A total variation discontinuous Galerkin approach for image restoration

The focal point of this paper is to propose and analyze a P 0 discontinuous Galerkin (DG) formulation for image denoising. The scheme is based on a total variation approach which has been applied successfully in previous papers on image processing. The main idea of the new scheme is to model the restoration process in terms of a discrete energy minimization problem and to derive a corresponding DG variational formulation. Furthermore, we will prove that the method exhibits a unique solution and that a natural maximum principle holds. In addition, a number of examples illustrate the effectiveness of the method.

Gibbs point process approximation: Total variation bounds using Stein's method

We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.

Total Variation Blind Deconvolution: The Devil Is in the Details

In this paper we study the problem of blind deconvolution. Our analysis is based on the algorithm of Chan and Wong [2] which popularized the use of sparse gradient priors via total variation. We use this algorithm because many methods in the literature are essentially adaptations of this framework. Such algorithm is an iterative alternating energy minimization where at each step either the sharp image or the blur function are reconstructed. Recent work of Levin et al. [14] showed that any algorithm that tries to minimize that same energy would fail, as the desired solution has a higher energy than the no-blur solution, where the sharp image is the blurry input and the blur is a Dirac delta. However, experimentally one can observe that Chan and Wong's algorithm converges to the desired solution even when initialized with the no-blur one. We provide both analysis and experiments to resolve this paradoxical conundrum. We find that both claims are right. The key to understanding how this is possible lies in the details of Chan and Wong's implementation and in how seemingly harmless choices result in dramatic effects. Our analysis reveals that the delayed scaling (normalization) in the iterative step of the blur kernel is fundamental to the convergence of the algorithm. This then results in a procedure that eludes the no-blur solution, despite it being a global minimum of the original energy. We introduce an adaptation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the state of the art.

A Clearer Picture of Total Variation Blind Deconvolution

Blind deconvolution is the problem of recovering a sharp image and a blur kernel from a noisy blurry image. Recently, there has been a significant effort on understanding the basic mechanisms to solve blind deconvolution. While this effort resulted in the deployment of effective algorithms, the theoretical findings generated contrasting views on why these approaches worked. On the one hand, one could observe experimentally that alternating energy minimization algorithms converge to the desired solution. On the other hand, it has been shown that such alternating minimization algorithms should fail to converge and one should instead use a so-called Variational Bayes approach. To clarify this conundrum, recent work showed that a good image and blur prior is instead what makes a blind deconvolution algorithm work. Unfortunately, this analysis did not apply to algorithms based on total variation regularization. In this manuscript, we provide both analysis and experiments to get a clearer picture of blind deconvolution. Our analysis reveals the very reason why an algorithm based on total variation works. We also introduce an implementation of this algorithm and show that, in spite of its extreme simplicity, it is very robust and achieves a performance comparable to the top performing algorithms.

Grain yield variation and association of major traits in brown-seeded genotypes of tef [Eragrostis tef (Zucc.)Trotter]

Background Tef [Eragrostis tef (Zucc.) Trotter] is the major cereal crop of Ethiopia where it is annually cultivated on more than three million hectares of land by over six million small-scale farmers. It is broadly grouped into white and brown-seeded type depending on grain color, although some intermediate color grains also exist. Earlier breeding experiments focused on white-seeded tef, and a number of improved varieties were released to the farming community. Thirty-six brown-seeded tef genotypes were evaluated using a 6 × 6 simple lattice design at three locations in the central highlands of Ethiopia to assess the productivity, heritability, and association among major pheno-morphic traits. Results The mean square due to genotypes, locations, and genotype by locations were significant (P < 0.01) for all traits studied. Genotypic and phenotypic coefficients of variations ranged from 2.5 to 20.3 % and from 4.3 to 21.7 %, respectively. Grain yield showed significant (P < 0.01) genotypic correlation with shoot biomass and harvest index, while it had highly significant (P < 0.01) phenotypic correlation with all the traits evaluated. Besides, association of lodging index with biomass and grain yield was negative and significant at phenotypic level while it was not significant at genotypic level. Cluster analysis grouped the 36 test genotypes into seven distinct classes. Furthermore, the first three principal components with eigenvalues greater than unity extracted 78.3 % of the total variation. Conclusion The current study, generally, revealed the identification of genotypes with superior grain yield and other desirable traits for further evaluation and eventual release to the farming community.

Index of Complexity, Outcome and Need scored on plaster and digital models

The aim of this study was to compare standard plaster models with their digital counterparts for the applicability of the Index of Complexity, Outcome, and Need (ICON). Generated study models of 30 randomly selected patients: 30 pre- (T(0)) and 30 post- (T(1)) treatment. Two examiners, calibrated in the ICON, scored the digital and plaster models. The overall ICON scores were evaluated for reliability and reproducibility using kappa statistics and reliability coefficients. The values for reliability of the total and weighted ICON scores were generally high for the T(0) sample (range 0.83-0.95) but less high for the T(1) sample (range 0.55-0.85). Differences in total ICON score between plaster and digital models resulted in mostly statistically insignificant values (P values ranging from 0.07 to 0.19), except for observer 1 in the T(1) sample. No statistically different values were found for the total ICON score on either plaster or digital models. ICON scores performed on computer-based models appear to be as accurate and reliable as ICON scores on plaster models.

Cosmogenic 180W variations in meteorites and re-assessment of a possible 184Os–180W decay system

We measured tungsten (W) isotopes in 23 iron meteorites and the metal phase of the CB chondrite Gujba in order to ascertain if there is evidence for a large-scale nucleosynthetic heterogeneity in the p-process isotope 180W in the solar nebula as recently suggested by Schulz et al. (2013). We observed large excesses in 180W (up to ≈ 6 ε) in some irons. However, significant within-group variations in magmatic IIAB and IVB irons are not consistent with a nucleosynthetic origin, and the collateral effects on 180W from an s-deficit in IVB irons cannot explain the total variation. We present a new model for the combined effects of spallation and neutron capture reactions on 180W in iron meteorites and show that at least some of the observed within-group variability is explained by cosmic ray effects. Neutron capture causes burnout of 180W, whereas spallation reactions lead to positive shifts in 180W. These effects depend on the target composition and cosmic-ray exposure duration; spallation effects increase with Re/W and Os/W ratios in the target and with exposure age. The correlation of 180W/184W with Os/W ratios in iron meteorites results in part from spallogenic production of 180W rather than from 184Os decay, contrary to a recent study by Peters et al. (2014). Residual ε180W excesses after correction for an s-deficit and for cosmic ray effects may be due to ingrowth of 180W from 184Os decay, but the magnitude of this ingrowth is at least a factor of ≈2 smaller than previously suggested. These much smaller effects strongly limit the applicability of the putative 184Os-180W system to investigate geological problems.

Functional evaluation of transplanted kidneys with diffusion-weighted and BOLD MR imaging: initial experience

PURPOSE: To prospectively evaluate feasibility and reproducibility of diffusion-weighted (DW) and blood oxygenation level-dependent (BOLD) magnetic resonance (MR) imaging in patients with renal allografts, as compared with these features in healthy volunteers with native kidneys. MATERIALS AND METHODS: The local ethics committee approved the study protocol; patients provided written informed consent. Fifteen patients with a renal allograft and in stable condition (nine men, six women; age range, 20-67 years) and 15 age- and sex-matched healthy volunteers underwent DW and BOLD MR imaging. Seven patients with renal allografts were examined twice to assess reproducibility of results. DW MR imaging yielded a total apparent diffusion coefficient including diffusion and microperfusion (ADC(tot)), as well as an ADC reflecting predominantly pure diffusion (ADC(D)) and the perfusion fraction. R2* of BOLD MR imaging enabled the estimation of renal oxygenation. Statistical analysis was performed, and analysis of variance was used for repeated measurements. Coefficients of variation between and within subjects were calculated to assess reproducibility. RESULTS: In patients, ADC(tot), ADC(D), and perfusion fraction were similar in the cortex and medulla. In volunteers, values in the medulla were similar to those in the cortex and medulla of patients; however, values in the cortex were higher than those in the medulla (P < .05). Medullary R2* was higher than cortical R2* in patients (12.9 sec(-1) +/- 2.1 [standard deviation] vs 11.0 sec(-1) +/- 0.6, P < .007) and volunteers (15.3 sec(-1) +/- 1.1 vs 11.5 sec(-1) +/- 0.5, P < .0001). However, medullary R2* was lower in patients than in volunteers (P < .004). Increased medullary R2* was paralleled by decreased diffusion in patients with allografts. A low coefficient of variation in the cortex and medulla within subjects was obtained for ADC(tot), ADC(D), and R2* (<5.2%), while coefficient of variation within subjects was higher for perfusion fraction (medulla, 15.1%; cortex, 8.6%). Diffusion and perfusion indexes correlated significantly with serum creatinine concentrations. CONCLUSION: DW and BOLD MR imaging are feasible and reproducible in patients with renal allografts.

Pelvic tilt is minimally changed by total hip arthroplasty

BACKGROUND While surgical navigation offers the opportunity to accurately place an acetabular component, questions remain as to the best goal for acetabular component positioning in individual patients. Overall functional orientation of the pelvis after surgery is one of the most important variables for the surgeon to consider when determining the proper goal for acetabular component orientation. QUESTIONS/PURPOSES We measured the variation in pelvic tilt in 30 patients before THA and the effect of THA on pelvic tilt in the same patients more than a year after THA. METHODS Each patient had a CT study for CT-based surgical navigation and standing and supine radiographs before and after surgery. Pelvic tilt was calculated for each of the radiographs using a novel and validated two-dimensional/three-dimensional matching technique. RESULTS Mean supine pelvic tilt changed less than 2°, from 4.4° ± 6.4° (range, -7.7° to 20.8°) before THA to 6.3° ± 6.6° (range, -5.7° to 19.6°) after THA. Mean standing pelvic tilt changed less than 1°, from 1.5° ± 7.2° (range, -13.1° to 12.8°) before THA to 2.0° ± 8.3° (range, -12.3° to 16.8°) after THA. Preoperative pelvic tilt correlated with postoperative tilt in both the supine (r(2) = 0.75) and standing (r(2) = 0.87) positions. CONCLUSIONS In this population, pelvic tilt had a small and predictable change after surgery. However, intersubject variability of pelvic tilt was high, suggesting preoperative pelvic tilt should be considered when determining desired acetabular component positioning on a patient-specific basis.

Comparison of Routine Brain Imaging at 3 T and 7 T.

OBJECTIVE The aim of this study was to compare quantitative and semiquantitative parameters (signal-to-noise ratio [SNR], contrast-to-noise ratio [CNR], image quality, diagnostic confidence) from a standard brain magnetic resonance imaging examination encompassing common neurological disorders such as demyelinating disease, gliomas, cerebrovascular disease, and epilepsy, with comparable sequence protocols and acquisition times at 3 T and at 7 T. MATERIALS AND METHODS Ten healthy volunteers and 4 subgroups of 40 patients in total underwent comparable magnetic resonance protocols with standard diffusion-weighted imaging, 2D and 3D turbo spin echo, 2D and 3D gradient echo and susceptibility-weighted imaging of the brain (10 sequences) at 3 T and 7 T. The subgroups comprised patients with either lesional (n = 5) or nonlesional (n = 4) epilepsy, intracerebral tumors (n = 11), demyelinating disease (n = 11) (relapsing-remitting multiple sclerosis [MS, n = 9], secondary progressive MS [n = 1], demyelinating disease not further specified [n = 1]), or chronic cerebrovascular disorders [n = 9]). For quantitative analysis, SNR and CNR were determined. For a semiquantitative assessment of the diagnostic confidence, a 10-point scale diagnostic confidence score (DCS) was applied. Two experienced radiologists with additional qualification in neuroradiology independently assessed, blinded to the field strength, 3 pathology-specific imaging criteria in each of the 4 disease groups and rated their diagnostic confidence. The overall image quality was semiquantitatively assessed using a 4-point scale taking into account whether diagnostic decision making was hampered by artifacts or not. RESULTS Without correction for spatial resolution, SNR was higher at 3 T except in the T2 SPACE 3D, DWI single shot, and DIR SPACE 3D sequences. The SNR corrected by the ratio of 3 T/7 T voxel sizes was higher at 7 T than at 3 T in 10 of 11 sequences (all except for T1 MP2RAGE 3D).In CNR, there was a wide variation between sequences and patient cohorts, but average CNR values were broadly similar at 3 T and 7 T.DCS values for all 4 pathologic entities were higher at 7 T than at 3 T. The DCS was significantly higher at 7 T for diagnosis and exclusion of cortical lesions in vascular disease. A tendency to higher DCS at 7 T for cortical lesions in MS was observed, and for the depiction of a central vein and iron deposits within MS lesions. Despite motion artifacts, DCS values were higher at 7 T for the diagnosis and exclusion of hippocampal sclerosis in mesial temporal lobe epilepsy (improved detection of the hippocampal subunits). Interrater agreement was 69.7% at 3 T and 93.3% at 7 T. There was no significant difference in the overall image quality score between 3 T and 7 T taking into account whether diagnostic decision making was hampered by artifacts or not. CONCLUSIONS Ultra-high-field magnetic resonance imaging at 7 T compared with 3 T yielded an improved diagnostic confidence in the most frequently encountered neurologic disorders. Higher spatial resolution and contrast were identified as the main contributory factors.