COmplex-Model-Based Estimation of thermal noise for fMRI data in the presence of artifacts

Due to the presence of artifacts induced by fast-imaging acquisition in functional magnetic resonance imaging (fMRI) studies, it is very difficult to estimate the variance of thermal noise by traditional methods in magnitude images. Moreover, the existence of incidental phase fluctuations impairs the validity of currently available solutions based on complex datasets. In this article, a time-domain model is proposed to generalize the analysis of complex datasets for nonbrain regions by incorporating artifacts and phase fluctuations. Based on this model, a novel estimation schema has been developed to find an appropriate set of voxels in nonbrain regions according to their levels of artifact and phase fluctuation. In addition, noise intensity from these voxels is estimated. The whole schema is named COmplex-Model-Based Estimation (COMBE). Theoretical and experimental results demonstrate that the proposed COMBE method provides a better estimation of thermal noise in fMRI studies compared with previously proposed methods and suggest that the new method can adapt to a broader range of applications, such as functional connectivity studies, evaluation of sequence designs and reconstruction schemas.     

The effect of physiological noise in phase functional magnetic resonance imaging: from blood oxygen level-dependent effects to direct detection of neuronal currents

Recently, the possibility to use both magnitude and phase image sets for the statistical evaluation of fMRI has been proposed, with the prospective of increasing both statistical power and the spatial specificity. In the present work, several issues that affect the spatial and temporal stability in fMRI phase time series in the presence of physiologic noise processes are reviewed, discussed and illustrated by experiments performed at 3 T. The observed phase value is a fingerprint of the underlying voxel averaged magnetic field variations. Those related to physiological processes can be considered static or dynamic in relation to the temporal scale of a 2D acquisition and will play out on different spatial scales as well: globally across the entire images slice, and locally depending on the constituents and their relative fractions inside the MRI voxel. The 'static' respiration-induced effects lead to magneto-mechanic scan-to-scan variations in the global magnetic field but may also contribute to local BOLD fluctuations due to respiration-related variations in arterial carbon dioxide. Likewise, the 'dynamic' cardiac-related effects will lead to global susceptibility effects caused by pulsatile motion of the brain as well as local blood pressure-related changes in BOLD and changes in blood flow velocity. Finally, subject motion may lead to variations in both local and global tissue susceptibility that will be especially pronounced close to air cavities. Since dissimilar manifestations of physiological processes can be expected in phase and in magnitude images, a direct relationship between phase and magnitude scan-to-scan fluctuations cannot be assumed a priori. Therefore three different models were defined for the phase stability, each dependent on the relation between phase and magnitude variations and the best will depend on the underlying noise processes. By experiments on healthy volunteers at rest, we showed that phase stability depends on the type of post-processing and can be improved by reducing the low-frequency respiration-induced mechano-magnetic effects. Although the manifestations of physiological noise were in general more pronounced in phase than in magnitude images, due to phase wraps and global Bo effects, we suggest that a phase stability similar to that found in magnitude could theoretically be achieved by adequate correction methods. Moreover, as suggested by our experimental data regarding BOLD-related phase effects, phase stability could even supersede magnitude stability in voxels covering dense microvascular networks with BOLD-related fluctuations as the dominant noise contributor. In the interest of the quality of both BOLD-based and nc-MRI methods, future studies are required to find alternative methods that can improve phase stability, designed to match the temporal and spatial scale of the underlying neuronal activity.     

A segmentation-based and partial-volume-compensated method for an accurate measurement of lateral ventricular volumes on T(1)-weighted magnetic resonance images

Lateral ventricular volumes based on segmented brain MR images can be significantly underestimated if partial volume effects are not considered. This is because a group of voxels in the neighborhood of lateral ventricles is often mis-classified as gray matter voxels due to partial volume effects. This group of voxels is actually a mixture of ventricular cerebro-spinal fluid and the white matter and therefore, a portion of it should be included as part of the lateral ventricular structure. In this note, we describe an automated method for the measurement of lateral ventricular volumes on segmented brain MR images. Image segmentation was carried in combination of intensity correction and thresholding. The method is featured with a procedure for addressing mis-classified voxels in the surrounding of lateral ventricles. A detailed analysis showed that lateral ventricular volumes could be underestimated by 10 to 30% depending upon the size of the lateral ventricular structure, if mis-classified voxels were not included. Validation of the method was done through comparison with the averaged manually traced volumes. Finally, the merit of the method is demonstrated in the evaluation of the rate of lateral ventricular enlargement.     

The investigation of noise in hard radiation detectors by pulse-amplitude analysis

The potentialities of pulse-amplitude analysis for noise measurements are demonstrated with p ⁺-n silicon detectors. It is suggested to use the detector current as a parameter and vary it by illuminating the samples. The instrument was calibrated by the shot noise of the photocurrent. The criteria for shot noise are the linearity of the noise squared vs. current dependence and its slope. It is shown that conventional instrumentation for pulse-amplitude analysis provides accurate yet rapid noise investigation. For the detectors studied, flicker noise was absent even when the trapped charge in the field oxide increases by one order of magnitude.     

Two methods for semi-automated quantification of changes in ventricular volume and their use in schizophrenia

Two semi-automated methods for quantification of ventricular volume change from baseline and follow-up magnetic resonance imaging scans have been developed. Technique 1 employs direct segmentation of the ventricles from both the scans using thresholding and contour extraction. Technique 2 operates on difference images produced by voxel based intensity subtraction of the baseline from the registered follow-up images. Here, all voxels with intensities above a noise threshold and in a restricted area are monitored to compute volumetric changes. In phantom measurements the first technique was accurate to 0.0046%, the second to 0.167% of the phantom volume. Results from normal volunteers was that the average ventricular volume changed by 1.52% and 1.54% for images acquired within 9 months using techniques 1 and 2, respectively. With schizophrenic patients mean change of 10.78% and 9.43% were found employing the first and second procedures, respectively. All measurements agreed with a radiologist’s visual grading of the changes. Robust, objective, fast, easy-to-use, and fairly accurate procedures have been developed and validated to quantify volumetric changes.     

A wavelet-based method for improving signal-to-noise ratio and contrast in MR images

Magnetic resonance (MR) images acquired with fast measurement often display poor signal-to-noise ratio (SNR) and contrast. With the advent of high temporal resolution imaging, there is a growing need to remove these noise artifacts. The noise in magnitude MR images is signal-dependent (Rician), whereas most de-noising algorithms assume additive Gaussian (white) noise. However, the Rician distribution only looks Gaussian at high SNR. Some recent work by Nowak employs a wavelet-based method for de-noising the square magnitude images, and explicitly takes into account the Rician nature of the noise distribution. In this article, we apply a wavelet de-noising algorithm directly to the complex image obtained as the Fourier transform of the raw k-space two-channel (real and imaginary) data. By retaining the complex image, we are able to de-noise not only magnitude images but also phase images. A multiscale (complex) wavelet-domain Wiener-type filter is derived. The algorithm preserves edges better when the Haar wavelet rather than smoother wavelets, such as those of Daubechies, are used. The algorithm was tested on a simulated image to which various levels of noise were added, on several EPI image sequences, each of different SNR, and on a pair of low SNR MR micro-images acquired using gradient echo and spin echo sequences. For the simulated data, the original image could be well recovered even for high values of noise (SNR approximately 0 dB), suggesting that the present algorithm may provide better recovery of the contrast than Nowak's method. The mean-square error, bias, and variance are computed for the simulated images. Over a range of amounts of added noise, the present method is shown to give smaller bias than when using a soft threshold, and smaller variance than a hard threshold; in general, it provides a better bias-variance balance than either hard or soft threshold methods. For the EPI (MR) images, contrast improvements of up to 8% (for SNR = 33 dB) were found. In general, the improvement in contrast was greater the lower the original SNR, for example, up to 50% contrast improvement for SNR of about 20 dB in micro-imaging. Applications of the algorithm to the segmentation of medical images, to micro-imaging and angiography (where the correct preservation of phase is important for flow encoding to be possible), as well as to de-noising time series of functional MR images, are discussed.     

Wavelet domain de-noising of time-courses in MR image sequences

Magnetic resonance images acquired with high temporal resolution often exhibit large noise artifacts, which arise from physiological sources as well as from the acquisition hardware. These artifacts can be detrimental to the quality and interpretation of the time-course data in functional MRI studies. A class of wavelet-domain de-noising algorithms estimates the underlying, noise-free signal by thresholding (or 'shrinking') the wavelet coefficients, assuming the underlying temporal noise of each pixel is uncorrelated and Gaussian. A Wiener-type shrinkage algorithm is developed in this paper, for de-noising either complex- or magnitude-valued image data sequences. Using the de-correlation properties of the wavelet transform, as elucidated by Johnstone and Silverman, the assumption of i.i.d. Gaussian noise can be abandoned, opening up the possibility of removing colored noise. Both wavelet- and wavelet-packet based algorithms are developed, and the Wiener method is compared to the traditional Hard and Soft wavelet thresholding methods of Donoho and Johnstone. The methods are applied to two types of data sets. In the first, an artificial set of complex-valued images was constructed, in which each pixel has a simulated bimodal time-course. Gaussian noise was added to each of the real and imaginary channels, and the noise removed from the complex image sequence as well as the magnitude image sequence (where the noise is Rician). The bias and variance between the original and restored paradigms was estimated for each method. It was found that the Wiener method gives better balance in bias and variance than either Hard or Soft methods. Furthermore, de-noising magnitude data provides comparable accuracy of the restored images to that obtained from de-noising complex data. In the second data set, an actual in vivo complex image sequence containing unknown physiological and instrumental noise was used. The same bimodal paradigm as in the first data set was added to pixels in a small localized region of interest. For the paradigm investigated here, the smooth Daubechies wavelets provide better de-noising characteristics than the discontinuous Haar wavelets. Also, it was found that wavelet packet de-noising offers no significant improvement over the computationally more efficient wavelet de-noising methods. For the in vivo data, it is desirable that the groups of "activated" time-courses are homogeneous. It was found that the internal homogeneity of the group of time-courses increases when de-noising is applied. This suggests using de-noising as a pre-processing tool for both exploratory and inferential data analysis methods in fMRI.     

The study and application of a new filtering method on electronic speckle pattern interferometric fringe

It is important for the study of digital image processing to remove noises and enhance images because of various noises in images. The article is concerned with the recursive algorithm-filtering technique, which is capable of effectively removing noise and rapidly leading to a continuous gray-level distribution of a random image. By applying the method on speckle images of defects of rubber material, it is shown that this technique is the most effective and speedy method for the filtering of ESPI fringe patterns. Comparing the images before and after filtering, we can see the advantages of the novel technique clearly. It can increase the accuracy of measurement both in phase measurement and in quantitative evaluations of defects.     

Phase vs. magnitude information in functional magnetic resonance imaging time series: toward understanding the noise

Although it has been shown that the phase of the MR signal from the brain is particularly prone to variation due to respiration, the overall physiological information contained in phase time series is not well understood. Here, we explore the different physiological processes contributing to the phase time series noise, identify their spatiotemporal characteristics and examine their relationship to BOLD-related and non-BOLD-related physiological noise in the magnitude time series. This was performed by manipulating the contribution of physiological noise to the total signal variance by modulating the TE and voxel volume, and using a short TR in order to adequately sample physiological signal fluctuations. The phase and magnitude signals were compared both before and after removal of signal fluctuations at the primary respiratory and cardiac frequencies with RETROICOR. We found that the temporal phase noise increased with TE at a faster rate than predicted by 1/TSNR as a result of physiological noise. As suggested by previous studies, the primary contributor to phase physiological noise was respiration-related effects which were manifested at a large scale (>1 cm). Notably, RETROICOR removed respiration-related large-scale artifacts and this resulted in considerable improvements in the temporal phase stability (7–90%). Physiological noise in the magnitude time series after RETROICOR consisted of low-frequency BOLD-related fluctuations (<0.13 Hz) localized to gray matter and the vasculature, and fluctuations in the vasculature correlated with slow (<0.1 Hz) variations in respiration volume and cardiac rhythm. Physiological noise in the phase signal after RETROICOR also occurred in frequencies below 0.13 Hz and was consistent with (1) residual large-scale magneto-mechanical effects correlated with slow variations in respiration volume and cardiac rhythm over time, and (2) local scale (<1 cm) effects localized in gray matter and vasculature most likely due to vascular dephasing mediated by a BOLD susceptibility change. While BOLD-related magnitude noise exhibited a TE dependence similar to BOLD, the ‘BOLD-related’ noise in the phase data increased with increasing TE and thus caused the overall phase noise to increase at a faster rate with TE than predicted by 1/TSNR. Interestingly, the spatial specificity of this effect was more evident for the higher resolution phase data, as opposed to the magnitude data, suggesting that at a higher spatial resolution the phase signal may contain more information on physiological processes than the magnitude signal.     

A statistical fMRI model for differential T2* contrast incorporating T1 and T2* of gray matter

Relaxation parameter estimation and brain activation detection are two main areas of study in magnetic resonance imaging (MRI) and functional magnetic resonance imaging (fMRI). Relaxation parameters can be used to distinguish voxels containing different types of tissue whereas activation determines voxels that are associated with neuronal activity. In fMRI, the standard practice has been to discard the first scans to avoid magnetic saturation effects. However, these first images have important information on the MR relaxivities for the type of tissue contained in voxels, which could provide pathological tissue discrimination. It is also well-known that the voxels located in gray matter (GM) contain neurons that are to be active while the subject is performing a task. As such, GM MR relaxivities can be incorporated into a statistical model in order to better detect brain activation. Moreover, although the MR magnetization physically depends on tissue and imaging parameters in a nonlinear fashion, a linear model is what is conventionally used in fMRI activation studies. In this study, we develop a statistical fMRI model for Differential T₂^? ConTrast Incorporating T₁ and T₂^? of GM, so-called DeTeCT-ING Model, that considers the physical magnetization equation to model MR magnetization; uses complex-valued time courses to estimate T₁ and T₂^? for each voxel; then incorporates gray matter MR relaxivities into the statistical model in order to better detect brain activation, all from a single pulse sequence by utilizing the first scans.     

Comparison of different methods for combining phase-contrast images obtained with multiple coils

The ability to determine coil sensitivities implies that a method optimized in terms of maximized signal-to-noise ratio (SNR) can be applied to the combination of multiple coil images. An optimization of SNR subsequently results in a minimized variance in quantitative velocity measurements using phase-contrast imaging. When coil sensitivities are unknown, the weighted mean method, utilizing the square of the signal magnitude as weights, is suitable for combination of multiple phase images. In this study, the optimized method using estimated coil sensitivities was compared to the weighted mean method both theoretically and experimentally. It is shown that absence of noise correlation between the different coil images implies no difference between the methods regarding the variance of the phase. In the practical situation, noise correlation does exist, implying an opportunity for further reduction of phase variance using the optimized method. In vitro and in vivo studies showed, however, no significant difference between the two methods studied.     

Relativistic field formulation of simultaneous quantum measurement

The simultaneous measurement of Dirac field operators is formulated in analogy to the work of von Neumann and Arthurs-Kelly. Meter fields are coupled to the system field with a relativistically invariant bilinear interaction. Measurement of vacuum meter field expectation values provides for the simultaneous measurement of noncommuting system components. It is shown that two meter coupling allows for a simultaneous minimum in the variance of the subsequent meter measurements. A pseudoscalar self-interaction of the Dirac field is shown to allow simultaneous measurement of positive energy field operators with negative energy meters. The simultaneous measurement ofn noncommuting field operators is obtained by coupling the system ton fermionic fields. Also, in this paper the related concept of mutual simultaneous measurement is developed. This requires that any operators in the enlarged Hilbert space are measurable by the remaining fields as meters. System embedding into a larger Hilbert space results in added noise due to the zero point motion of the meter fields. By the negentropy principle of Brillouin, the added noise is equivalent to entropy. A criterion determining the interaction among fields is that the averaged added noise in the components of each quantum field is minimized. This criterion defines an optimum fermionic mass matrix through the determination of the entangling interaction.1. This work was sponsored by the Department of the Air Force under contract F19628-90-C-0002.     

Quantitative phase imaging using actively stabilized phase-shifting low-coherence interferometry

We describe a quantitative phase-imaging interferometer in which phase shifting and noise cancellation are performed by an active feedback loop using a reference laser. Depth gating via low-coherence light allows phase measurement from weakly reflecting biological samples. We demonstrate phase images from a test structure and living cells.     

Adaptive quadrature filters for multiple phase-stepping images

We present a new technique for the recovery of local phase from multiple phase-stepping fringe images that uses adaptive quadrature filters constructed by use of Bayesian estimation theory and complex-valued Markov random fields as prior models. It is shown that with this technique it is possible to perform accurate phase reconstructions even for extremely noisy fringe images and that the performance of this technique is nearly independent of the particular noise model, as long as the noise spectrum is wideband.     

The ellipsoidal area ratio: an alternative anisotropy index for diffusion tensor imaging

In the processing and analysis of diffusion tensor imaging (DTI) data, certain predefined morphological features of diffusion tensors are often represented as simplified scalar indices, termed diffusion anisotropy indices (DAIs). When comparing tensor morphologies across differing voxels of an image, or across corresponding voxels in different images, DAIs are mathematically and statistically more tractable than are the full tensors, which are probabilistic ellipsoids consisting of three orthogonal vectors that each has a direction and an associated scalar magnitude. We have developed a new DAI, the "ellipsoidal area ratio" (EAR), to represent the degree of anisotropy in the morphological features of a diffusion tensor. The EAR is a normalized geometrical measure of surface curvature in the 3D diffusion ellipsoid. Monte Carlo simulations and applications to the study of in vivo human data demonstrate that, at low noise levels, EAR provides a similar contrast-to-noise ratio (CNR) but a higher signal-to-noise ratio (SNR) than does fractional anisotropy (FA), which is currently the most popular anisotropy index in active use. Moreover, at the high noise levels encountered most commonly in real-world DTI datasets, EAR compared with FA is consistently much more robust to perturbations from noise and it provides a higher CNR, features useful for the analysis of DTI data that are inherently noise sensitive.     

Gradient measurement technique to identify phase transitions in nano-dispersed liquid crystalline compounds

Characterization and phase transitions in pure and 0.5% BaTiO₃ nano-dispersed liquid crystalline (LC) N-(p-n-heptyloxybenzylidene)-p-n-nonyloxy aniline, 7O.O9, com-pounds are carried out using a polarizing microscope attached with hot stage and camera. We observed that when any of these images are distorted, different local structures suffer from various degradations in a gradient magnitude. So, we examined the pixel-wise gradient magnitude similarity between the reference and distorted images combined with a novel pooling strategy – the standard deviation of the GMS map – to determine the overall phase transition variations. In this regard, MATLAB software is used for gradient measurement technique to identify the phase transitions and transition temperature of the pure and nano-dispersed LC compounds. The image analysis of this method proposed is in good agreement with the standard methods like polarizing microscope (POM) and differential scanning calorimeter (DSC). 0.5% BaTiO₃ nano-dispersed 7O.O9 compound induces cholesteric phase quenching the nematic phase, which the pure compound exhibits.     

Detection of multiple sinusoids in unknown colored noise using truncated cepstrum thresholding and local signal-to-noise-ratio

Although cepstrum-based harmonics-to-noise-ratio techniques have been widely used in speech processing, they are as yet not applied to detect multiple sinusoids in unknown colored noise. By studying the impact of sinusoids on cepstral coefficients in theory, a truncated cepstrum thresholding technique is proposed to estimate the unknown colored noise power spectral density, which can be used to estimate the local signal-to-noise-ratio (LSNR) in the frequency domain. This paper suggests the use of the LSNR as a test statistic to detect the sinusoids in unknown colored noise. Numerical simulation results show that the proposed test statistic is much better than the existing test statistics in unknown colored noise environments.     

Mössbauer study of structural inhomogeneities formed upon the FCC–L10 transformation in equiatomic FePd alloy from different initial states

A comparative Mössbauer study of structural inhomogeneities that arise in the course of А1→ L1₀ phase transformation in nondeformed (as cast and quenched from 950°C and melt-spun from the ingot) and severely deformed samples of equiatomic FePd alloy upon ordering annealing at Т?=?450°С has been performed. According to the known experimental works, the chosen temperature of annealing is optimal for achieving the highest coercive force H_c in both quenched and deformed samples. It is shown that in the high-coercivity state both quenched and deformed samples FePd possess an inhomogeneous tetragonal structure, which is preserved even after quite a prolonged (40–100?h) annealing. All the samples contain, along with the configurations of the nearest neighbourhood that are assigned to the ordered L1₀ phase, significant volume fractions of configurations typical of nonequiatomic compositions. This conclusion is inconsistent with the commonly accepted concept on single-phase L1₀ type alloys with maximal values of H_c. An inference is made that the structural inhomogeneities detected in the samples under study result from the mismatch of the position of the point of congruent А1→ L1₀ transformation (≈58 at.% Pd) in the phase diagram of the FePd system to equiatomic composition.     

Determination of optical properties of tissues

Recent results and used way of tissue optical properties measurements in vitro with laser goniophotometer are presented. The optical properties were obtained on the basis of an indirect technique using solution of the radiative transfer equation, which relate the optical parameters of tissue with the measured parameters of reflected and transmitted radiation. The angular patterns of reflected and transmitted radiation by optically thick saline-soaked samples of tumor tissue, namely, mammary fibroadenoma, were measured at the wavelength of 0.63 μm, and the measurement data were inverted to find the absorption and extinction coefficients and the parameters of the phase function of these tumor samples. Obtained values of the optical parameters have been found to be of the same order of magnitude as the earlier reported data for similar tumor samples.     

Surface contouring by phase-shifting digital holography

Surface contouring by phase-shifting digital holography is proposed that provides surface height from a change of reconstructed object phases due to the tilt of object illumination. Surface height from a reference plane is directly obtained from the phase change. Its sensitivity depends on the tilt angle as well as on the initial incident angle. By proper selection of the angles we can derive surface height without phase unwrapping. The sensitivity can be enhanced by increasing the tilt angle. Then we need phase unwrapping that is sensitive to noise due to laser speckles in the reconstructed images. This noise could be suppressed by selecting phase values at points of the maximum product of amplitudes before and after the illumination change in the course of data reduction from 1024×1024 to 512×512 and by selecting paths for phase unwrapping by looking for the intensity maximum. The observed height resolution is 20 μm. Effects of numerical focusing have also been investigated. The present method has the same sensitivity as the fringe projection method, but it has larger measurement depth and is also applicable to the deformation measurement with the same arrangement.