3D far-field Lidar sensing and computational modeling for human identification.

3D sensors offer depth sensing that may be used for task-specific data processing and computational modeling. Many existing methods for human identification using 3D depth sensors primarily focus on Kinect data, where the range is very limited. This work considers a 3D long-range Lidar sensor for far-field imaging of human subjects in 3D Lidar full motion video (FMV) of "walking" action. 3D Lidar FMV data for human subjects are used to develop computational modeling for automated human silhouette and skeleton extraction followed by subject identification. We propose a matrix completion algorithm to handle missing data in 3D FMV due to self-occlusion and occlusion from other subjects for 3D skeleton extraction. We further study the effect of noise in the 3D low resolution far-field Lidar data in human silhouette extraction performance of the model. Moreover, this work addresses challenges associated with far-field 3D Lidar including learning with a limited amount of data and low resolution. Moreover, we evaluate the proposed computational algorithm using a gallery of 10 subjects for human identification and show that our method is competitive with the state-of-the-art OpenPose and V2VPose skeleton extraction models using the same dataset for human identification.

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead.

Electron cryomicroscopy (cryoEM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize macromolecular complexes such as ribosomes, viruses, and ion channels. Determination of structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryoEM a scientific rebirth. As a result of these technological advances image processing and analysis have yielded molecular structures at atomic resolution. Nevertheless there continue to be challenges in image processing, and in this article we will touch on the most essential in order to derive an accurate three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. We will then highlight new approaches for each image processing subproblem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking.

An unusual but reversible cause of ventricular fibrillation.

A 61-year-old woman was admitted with general malaise, chest pain and breathlessness. During her inpatient stay she sustained a ventricular fibrillation (VF) arrest which was successfully terminated with direct current cardioversion. Cardiac investigations revealed poor left ventricular systolic function but unequivocally normal coronary arteries. During the course of her admission a macular rash developed and following investigations including a renal biopsy, a new diagnosis of systemic lupus erythematosus (SLE) and related myocarditis was reached. First presentation of lupus with myocarditis and VF is uncommon, however reaching the correct diagnosis is important as due to the reversible nature of the condition and improvement in left ventricular systolic function with medical therapy, an implantable cardioverter defibrillator (ICD) might not be appropriate. Our case report demonstrates the importance of screening for reversible conditions when considering ICD therapy for secondary prevention of malignant arrhythmias.

Robust cardiomyocyte-specific gene expression following systemic injection of AAV: in vivo gene delivery follows a Poisson distribution.

Newly isolated serotypes of AAV readily cross the endothelial barrier to provide efficient transgene delivery throughout the body. However, tissue-specific expression is preferred in most experimental studies and gene therapy protocols. Previous efforts to restrict gene expression to the myocardium often relied on direct injection into heart muscle or intracoronary perfusion. Here, we report an AAV vector system employing the cardiac troponin T (cTnT) promoter. Using luciferase and enhanced green fluorescence protein (eGFP), the efficiency and specificity of cardiac reporter gene expression using AAV serotype capsids: AAV-1, 2, 6, 8 or 9 were tested after systemic administration to 1-week-old mice. Luciferase assays showed that the cTnT promoter worked in combination with each of the AAV serotype capsids to provide cardiomyocyte-specific gene expression, but AAV-9 followed closely by AAV-8 was the most efficient. AAV9-mediated gene expression from the cTnT promoter was 640-fold greater in the heart compared with the next highest tissue (liver). eGFP fluorescence indicated a transduction efficiency of 96% using AAV-9 at a dose of only 3.15 × 10(10) viral particles per mouse. Moreover, the intensity of cardiomyocyte eGFP fluorescence measured on a cell-by-cell basis revealed that AAV-mediated gene expression in the heart can be modeled as a Poisson distribution, requiring an average of nearly two vector genomes per cell to attain an 85% transduction efficiency.

Targeted ultrasound contrast agent for molecular imaging of inflammation in high-shear flow.

Targeted ultrasound contrast materials (gas-filled microbubbles carrying ligands to endothelial selectins or integrins) have been investigated as potential molecular imaging agents. Such microbubbles normally exhibit good targeting capability at the slower flow conditions. However, in the conditions of vigorous flow, binding may be limited. Here, we describe a microbubble capable of efficient binding to targets both in slow and fast flow (exceeding 4 dyne/cm(2) wall shear stress) using a clustered polymeric form of the fast-binding selectin ligand sialyl Lewis(X). Microbubbles were prepared from decafluorobutane gas and stabilized with a monolayer of phosphatidylcholine, PEG stearate and biotin-PEG-lipid. Biotinylated PSLe(x) (sialyl Lewis(X) polyacrylamide) or biotinylated anti-P-selectin antibody (RB40.34) was attached to microbubbles via a streptavidin bridge. In a parallel plate flow chamber targeted adhesion model, PSLe(x) bubbles demonstrated specific adhesion, retention and slow rolling on P-selectin-coated plates. Efficiency of firm targeted adhesion to a P-selectin surface (140 molecules/microm(2)) was comparable for antibody-carrying bubbles and PSLe(x)-targeted bubbles at 0.68 dyne/cm(2) shear stress. At fast flow (4.45 dyne/cm(2)), PSLe(x)-targeted bubbles maintained their ability to bind, while antibody-mediated targeting dropped more than 20-fold. At lower surface density of P-selectin (7 molecules/microm(2)), targeting via PSLe(x) was more efficient than via antibody under all the flow conditions tested. Negative control casein-coated plates did not retain bubbles in the range of flow conditions studied. To confirm echogenicity, targeted PSLe(x)-bubbles were visualized on P-selectin-coated polystyrene plates by ultrasound imaging with a clinical scanner operated in pulse inversion mode; control plates lacking targeted bubbles did not show significant acoustic backscatter. In vivo, in a murine model of inflammation in the femoral vein setting, targeting efficacy of intravenously administered PSLe(x)-microbubbles was comparable with targeting mediated by anti-P-selectin antibody, and significantly exceeded the accumulation of non-targeted control bubbles. In the inflamed femoral artery setting, PSLe(x)-mediated microbubble targeting was superior to antibody-mediated targeting.

Selectin ligands promote ultrasound contrast agent adhesion under shear flow.

Contrast-enhanced ultrasound imaging has shown promise in the field of molecular imaging. This technique relies upon the adhesion of ultrasound contrast agent (UCA) to targeted molecular markers of disease. This is accomplished by coating the surface of the contrast agent with a ligand that specifically binds to the intended molecular marker. Most UCA particles remain in the blood space, and their retention is influenced by the forces imposed by blood flow. For a UCA bound to a molecular target on the vascular endothelium, blood flow imposes a dislodging force that counteracts retention. Additionally, contrast agent adhesion to the molecular marker requires rapid binding kinetics, especially in rapid blood flow. The ability of a ligand:target bond complex to mediate fast adhesion and withstand dislodging force is necessary for efficient ultrasound-based molecular imaging. In the current study, we describe a flow-based adhesion assay which, combined with a novel automated tracking algorithm, enables quick determination of the ability of a targeting ligand to mediate effective contrast agent adhesion. This system was used to explore the adhesion of UCA targeted to the proinflammatory endothelial protein P-selectin via four targeting ligands, which revealed several interesting adhesive behaviors. Contrast agents targeted with glycoconjugate ligands modeled on P-selectin glycoprotein ligand 1 exhibited primarily unstable or transient adhesion, while UCA targeted with an anti-P-selectin monoclonal antibody exhibited primarily firm adhesion, although the efficiency with which these agents were recruited to the target surface was relatively low.

Tissue distribution and functional expression of a cDNA encoding a novel mixed lineage kinase.

Hypertrophy is an adaptive response of the heart to myocardial injury or hemodynamic overload that may progress and contribute to cardiac decompensation and eventually to heart failure. The signaling pathways controlling this response in the cardiac myocyte are poorly understood. A data mining effort of a human failed heart cDNA library was undertaken in an effort to identify novel signaling molecules involved in cardiac hypertrophy. This effort identified a novel kinase (MLK7) homologous to the mixed lineage kinase family of proteins. The mixed lineage kinases are mitogen-activated protein kinase kinase kinases (MAPKKKs) which activate stress activated protein kinase/c-Jun N-terminal kinase (SAPK/JNK) and p38 kinase pathways. They contain a catalytic domain with homology to both serine/threonine and tyrosine-specific kinases and a dual leucine zipper. MLK7 is identical to leucine zipper and sterile-alpha motif protein kinase (ZAK) through the leucine zipper domain but has a completely divergent COOH-terminus and shares approximately 40% homology with the other MLKs overall. Expression of MLK7 mRNA is most abundant in skeletal muscle and heart, with expression restricted to the cardiac myocyte. The recombinant histidine tagged MLK7 expressed and purified from insect cells exhibited serine/threonine kinase activity in vitro with myelin basic protein as substrate. When expressed in cardiac myocytes, MLK7 activated SAPK/JNK1, and ERK and p38 to a lesser extent. Additionally, MLK7 altered fetal gene expression and increased protein synthesis in cardiac myocytes. These data suggest that MLK7 is a new member of the mixed lineage kinase family that modulates cardiac SAPK/JNK pathway and may play a role in cardiac hypertrophy and progression to heart failure.

Role of PRL-3, a human muscle-specific tyrosine phosphatase, in angiotensin-II signaling.

Action of protein kinases and phosphatases contributes to myocardial hypertrophy. PRL-3, a protein tyrosine phosphatase, was identified in a cDNA library from an explanted human heart obtained from a patient with idiopathic cardiomyopathy. PRL-3 is expressed in heart and skeletal muscle, exhibiting approximately 76% identity to the ubiquitous tyrosine phosphatase PRL-1, which was reported to increase cell proliferation. PRL-3 was cloned into E. coli and purified using affinity chromatography. PRL-3 activity was determined using the substrate 6,8-difluoro-4-methylumbelliferyl phosphate, and was inhibited by vanadate and analogs. HEK293 cells expressing PRL-3 demonstrated increased growth rates versus nontransfected cells or cells transfected with the catalytically inactive C104S PRL-3 mutant. The tyrosine phosphatase inhibitor, potassium bisperoxo (bipyridine) oxovanadate V, normalizes the growth rate of PRL-3 expressing cells to that of parental HEK293 cells in a concentration-dependent manner. Using FLIPR analysis, parental HEK293 cells mobilize calcium when stimulated with angiotensin-II (AngII). However, calcium mobilization is inhibited in cells expressing wild-type PRL-3 when stimulated with AngII, while cells expressing the inactive mutant of PRL-3 mobilize calcium to the same extent as parental HEK293 cells. Western blots comparing PRL-3 transfected cells to parental HEK293 cells showed dephosphorylation of p130(cas) in response to AngII. These data suggest a role for PRL-3 in the modulation of intracellular calcium transients induced by AngII.

A novel angiotensin-converting enzyme-related carboxypeptidase (ACE2) converts angiotensin I to angiotensin 1-9.

ACE2, the first known human homologue of angiotensin-converting enzyme (ACE), was identified from 5' sequencing of a human heart failure ventricle cDNA library. ACE2 has an apparent signal peptide, a single metalloprotease active site, and a transmembrane domain. The metalloprotease catalytic domains of ACE2 and ACE are 42% identical, and comparison of the genomic structures indicates that the two genes arose through duplication. In contrast to the more ubiquitous ACE, ACE2 transcripts are found only in heart, kidney, and testis of 23 human tissues examined. Immunohistochemistry shows ACE2 protein predominantly in the endothelium of coronary and intrarenal vessels and in renal tubular epithelium. Active ACE2 enzyme is secreted from transfected cells by cleavage N-terminal to the transmembrane domain. Recombinant ACE2 hydrolyzes the carboxy terminal leucine from angiotensin I to generate angiotensin 1-9, which is converted to smaller angiotensin peptides by ACE in vitro and by cardiomyocytes in culture. ACE2 can also cleave des-Arg bradykinin and neurotensin but not bradykinin or 15 other vasoactive and hormonal peptides tested. ACE2 is not inhibited by lisinopril or captopril. The organ- and cell-specific expression of ACE2 and its unique cleavage of key vasoactive peptides suggest an essential role for ACE2 in the local renin-angiotensin system of the heart and kidney. The full text of this article is available at http://www. circresaha.org.

Amniotic fluid homocysteine levels, 5,10-methylenetetrahydrafolate reductase genotypes, and neural tube closure sites.

A specific gene mutation leading to altered homocysteine metabolism has been identified in parents and fetuses with neural tube defects (NTDs). In addition, current animal and human data indicate that spine closure occurs simultaneously in five separate sites that then fuse. We sought to determine whether either this mutation or abnormal amniotic fluid homocysteine levels are associated with all five neural tube closure sites. We retrieved stored amniotic fluid from cases of isolated fetal neural tube defect diagnosed from 1988 to 1998 (n = 80) and from normal controls matched for race, month and year of amniocentesis, and maternal age. Cases were categorized according to defect site by using all available medical records. The presence or absence of the 677C-->T mutation of 5, 10-methylenetetrahydrafolate reductase (MTHFR) gene was determined, and homocysteine levels were measured; case and controls were compared. Significantly more cases than controls were heterozygous or homozygous for the 677C-->T MTHFR mutation (44% vs. 17%, P < or = 0. 001). Likewise, cases were significantly more likely than controls to have amniotic fluid homocysteine levels >90th centile (>1.85 micromol/L), 27% vs. 10%, P = 0.02. Most (83%) of control cases had both normal MTHFR alleles and normal amniotic fluid homocysteine levels (normal/normal), whereas only 56% of NTD case were normal/normal (P = 0.001). When evaluated by defect site, only defects involving the cervical-lumbar spine, lumbosacral spine, and occipital encephalocele were significantly less likely to be normal/normal than controls (P = 0.007, 0.0003, and 0.007, respectively), suggesting a strong association with the 677C-->T allele. In contrast, anencephaly, exencephaly, and defects confined to the sacrum included many cases that had both normal MTHFR alleles and normal homocysteine and were not significantly different from controls. The 677C-->T MTHFR mutation and elevated homocysteine levels appear to be disproportionately associated with defects spanning the cervical-lumbar spine, lumbosacral spine, and occipital encephalocele. In contrast, anencephaly, exencephaly, and defects confined to the sacrum may not be related to altered homocysteine metabolism.

Role of amniotic fluid homocysteine level and of fetal 5, 10-methylenetetrahydrafolate reductase genotype in the etiology of neural tube defects.

A mutation in the gene 5,10-methylenetetrahydrofolate reductase (MTHFR), leading to altered homocysteine metabolism, has been identified in parents and fetuses with fetal neural tube defects. We sought to determine which is of greater importance in fetal neural tube defect formation: the fetal MTHFR mutation or elevated amniotic fluid homocysteine level. We retrieved stored amniotic fluid from cases of isolated fetal neural tube defect diagnosed from 1988 to 1998 (n = 80), and from normal controls matched for race, month and year of amniocentesis, and maternal age. The presence or absence of the 677C-->T mutation of MTHFR was determined and homocysteine levels were measured; cases and controls were compared. Significantly more cases than controls were heterozygous or homozygous for the 677C-->T MTHFR mutation (44% vs 17%, P < or = 0.001). Cases were also significantly more likely than controls to have an amniotic fluid homocysteine level above the 90th centile (>1.85 micromol per liter); 27% vs 10%, P = 0.02. Thirty one cases and 12 controls had an abnormal genotype; however, amniotic fluid homocysteine levels were not significantly different between these two groups (6/31, or 19% of cases had an elevated homocysteine compared to 1/12, or 8% of controls; P = 0.65). In contrast, 40 cases and 60 controls had a normal genotype; the neural tube defect cases had significantly higher homocysteine levels (13/40, or 32% of cases had an elevated homocysteine level compared to only 6/60, or 10% of controls; P = 0.008). Although both abnormal fetal MTHFR genotype and abnormal amniotic fluid homocysteine concentration are significantly associated with neural tube defects, the association with amniotic fluid homocysteine concentration is significant regardless of the fetal MTHFR genotype. The relationship between maternal and fetal homocysteine metabolism is complex.

Scale space classification using area morphology.

We explore the application of area morphology to image classification. From the input image, a scale space is created by successive application of an area morphology operator. The pixels within the scale space corresponding to the same image location form a scale space vector. A scale space vector therefore contains the intensity of a particular pixel for a given set of scales, determined in this approach by image granulometry. Using the standard k-means algorithm or the fuzzy c-means algorithm, the image pixels can be classified by clustering the associated scale space vectors. The scale space classifier presented here is rooted in the novel area open-close and area close-open scale spaces. Unlike other scale generating filters, the area operators affect the image by removing connected components within the image level sets that do not satisfy the minimum area criterion. To show that the area open-close and area close-open scale spaces provide an effective multiscale structure for image classification, we demonstrate the fidelity, causality, and edge localization properties for the scale spaces. The analysis also reveals that the area open-close and area close-open scale spaces improve classification by clustering members of similar objects more effectively than the fixed scale classifier. Experimental results are provided that demonstrate the reduction in intra-region classification error and in overall classification error given by the scale space classifier for classification applications where object scale is important. In both visual and objective comparisons, the scale space approach outperforms the traditional fixed scale clustering algorithms and the parametric Bayesian classifier for classification tasks that depend on object scale.

The HDL receptor SR-BI: a new therapeutic target for atherosclerosis?

Although high-density lipoprotein (HDL) metabolism is a crucial process for cholesterol homeostasis and coronary heart disease, therapeutic approaches for selective modification of plasma HDL levels are not currently available. The discovery of well-defined cell-surface HDL receptors should provide new avenues for treatment of atherosclerotic cardiovascular disease. In fact, SR-BI, a recently identified receptor for selective HDL cholesterol uptake, is relevant for physiological processes (for example, HDL metabolism, steroidogenesis and biliary cholesterol secretion) and pathophysiological conditions (for example, atherosclerosis) in animal models. If SR-BI has similar activities in humans, it might represent a new therapeutic target for atherosclerosis.

Association of polymorphisms at the SR-BI gene locus with plasma lipid levels and body mass index in a white population.

The scavenger receptor class B type I (SR-BI) is a lipoprotein receptor that has been shown to be important in high density lipoprotein cholesterol (HDL-C) metabolism in mice. To determine its role in humans, we have characterized the human SR-BI gene and investigated its genetic variation in 489 white men and women. Five variants were demonstrated: 2 in introns (3 and 5) and 3 in exons (1, 8, and 11). Three variants at exons 1 and 8 and intron 5 with allele frequencies >0.1 were used to examine associations with lipid or anthropometric variables. The exon 1 variant was significantly (P<0.05) associated with increased HDL-C and lower low density lipoprotein cholesterol (LDL-C) values in men, but no associations were observed in women. The exon 8 variant was associated in women with lower LDL-C concentrations (3.05+/-0.98 mmol/L and 3.00+/-0.93 mmol/L for heterozygotes and homozygotes, respectively) compared with women homozygous for the common allele (3.39+/-1.09 mmol/L, P=0. 043). No associations for this variant were observed in men. Women carriers of the intron 5 variant showed a higher body mass index (23. 8+/-3.8 kg/m2, P=0.031) than those women homozygous for the common allele (22.4+/-3.4 kg/m2). Similar results were observed after haplotype analysis. Multiple regression analysis using HDL-C, LDL-C, and body mass index as dependent variables and age, sex, and each of the genetic variants as predictors also provided similar results. The associations found with both LDL-C and HDL-C suggest that SR-BI may play a role in the metabolism of both lipoprotein classes in humans.

Piecewise and local image models for regularized image restoration using cross-validation.

We describe two broad classes of useful and physically meaningful image models that can be used to construct novel smoothing constraints for use in the regularized image restoration problem. The two classes, termed piecewise image models (PIMs) and focal image models (LIMs), respectively, capture unique image properties that can be adapted to the image and that reflect structurally significant surface characteristics. Members of the PIM and LIM classes are easily formed into regularization operators that replace differential-type constraints. We also develop an adaptive strategy for selecting the best PIM or LIM for a given problem (from among the defined class), and we explain the construction of the corresponding regularization operators. Considerable attention is also given to determining the regularization parameter via a cross-validation technique, and also to the selection of an optimization strategy for solving the problem. Several results are provided that illustrate the processes of model selection, parameter selection, and image restoration. The overall approach provides a new viewpoint on the restoration problem through the use of new image models that capture salient image features that are not well represented through traditional approaches.

The efficient cellular uptake of high density lipoprotein lipids via scavenger receptor class B type I requires not only receptor-mediated surface binding but also receptor-specific lipid transfer mediated by its extracellular domain.

The class B type I scavenger receptor, (SR-BI), is a member of the CD36 superfamily of proteins and is a physiologically relevant, high affinity cell surface high density lipoprotein (HDL) receptor that mediates selective lipid uptake. The mechanism of selective lipid uptake is fundamentally different from that of classic receptor-mediated uptake via coated pits and vesicles (e.g. the low density lipoprotein receptor pathway) in that it involves efficient transfer of the lipids, but not the outer shell proteins, from HDL to cells. The abilities of SR-BI and CD36, both of which are class B scavenger receptors, to bind HDL and mediate cellular uptake of HDL-associated lipid when transiently expressed in COS cells were examined. For these experiments, the binding of HDL to cells was assessed using either 125I- or Alexa (a fluorescent dye)-HDL in which the apolipoproteins on the surface of the HDL particles were covalently modified. Lipid transfer was measured using HDL noncovalently labeled by the fluorescent lipid 1,1'-dioctadecyl-3,3, 3',3'-tetramethylindocarbocyanine perchlorate. Although both mSR-BI and human CD36 (hCD36) could mediate the binding of HDL in a punctate pattern across the surfaces of cells, only mSR-BI efficiently mediated the transfer of lipid to the cells. Analysis of point mutants established that the major sites of fatty acylation of mSR-BI are Cys462 and Cys470 and that fatty acylation is not required for receptor clustering, HDL binding, or efficient lipid transfer. Generation of mSR-BI/hCD36 domain swap chimeras showed that the differences in lipid uptake activities between mSR-BI and hCD36 were not due to differences between their two sets of transmembrane and cytoplasmic domains but rather result from differences in their large extracellular loop domains. These results show that high affinity binding to a cell surface receptor is not sufficient to ensure efficient cellular lipid uptake from HDL. Thus, SR-BI-mediated binding combined with SR-BI-dependent facilitated transfer of lipid from the HDL particle to the cell appears to be the most likely mechanism for the bulk of the selective uptake of cholesteryl esters from HDL to the liver and steroidogenic tissues.

Targeted mutation reveals a central role for SR-BI in hepatic selective uptake of high density lipoprotein cholesterol.

Scavenger receptor BI (SR-BI) is a cell surface receptor that binds high density lipoproteins (HDL) and mediates selective uptake of HDL cholesteryl esters (CE) in transfected cells. To address the physiological role of SR-BI in HDL cholesterol homeostasis, mice were generated bearing an SR-BI promoter mutation that resulted in decreased expression of the receptor in homozygous mutant (designated SR-BI att) mice. Hepatic expression of the receptor was reduced by 53% with a corresponding increase in total plasma cholesterol levels of 50-70% in SR-BI att mice, attributable almost exclusively to elevated plasma HDL. In addition to increased HDL-CE, HDL phospholipids and apo A-1 levels were elevated, and there was an increase in HDL particle size in mutant mice. Metabolic studies using HDL bearing nondegradable radiolabels in both the protein and lipid components demonstrated that reducing hepatic SR-BI expression by half was associated with a decrease of 47% in selective uptake of CE by the liver, and a corresponding reduction of 53% in selective removal of HDL-CE from plasma. Taken together, these findings strongly support a pivotal role for hepatic SR-BI expression in regulating plasma HDL levels and indicate that SR-BI is the major molecule mediating selective CE uptake by the liver. The inverse correlation between plasma HDL levels and atherosclerosis further suggests that SR-BI may influence the development of coronary artery disease.

Multigrid anisotropic diffusion.

A multigrid anisotropic diffusion algorithm for image processing is presented. The multigrid implementation provides an efficient hierarchical relaxation method that facilitates the application of anisotropic diffusion to time-critical processes. Through a multigrid V-cycle, the anisotropic diffusion equations are successively transferred to coarser grids and used in a coarse-to-fine error correction scheme. When a coarse grid with a trivial solution is reached, the coarse grid estimates of the residual error can be propagated to the original grid and used to refine the solution. The main benefits of the multigrid approach are rapid intraregion smoothing and reduction of artifacts due to the elimination of low-frequency error. The theory of multigrid anisotropic diffusion is developed. Then, the intergrid transfer functions, relaxation techniques, diffusion coefficients, and boundary conditions are discussed. The analysis includes the examination of the storage requirements, the computational cost, and the solution quality. Finally, experimental results are reported that demonstrate the effectiveness of the multigrid approach.