a homogeneity corrected image. This segmented method is compared to a conjugate phase reconstruction in terms of degree of correction and execution time. The authors apply this method to in vivo images using projection-reconstruction and spiral-scan sequences. > <s> BIB007 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> A volume MR phased array was constructed with two coils placed anteriorly and two coils posteriorly. Data acquired simultaneously from the four coils on a phantom were combined into a single image having a signal-to-noise ratio 80% better than that from the body coil. Additional comparisons of the four-coil phased array with a two-coil phased array and a Helmholtz pair having the same overall dimensions show how variations of signal amplitude and phase in the individual coils affect the composite SNR. Images of the male and female pelvis demonstrate how the improved SNR can be used to reduce the number of excitations, decrease the field of view, increase the echo time, or reduce the slice thickness. © 1991 Academic Press. Inc. <s> BIB008 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> The specialised radiofrequency (RF) coils used in MRI such as head or surface coils can give rise to marked image intensity nonuniformities. There are two situations in which it is essential to correct this: (1) When a global intensity threshold is used to segment particular tissues; and (2) in proton density images, from which the proton concentration can be measured provided that the system gain is uniform or known over the whole image. We describe experiments to determine the magnitude and sources of nonuniformity in a 0.5-T system, and assess methods devised to correct for them in scans of any orientation, including oblique scans at arbitrary angles to the magnet axis and arbitrary offsets from the magnet iso-centre. A correction based on the response of a system to a uniform phantom was implemented. Tests of the correction with orthogonal views demonstrate that the uniformity of images of any orientation can be improved significantly with a correction matrix from just one orientation and still further with two matrices, one axial and the other either coronal or sagittal. We expect further improvements to be possible if gradient coil eddy current effects can be reduced. <s> BIB009 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> The usefulness of statistical clustering algorithms developed for automatic segmentation of lesions and organs in magnetic resonance imaging (MRI) intensity data sets suffers from spatial nonstationarities introduced into the data sets by the acquisition instrumentation. The major intensity inhomogeneity in MRI is caused by variations in the B1-field of the radio frequency (RF) coil. A three-step method was developed to model and then reduce the effect. Using a least squares formulation, the inhomogeneity is modeled as a maximum variation order two polynomial. In the log domain the polynomial model is subtracted from the actual patient data set resulting in a compensated data set. The compensated data set is exponentiated and rescaled. Statistical comparisons indicate volumes of significant corruption undergo a large reduction in the inhomogeneity, whereas volumes of minimal corruption are not significantly changed. Acting as a preprocessor, the proposed technique can enhance the role of statistical segmentation algorithms in body MRI data sets. <s> BIB010 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> This manuscript describes a number of sources of nonuniformity for spin echo images at 1.5 T. Both coil tuning and crosstalk can have significant effects on image nonuniformity. For short repetition times, nonuniformity increases with decreasing TR, possibly due to gradient eddy currents. In sections of RF coils with poor RF uniformity, image nonuniformity varies with both echo time and the number of echoes in a multiecho sequence. For the particular imager used, there are small differences between transverse and sagittal/coronal nonuniformity. The temporal stability of image nonuniformity is very good. The use of uniform oil phantoms is shown to be superior to low pass filtered images for correction of image nonuniformity. <s> BIB011 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> An analytic correction method was developed and applied to correct the signal intensity nonuniformity caused by the inhomogeneous reception profile of surface coils used—because of their higher sensitivity—for magnetic resonance imaging of the brain at 1.5 T. The reception profile was analytically modeled by using the Blot–Savart law. The correction considerably improved visual interpretation of the images by modeling and removing the dependence of signal intensity on distance from the coil. The method can be used for single or multiple coils of any planar geometry and in any orientation. Application of this technique allows imaging of the brain with surface coils, yielding increased resolution and signal-to-noise ratio, without the penalty of image nonuniformity. <s> BIB012 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> The authors describe a method for accurate In vivo muttislice imaging of the active component of the B1 field which is based on a previously proposed method, which uses the signal intensity ratio of two images measured with different excitation angles, and a repetition time TR≥ 5 T1 The new method essentially reduces repetition and scan time by means of an additional compensating pulse. The suppression of T1 effects by this pulse are verified with simulations and measurements. Further investigations concerned the influence of slice selective excitation and magnetization transfer in multislice imaging to the B1 field determination. The stability and accuracy of the presented method is shown by several phantom and in vivo measurements. With the described method the active B1 field can be determined in vivo in 23 cross-sections in less than 6 min. <s> BIB013 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Inhomogeneity of the transmitted or received B1 field leads to intensity variations in MR images and spatial dependence in apparent concentration in MR spectra. We describe a simple method for investigating such variations. The transmitted B1 field can be measured both in vivo and in vitro which allows investigation of sample dependent effects that can not be measured on phantoms. For homogeneous regions the method also allows the received B1 field to be measured both in vivo and in vitro. Our method uses only a standard spin echo pulse sequence and simple region of interest analysis and should be implementable on any commercial scanner. The method is demonstrated using a variety of transmission and reception radiofrequency coils both in vivo and in vitro. <s> BIB014 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Reliable interpretation of the MR signal intensity over the FOV of an image must consider the spatial heterogeneity of instrumental sensitivity. A major source of such variation is the nonuniformity of the B1 magnetic field of the radiofrequency coil. This heterogeneity can be minimized by coil design but is exaggerated by surface coils, which are used to maximize the signal-to-noise ratio for some applications. This paper describes a rapid method for mapping the B1 field over the sample of interest, using 1H echo-planar imaging, to correct for B1 distortions. The method applies to 1H imaging and has been extended to non-1H imaging by using dual-frequency coils in which the B1 distributions are matched for the 1H frequency and the frequency of interest. The approach is demonstrated in phantoms, animals, and humans and for sodium imaging. <s> BIB015 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Current MRI nonuniformity correction techniques are reviewed and investigated. Many approaches are used to remedy this artifact, but it is not clear which method is the most appropriate in a given situation, as the applications have been with different MRI coils and different clinical applications. In this work four widely used nonuniformity correction techniques are investigated in order to assess the effect on tumor response measurements (change in tumor volume over time): a phantom correction method, an image smoothing technique, homomorphic filtering, and surface fitting approach. Six braintumor cases with baseline and follow-up MRIs after treatment with varying degrees of difficulty of segmentation were analyzed without and with each of the nonuniformity corrections. Different methods give significantly different correction images, indicating that rf nonuniformity correction is not yet well understood. No improvement in tumor segmentation or in tumor growth/shrinkage assessment was achieved using any of the evaluated corrections. <s> BIB016 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> The purpose of this work was to optimize and increase the accuracy of tissue segmentation of the brain magnetic resonance (MR) images based on multispectral 3D feature maps. We used three sets of MR images as input to the in-house developed semi-automated 3D tissue segmentation algorithm: proton density (PD) and T2-weighted fast spin echo and, T1-weighted spin echo. First, to eliminate the random noise, non-linear anisotropic diffusion type filtering was applied to all the images. Second, to reduce the nonuniformity of the images, we devised and applied a correction algorithm based on uniform phantoms. Following these steps, the qualified observer "seeded" (identified training points) the tissue of interest. To reduce the operator dependent errors, cluster optimization was also used; this clustering algorithm identifies the densest clusters pertaining to the tissues. Finally, the images were segmented using k-NN (k-Nearest Neighborhood) algorithm and a stack of color-coded segmented images were created along with the connectivity algorithm to generate the entire surface of the brain. The application of pre-processing optimization steps substantially improved the 3D tissue segmentation methodology. <s> BIB017 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> A new method is described for compensating for the bias introduced by variations in radiofrequency (RF) field strength and main magnetic field strength when making quantitative T(2) measurements using MRI. Field measurements made during the MRI study are used in combination with a signal model for off-resonance and imperfect RF pulses to correct the estimated T(2) value at every voxel. Applicable to both multicomponent and conventional single-component T(2) studies, the method has been validated experimentally using paramagnetic salt solutions in a multicompartment phantom. Studies of the human head are used to demonstrate the method in practice. <s> BIB018 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> The RF B1 distribution was studied, theoretically and experimentally, in phantoms and in the head of volunteers using a 3 T MRI system equipped with a birdcage coil. Agreement between numerical simulation and experiment demonstrates that B1 distortion at high field can be explained with 3D full-Maxwell calculations. It was found that the B1 distribution in the transverse plane is strongly dependent on the dielectric properties of the sample. We show that this is a consequence of RF penetration effects combined with RF standing wave effects. In contrast, along the birdcage coil z-axis the B1 distribution is determined mainly by the coil geometry. In the transverse plane, the region of B1 uniformity (within 10% of the maximum) was 15 cm with oil, 6 cm with distilled water, 11 cm with saline, and 10 cm in the head. Along z the B1 uniformity was 9 cm with phantoms and 7 cm in the head. Magn Reson Med 46:379–385, 2001. © 2001 Wiley-Liss, Inc. <s> BIB019 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> This paper presents a method to correct intensity nonuniformity in spin-echo T1-weighted images and particularly the inhomogeneities due to RF transmission imperfections which have tissue-dependent effects through the T1 relaxation times. This method is based on the use of a uniform phantom, first for classic normalization by division by the phantom images, and second for T1-correction using the RF transmitted cartography. We present experimental results from a bi-phasic (oil/water) phantom and from a salmon with a 0.2 T imager. The results demonstrate the efficiency of the method in the two cases and its ability to cope with partial volume effect. <s> BIB020 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Calculations and experiments were used to examine the B(1) field behavior and signal intensity distribution in a 16-cm diameter spherical phantom excited by a 10-cm diameter surface coil at 300 MHz. In this simple system at this high frequency very complex RF field behavior exists, resulting in different excitation and reception distributions. Included in this work is a straightforward demonstration that coil receptivity is proportional to the magnitude of the circularly polarized component of the B(1) field that rotates in the direction opposite to that of nuclear precession. It is clearly apparent that even in very simple systems in head-sized samples at this frequency it is important to consider the separate excitation and reception distributions in order to understand the signal intensity distribution. <s> BIB021 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> We propose a novel bias correction method for magnetic resonance (MR) imaging that uses complementary body coil and surface coil images. The former are spatially homogeneous but have low signal intensity; the latter provide excellent signal response but have large bias fields. We present a variational framework where we optimize an energy functional to estimate the bias field and the underlying image using both observed images. The energy functional contains smoothness-enforcing regularization for both the image and the bias field. We present extensions of our basic framework to a variety of imaging protocols. We solve the optimization problem using a computationally efficient numerical algorithm based on coordinate descent, preconditioned conjugate gradient, half-quadratic regularization, and multigrid techniques. We show qualitative and quantitative results demonstrating the effectiveness of the proposed method in producing debiased and denoised MR images. <s> BIB022 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> In magnetic resonance imaging, magnetic field inhomogeneities cause distortions in images that are reconstructed by conventional fast Fourier transform (FFT) methods. Several noniterative image reconstruction methods are used currently to compensate for field inhomogeneities, but these methods assume that the field map that characterizes the off-resonance frequencies is spatially smooth. Recently, iterative methods have been proposed that can circumvent this assumption and provide improved compensation for off-resonance effects. However, straightforward implementations of such iterative methods suffer from inconveniently long computation times. This paper describes a tool for accelerating iterative reconstruction of field-corrected MR images: a novel time-segmented approximation to the MR signal equation. We use a min-max formulation to derive the temporal interpolator. Speedups of around 60 were achieved by combining this temporal interpolator with a nonuniform fast Fourier transform with normalized root mean squared approximation errors of 0.07%. The proposed method provides fast, accurate, field-corrected image reconstruction even when the field map is not smooth. <s> BIB023 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> To characterize gradient field nonuniformity and its effect on velocity encoding in phase contrast (PC) MRI, a generalized model that describes this phenomenon and enables the accurate reconstruction of velocities is presented. In addition to considerable geometric distortions, inhomogeneous gradient fields can introduce deviations from the nominal gradient strength and orientation, and therefore spatially-dependent first gradient moments. Resulting errors in the measured phase shifts used for velocity encoding can therefore cause significant deviations in velocity quantification. The true magnitude and direction of the underlying velocities can be recovered from the phase difference images by a generalized PC velocity reconstruction, which requires the acquisition of full three-directional velocity information. The generalized reconstruction of velocities is applied using a matrix formalism that includes relative gradient field deviations derived from a theoretical model of local gradient field nonuniformity. In addition, an approximate solution for the correction of one-directional velocity encoding is given. Depending on the spatial location of the velocity measurements, errors in velocity magnitude can be as high as 60%, while errors in the velocity encoding direction can be up to 45 degrees. Results of phantom measurements demonstrate that effects of gradient field nonuniformity on PC-MRI can be corrected with the proposed method. <s> BIB024 </s> A Review on MR Image Intensity Inhomogeneity Correction <s> INTRODUCTION <s> Signal intensity nonuniformities in high field MR imaging limit the ability of MRI to provide quantitative information and can negatively impact diagnostic scan quality. In this paper, a simple method is described for correcting these effects based on in vivo measurement of the transmission field B1+ and reception sensitivity maps. These maps can be obtained in vivo with either gradient echo (GE) or spin echo (SE) imaging sequences, but the SE approach exhibits an advantage over the GE approach for correcting images over a range of flip angles. In a uniform phantom, this approach reduced the ratio of the signal SD to its mean from around 30% before correction to approximately 6% for the SE approach and 9% for the GE approach after correction. The application of the SE approach for correcting intensity nonuniformities is demonstrated in vivo with human brain images obtained using a conventional spin echo sequence at 3.0 T. Furthermore, it is also shown that this in vivo B1+ and reception sensitivity mapping can be performed using segmented echo planar imaging sequences providing acquisition times of less than 2 min. Although the correction presented here is demonstrated with a simultaneous transmit and receive volume coil, it can be extended to the case of separate transmission and reception coils, including surface and phase array coils. <s> BIB025
With the frequent application of the magnetic resonance (MR) imaging method to clinical diagnosis, automatic analysis of the acquired images using techniques from computer vision and pattern recognition has received considerable attention. In developing such computer-aided diagnosis tools, a commonly encountered problem is to correct the intensity inhomogeneity (IIH) in MR images. The IIH (also termed as the intensity nonuniformity, the bias field, or the gain field in the literature) usually refers to the slow, nonanatomic intensity variations of the same tissue over the image domain. It can be due to imaging instrumentation (such as radio-frequency nonuniformity, static field inhomogeneity, etc.) or the patient movement BIB001  BIB011 BIB014 BIB019 . This artifact is particularly severe in MR images captured by surface coils. Two real MR images with severe IIH artifact are shown in Figure 1 (a), where one can see that the intensity varies significantly for the pixels of the same tissue and the intensity values overlap markedly between the pixels of the different tissues. For comparison, the IIH corrected images by a surface fitting technique  are given in Figure 1(b) , from which the improvement in image quality is clearly visible. The estimated IIH maps are given in Figure 1(c) . Let x denote the measured intensity and x the true intensity. Then the most popular model in describing the IIH effect is where α denotes the IIH effect and ξ the noise. Notation of bold letters refers to 2D or 3D MR data. Figure 2 displays the widely used BrainWeb  simulated MR images, where on To simplify the computation, one often ignores the noise and takes the logarithmic transform of intensity y i = log x i = log x i + log α i = y i + β i , where x i is the intensity at voxel i (i = 1, . . . , n). Here, to avoid numerical problems, care should be taken for those pixels/voxels with low intensities, which are usually excluded from computation. In general, the presence of IIH can significantly reduce the accuracy of image segmentation and registration, hence decreasing the reliability of subsequent quantitative measurement. A number of techniques have been proposed to deal with this issue. In general, if a map of the IIH in the image domain (Figure 1 (c) for instance) is known or can be estimated, then it is simple to correct the IIH by division in BIB001 or subtraction in the log-domain  . One can obtain the IIH map from measurement in vivo BIB004 BIB005 BIB013  BIB015 BIB018 BIB022 BIB025 , typically of a uniform phantom, BIB003 BIB009 BIB010 BIB017 BIB020 , which often requires extra measurement (and increases the scanning time) or needs additional hardware which may not be readily available in some clinical departments. Also there are theoretical modeling approaches [ BIB002 BIB006 BIB007 BIB008 BIB012 BIB021 BIB023 BIB024 to approximate the IIH map. However, due to the complexity that causes the IIH, it is difficult to model the IIH under a variety of imaging conditions. In particular, the object-induced IIH is hard to be accounted for by phantom study or theoretical modeling. More often, the IIH map is derived retrospectively from the image data alone. A number of research efforts have been put in this direction and many techniques have been proposed. Popular mathematical models for IIH description can be classified as follows: (1) low-frequency model, which assumes the IIH to constitute low-frequency components in frequency domain and the IIH map can be recovered by lowpass filtering; (2) hypersurface model, which fits the IIH map by a smooth functional, whose parameters are usually obtained using regression; (3) statistical model, which assumes the IIH to be a random variable or a random process and the IIH map can be derived through statistical estimation; (4) others, which are based on different principles, and sometimes without explicit assumptions on the IIH field. With this in mind, the IIH correction methods are categorized into lowpass filtering, statistical modeling, surface fitting and others, which are detailed, respectively, in the following sections. For an early literature review, interested readers are referred to BIB016 , where an evaluation of the IIH correction effect for brain tumor segmentation is also reported. This paper attempts to summarize the recent progress and focus will be on mathematical modeling for IIH removal. Nevertheless, it is by no means an exhaustive summary. For simplicity, the description will be on single-channel data only.