Interobserver reproducibility of quantitative cartilage measurements: comparison of B-spline snakes and manual segmentation.

The objective of this work was to develop a segmentation technique for thickness measurements of the articular cartilage in MR images and to assess the interobserver reproducibility of the method in comparison with manual segmentation. The algorithm is based on a B-spline snakes approach and is able to delineate the cartilage boundaries in real time and with minimal user interaction. The interobserver reproducibility of the method, ranging from 3.3 to 13.6% for various section orientations and joint surfaces, proved to be significantly superior to manual segmentation.     

Inter-rater and intra-rater reliability of subchondral bone and cartilage thickness measurement from MRI

MRI is often used to visualize and quantify the articular cartilage layer of load bearing joints affected by degenerative diseases, such as osteoarthritis (OA). Although the role played by the subchondral bone in the etiology and/or progression of OA may be important, the ability to visualize and quantify subchondral bone with MRI has received little attention. In this report we examined the inter-rater and intra-rater reliability of subchondral bone and cartilage thickness measurements from MR images of cadaver femoral head specimens. A 3D-SPGR pulse sequence tuned to eliminate chemical shift artifact through phase cancellation was used to image the specimens. Three raters manually segmented four specimens on two different occasions. Subchondral bone and cartilage thickness measurements were calculated from the segmented images. Inter-rater and intra-rater reliabilities were very high (>.98) for both cartilage and subchondral bone thickness measurements. We conclude that subchondral bone thickness can be measured as reliably as cartilage thickness from MR images.     

Wavelet-based characterization of vertebral trabecular bone structure from magnetic resonance images at 3 T compared with micro-computed tomographic measurements

Trabecular bone structure and bone density contribute to the strength of bone and are important in the study of osteoporosis. Wavelets are a powerful tool in characterizing and quantifying texture in an image. The purpose of this study was to validate wavelets as a tool in computing trabecular bone thickness directly from gray-level images. To this end, eight cylindrical cores of vertebral trabecular bone were imaged using 3-T magnetic resonance imaging (MRI) and micro-computed tomography (microCT). Thickness measurements of the trabecular bone from the wavelet-based analysis were compared with standard 2D structural parameters analogous to bone histomorphometry (MR images) and direct 3D distance transformation methods (microCT images). Additionally, bone volume fraction was determined using each method. The average difference in trabecular thickness between the wavelet and standard methods was less than the size of 1 pixel size for both MRI and microCT analysis. A correlation (R) of .94 for microCT measurements and that of .52 for MRI were found for the bone volume fraction. Based on these results, we conclude that wavelet-based methods deliver results comparable with those from established MR histomorphometric measurements. Because the wavelet transform is more robust with respect to image noise and operates directly on gray-level images, it could be a powerful tool for computing structural bone parameters from MR images acquired using high resolution and thus limited signal scenarios.     

Optimization and validation of a rapid high-resolution T1-w 3D FLASH water excitation MRI sequence for the quantitative assessment of articular cartilage volume and thickness

In view of follow up, survey and development of therapeutic strategies for osteoarthritis where cartilage deterioration plays an important role, a non invasive, reliable and quantitative assessment of the articular cartilage is desirable. The currently available high resolution T(1)-weighted (T1-w) 3D FLASH pulse sequences with frequency selective fat suppression are very time consuming. We have 1) optimized a high resolution T1-w 3D FLASH water excitation (WE) sequence for short acquisition time and cartilage visualization, and 2) validated this sequence for cartilage volume and thickness quantification. The spectral fat presaturation was replaced by selective water excitation. The flip angle of the WE sequence was optimized for the contrast to noise (C/N(cart)) ratio of cartilage. Sagittal datasets (voxel size: 0.31 x 0.31 x 2 mm(3)) of the knees of nine healthy volunteers were acquired both, with the 3D FLASH WE (17.2/6.6/30 degrees ) sequence (WE) and a previously validated 3D FLASH fat saturated (42/11/30 degrees ) sequence (FS). For validation of the WE sequence, cartilage volume, mean and maximal cartilage thickness of the two sequences were compared. Reproducibility was assessed by calculating the coefficient of variation (COV %) of 4 consecutive WE data sets in the volunteers. The acquisition time was reduced from 16'30" (FS) down to 7'14" for the WE sequence. Image contrast and visualization of the cartilage was very similar, but delineation of the basal layer of the cartilage was slightly improved with the WE sequence. A flip angle of 30 degrees provided the best C/N(cart) ratios (WE). Reproducibility (COV) was between 1.9 and 5.9%. Cartilage volume and thickness agreed within 4% between FS and WE sequence. The WE sequence allows for rapid, valid and reproducible quantification of articular cartilage volume and thickness, prerequisites for follow-up examinations. The reduced acquisition time (50% of FS) enables routine clinical application and thus may contribute to a broader assessment of osteoarthritis.     

Reproducibility of the quantitative assessment of cartilage morphology and trabecular bone structure with magnetic resonance imaging at 7 T

To assess the reproducibility of quantitative measurements of cartilage morphology and trabecular bone structure of the knee at 7 T, high-resolution sagittal spoiled gradient-echo images and high-resolution axial fully refocused steady-state free-precession (SSFP) images from six healthy volunteers were acquired with a 7-T scanner. The subjects were repositioned between repeated scans to test the reproducibility of the measurements. The reproducibility of each measurement was evaluated using the coefficient(s) of variation (CV). The computed CV were 1.13% and 1.55% for cartilage thickness and cartilage volume, respectively, and were 2.86%, 1.07%, 2.27% and 3.30% for apparent bone volume over total volume fraction (app.BV/TV), apparent trabecular number (app.Tb.N), apparent trabecular separation (app.Tb.Sp) and apparent trabecular thickness (app.Tb.Th), respectively. The results demonstrate that quantitative assessment of cartilage morphology and trabecular bone structure is reproducible at 7 T and motivates future musculoskeletal applications seeking the high-field strength's superior signal-to-noise ratio.     

Optimised in vivo visualisation of cortical structures in the human brain at 3 T using IR-TSE

The primary visual cortex in humans can be identified using magnetic resonance imaging (MRI) in vivo by detection of the stria of Gennari. To fully characterize this area, high spatial resolution is essential, including the use of very thin image slices to avoid loss of definition due to partial volume effects. A three-dimensional magnetization-prepared turbo spin-echo sequence, with appropriate parameter optimization, provided high-resolution imaging (0.4 x 0.4 x 0.5 mm3) on a clinical 3-T scanner with adequate contrast to noise ratio. These images allowed visualisation of the stria of Gennari in every slice of a volume covering most of the occipital cortex, in each of six healthy volunteers. The effective longitudinal relaxation time was measured with the isotropic resolution turbo spin echo sequence and found to be substantially shorter than values measured with a dedicated relaxometric sequence. The shortening was attributed to magnetization transfer effects, as supported by the investigation of its slab and turbo-factor dependence.     

Quantitation of normal canine hippocampus formation volume: Correlation of MRI with gross histology

The hippocampal formation possesses an important role in the development and maintenance of short-term memory. In this study, magnetic resonance imaging (MRI) and gross histology were used to quantify the volume of the hippocampal formation in canines. High resolution MRI, using 1 mm thick slices and an intraplanar resolution of 0.35 mm was performed at 2.0 T both in vivo and in vitro following in situ fixation. The volumes of the hippocampal formations were determined from MR images and compared to those obtained from one mm thick gross histologic sections. The average volume of the canine hippocampal formation, measured from in vivo and in vitro MR images was 476.0 ± 79.5 and 467.3 ± 53.7 mm³, respectively. Determined from gross histology, the volume of the hippocampal formation was 463.6 ± 24.1 mm³. Quantitation of the canine hippocampal formation using in vivo MRI showed good correlation with in vitro MRI and histology, verifying the reliability and reproducibility of in vivo MRI measurements. High resolution MRI using 1 mm thick slices through the whole canine hippocampal formation is necessary for accurate volume determination of a structure of this size.     

Complex denoising of MR data via wavelet analysis: application for functional MRI

A fast post-processing method for noise reduction of MR images, termed complex-denoising, is presented. The method is based on shrinking noisy discrete wavelet transform coefficients via thresholding, and it can be used for any MRI data-set with no need for high power computers. Unlike previous wavelet application to MR images, the denoising algorithm is applied, separately, to the two orthogonal sets of the complex MR image. The norm of the combined data are used to construct the image. With this method, signal-noise decoupling and Gaussian white noise assumptions used in the wavelet noise suppression scheme, are better fulfilled. The performance of the method is tested by carrying out a qualitative and quantitative comparison of a single-average image, complex-denoised image, multiple-average images, and a magnitude-denoised image, of a standard phantom. The comparison shows that the complex-denoising scheme improves the signal-to-noise and contrast-to-noise ratios more than the magnitude-denoising scheme, particularly in low SNR regions. To demonstrate the method strength, it is applied to fMRI data of somatosensory rat stimulation. It is shown that the activation area in a cross-correlation analysis is approximately 63% larger in the complex-denoised versus original data sets when equal threshold value is used. Application of the method of Principal Component Analysis to the complex-denoised, magnitude-denoised, and original data sets results in a similar but higher variance of the first few principal components obtained from the former data set as compared to those obtained from the later two sets.     

H double-quantum filtered MR imaging of joints tissues: bound water specific imaging of tendons, ligaments and cartilage

The ¹H double-quantum filtered (DQF) NMR and DQF MRI is applied to the joint tissues of rabbits for selective visualization of tendons, menisci and articular cartilage. The ¹H DQF NMR selectively filters double-quantum coherence arising from the ¹H dipolar interaction of the “bound” water in these tissues. The double-quantum creation time dependency of the DQF signal intensity is determined by the molecular environment of the “bound” water. Therefore, each tissue has a unique creation time at which the DQF signal reaches its maximum intensity, τ_max (Achilles tendon: 0.46 ± 0.02 ms, patella: 0.55 ± 0.8 ms, anterior cruciate ligament: 0.60 ± 0.05 ms, meniscus: 0.78 ± 0.02 ms, skin: 0.81 ± 0.07 ms). We have presented the creation-time-contrasted DQF images of the meniscus, patella, foot, and knee joint. Compared with conventional T₂*-weighted gradient-echo (GRE) MR images, tendons, ligaments, menisci, and articular cartilage were more clearly seen in the DQF MR images. All these tissues were distinctly discriminated from each other by their creation times. DQF MR images of foot and knee joints can selectively demonstrated tendons, ligaments, and cartilage, which make it easier to understand the complicated anatomic structure of joints. Because the DQF NMR signal intensity and τ_max are sensitive to the order structure of the “bound” water, it might be possible to introduce the creation-time dependent-contrast of ¹H DQF MR images as a new tool for analyzing the changes in the ordered structure of the tissue.     

Spatial and temporal resolution effects on dynamic contrast-enhanced magnetic resonance mammography

We tested the hypothesis that partial volume effects due to poor in-plane resolution and/or low temporal resolution used in clinical dynamic contrast-enhanced magnetic resonance imaging results in erroneous diagnostic information based on inaccurate estimates of tumor contrast agent extravasation and tested whether reduced encoding techniques can correct for dynamic data volume averaging. Image spatial resolution was reduced from 469 x 469 microm2 to those reported below by selecting a subset of k-space data. We then compared the top five K(trans)/V(T) "hot spots" obtained from the original data set, 469 x 469-microm in-plane spatial resolution and an 18-s temporal resolution processed by fast Fourier transform (FFT), with values obtained from data sets having in-plane spatial resolutions of 938 x 938, 1875 x 1875 and 2500 x 2500 microm2 and a temporal resolution of 18 s, or data sets with temporal resolutions of 36, 54 and 72 and a spatial resolution of 469 x 469 microm2, and found them to statistically differ from the parent data sets. We then tested four different post processing methods for improving the spatial resolution without sacrificing temporal resolution: zero-filled FFT, keyhole, reduced-encoding imaging by generalized-series reconstruction (RIGR) and two-reference RIGR (TRIGR). The top five values of K(trans)/V(T) obtained from data sets, the in-plane spatial resolutions of which were improved to 469 x 469 microm2 by zero-filling FFT, Keyhole and RIGR, statistically differed from those obtained from the original 469 x 469 microm2 FFT parent image data set. Only the 938 x 938 and 1875 x 1875 microm2 data sets reconstructed to 469 x 469 microm2 with TRIGR reconstruction method yielded values of the top five K(trans)/V(T) hot spots statistically the same as the original parent data set, 469 x 469 microm2 in-plane spatial and 18-s temporal-resolution FFT. That is, partial volume effects from data sets of different in-plane spatial resolution resulted in statistically different values of the top five K(trans)/V(T) hot spots relative to a high spatial and temporal resolution data set, and TRIGR reconstruction of these low resolution data sets to high resolution images provided statistically similar values with a savings in temporal resolution of 2 to 4 times.     

A nonrigid registration algorithm for longitudinal breast MR images and the analysis of breast tumor response

Dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) can estimate parameters relating to blood flow and tissue volume fractions and therefore may be used to characterize the response of breast tumors to treatment. To assess treatment response, values of these DCE-MRI parameters are observed at different time points during the course of treatment. We propose a method whereby DCE-MRI data sets obtained in separate imaging sessions can be co-registered to a common image space, thereby retaining spatial information so that serial DCE-MRI parameter maps can be compared on a voxel-by-voxel basis. In performing inter-session breast registration, one must account for patient repositioning and breast deformation, as well as changes in tumor shape and volume relative to other imaging sessions. One challenge is to optimally register the normal tissues while simultaneously preventing tumor distortion. We accomplish this by extending the adaptive bases algorithm through adding a tumor-volume preserving constraint in the cost function. We also propose a novel method to generate the simulated breast magnetic resonance (MR) images, which can be used to evaluate the proposed registration algorithm quantitatively. The proposed nonrigid registration algorithm is applied to both simulated and real longitudinal 3D high resolution MR images and the obtained transformations are then applied to lower resolution physiological parameter maps obtained via DCE-MRI. The registration results demonstrate the proposed algorithm can successfully register breast MR images acquired at different time points and allow for analysis of the registered parameter maps.     

Enhancement of histological volumes through averaging and their use for the analysis of magnetic resonance images

Magnetic resonance imaging (MRI) of small animals is routinely performed in research centers. But despite its many advantages, MR still suffers from limited spatial resolution which makes the interpretation and quantitative analysis of the images difficult, particularly for small structures of interest within areas of significant heterogeneity. One possibility to address this issue is to complement the MR images with histological data, which requires reconstructing 3D volumes from a series of 2D images. A number of methods have been proposed recently in the literature to address this issue, but deformation or tearing during the slicing process often produces reconstructed volumes with visible artifacts and imperfections. In this paper, we show that a possible solution to this problem is to work with several histological volumes, reconstruct each of these separately and then compute an average. The resulting histological atlas shows structures and substructures more clearly than any individual volume. We also propose an original approach to normalize intensity values across slices, a required preprocessing step when reconstructing histological volumes. We show that the histological atlas we have created can be used to localize structures and substructures, which cannot be seen easily in MR images. We also create an MR atlas that is associated with the histological atlas. We show that using the histological volumes to create the MR atlas is better than using the MR volumes only. Finally, we validate our approach quantitatively on MR image volumes by comparing volumetric measurements obtained manually and obtained automatically with our atlases.     

Reproducibility of MRI-derived measurements of right ventricular volumes and myocardial mass

Magnetic resonance (MR) imaging has been shown to provide accurate measurements of right ventricular (RV) volumes and myocardial mass. The purpose of this study was to evaluate the reproducibility of MR imaging, which in clinical practice may be as important as its absolute accuracy. The reproducibility of MR imaging measurements of the right ventricle was assessed by analyzing 40 serial functional MR imaging examinations of the right ventricle with variance component analysis. Standard deviations and 95% ranges for change were: for RV myocardial mass, 5.9 and 16 g; and for RV ejection fraction, 6.0% and 16%, respectively. Reproducibility was similar for cine and spin-echo MR imaging. The intraobserver and interobserver errors were especially large, indicating that observer subjectivity is the limiting factor in the interpretation of the MR images. This study suggests that the reproducibility of RV measurements is adequate to detect RV hypertrophy and a low ejection fraction in the individual patient. For accurate follow-up examinations, whereby smaller changes are to be detected, the reproducibility of MR imaging measurements may not be sufficient. More effort is needed to improve the reproducibility of MR imaging measurements.     

Nonlocal maximum likelihood estimation method for denoising multiple-coil magnetic resonance images

Effective denoising is vital for proper analysis and accurate quantitative measurements from magnetic resonance (MR) images. Even though many methods were proposed to denoise MR images, only few deal with the estimation of true signal from MR images acquired with phased-array coils. If the magnitude data from phased array coils are reconstructed as the root sum of squares, in the absence of noise correlations and subsampling, the data is assumed to follow a non central-χ distribution. However, when the k-space is subsampled to increase the acquisition speed (as in GRAPPA like methods), noise becomes spatially varying. In this note, we propose a method to denoise multiple-coil acquired MR images. Both the non central-χ distribution and the spatially varying nature of the noise is taken into account in the proposed method. Experiments were conducted on both simulated and real data sets to validate and to demonstrate the effectiveness of the proposed method.     

Low-field one-dimensional and direction-dependent relaxation imaging of bovine articular cartilage

The structure of articular cartilage is separated into three layers of differently oriented collagen fibers, which is accompanied by a gradient of increasing glycosaminoglycan (GAG) and decreasing water concentration from the top layer towards the bone interface. The combined effect of these structural variations results in a change of the longitudinal and transverse relaxation times as a function of the distance from the cartilage surface. In this paper, this dependence is investigated at a magnetic field strength of 0.27 T with a one-dimensional depth resolution of 50 μm on bovine hip and stifle joint articular cartilage. By employing this method, advantage is taken of the increasing contrast of the longitudinal relaxation rate found at lower magnetic field strengths. Furthermore, evidence for an orientational dependence of relaxation times with respect to an axis normal to the surface plane is given, an observation that has recently been reported using high-field MRI and that was explained by preferential orientations of collagen bundles in each of the three cartilage zones. In order to quantify the extent of a further contrast mechanism and to estimate spatially dependent glycosaminoglycan concentrations, the data are supplemented by proton relaxation times that were acquired in bovine articular cartilage that was soaked in a 0.8 mM aqueous Gd++ solution.     

Incorporating prior knowledge via volumetric deep residual network to optimize the reconstruction of sparsely sampled MRI

For sparse sampling that accelerates magnetic resonance (MR) image acquisition, non-linear reconstruction algorithms have been developed, which incorporated patient specific a prior information. More generic a prior information could be acquired via deep learning and utilized for image reconstruction. In this study, we developed a volumetric hierarchical deep residual convolutional neural network, referred to as T-Net, to provide a data-driven end-to-end mapping from sparsely sampled MR images to fully sampled MR images, where cartilage MR images were acquired using an Ultra-short TE sequence and retrospectively undersampled using pseudo-random Cartesian and radial acquisition schemes. The network had a hierarchical architecture that promoted the sparsity of feature maps and increased the receptive field, which were valuable for signal synthesis and artifact suppression. Relatively dense local connections and global shortcuts were established to facilitate residual learning and compensate for details lost in hierarchical processing. Additionally, volumetric processing was adopted to fully exploit spatial continuity in three-dimensional space. Data consistency was further enforced. The network was trained with 336 three-dimensional images (each consisting of 32 slices) and tested by 24 images. The incorporation of a priori information acquired via deep learning facilitated high acceleration factors (as high as 8) while maintaining high image fidelity (quantitatively evaluated using the structural similarity index measurement). The proposed T-Net had an improved performance as compared to several state-of-the-art networks.     

A non-invasive technique for 3-dimensional assessment of articular cartilage thickness based on MRI part 2: Validation using CT arthrography

Established methods for the measurement of articular cartilage thickness are invasive and cannot be sequentially applied in living subjects. In the present study, the distribution of cartilage thickness throughout entire joint surfaces was determined from MR images obtained with a fat-suppressed gradient-echo sequence at a resolution of 0.31 × 0.31 × 2.00 mm³, and compared to that derived from CT arthrography. A minimal distance algorithm was employed to produce 3D cartilage thickness maps of seven cadaveric human knee joints. The mean amount of deviation of the cartilage volumes was 5.6% (±4.6), statistical analysis showing that there was high agreement between the two methods (r = 0.995, slope = 1.037, y-intercept = -90.5 mm³). The 3D thickness maps yielded a striking agreement between the two methods, the maximum values generally yielding a deviation of none or one thickness interval of 0.5 mm. This investigation shows that accurate 3D assessment of articular cartilage thickness can be performed with MRI, this technique having the advantage that it is suitable for investigating living subjects.     

A study of the relationship between molecular biomarkers of joint degeneration and the magnetic resonance-measured characteristics of cartilage in 16 symptomatic knees

We used quantitative magnetic resonance (MR) imaging to determine if relationships exist between proposed molecular biomarkers for degenerative joint disease (DJD) and structural characteristics of articular cartilage. Subjects were eight male and eight female volunteers diagnosed with osteoarthritis. Magnetic resonance images of the symptomatic knee were taken and blood samples were drawn. Concentrations of serum cartilage oligomeric matrix protein (COMP) and cleaved collagen neoepitope were compared to cartilage volume and cartilage T2, respectively, in four compartments of the tibiofemoral joint. A significant, negative correlation was found between serum COMP and medial tibia volume in the male subject group (rho=-.738, P=.037). A significant, positive correlation (rho=.881, P=.0039) was found between serum COMP and lateral femur volume in the female subject group. In both groups, positive correlations were found between serum C2C and cartilage T2, which were significant in two compartments of the male group (rho=.714, P=.047; rho=.738, P=.037) and similarly strong, but not statistically significant (rho=.750, P=.052), in one compartment of the female group. We identify strong and biologically relevant correlations between two proposed molecular biomarkers for DJD and MR measures of symptomatic knees of a small number of arthritic patients. Our findings support the hypothesis that cartilage molecular biomarkers reflect the molecular processes of cartilage degeneration and loss.     

Physiological assessment of in vivo human knee articular cartilage using sodium MR imaging at 1.5 T

Osteoarthritis is a common joint disorder that is most prevalent in the knee joint. Knee osteoarthritis (OA) can be characterized by the gradual loss of articular cartilage (AC). Formation of lesion, fissures and cracks on the cartilage surface has been associated with degenerative AC and can be measured by morphological assessment. In addition, loss of proteoglycan from extracellular matrix of the AC can be measured at early stage of cartilage degradation by physiological assessment. In this case, a biochemical phenomenon of cartilage is used to assess the changes at early degeneration of AC. In this paper, a method to measure local sodium concentration in AC due to proteoglycan has been investigated. A clinical 1.5-T magnetic resonance imaging (MRI) with multinuclear spectroscopic facility is used to acquire sodium images and quantify local sodium content of AC. An optimised 3D gradient-echo sequence with low echo time has been used for MR scan. The estimated sodium concentration in AC region from four different data sets is found to be ~ 225 ± 19 mmol/l, which matches the values that has been reported for the normal AC. This study shows that sodium images acquired at clinical 1.5-T MRI system can generate an adequate quantitative data that enable the estimation of sodium concentration in AC. We conclude that this method is potentially suitable for non-invasive physiological (sodium content) measurement of articular cartilage.     

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.