ANOVA kernels and RKHS of zero mean functions for model-based sensitivity analysis

Given a reproducing kernel Hilbert space (H,〈.,.〉)(H,〈.,.〉) of real-valued functions and a suitable measure μμ over the source space D⊂RD⊂R, we decompose HH as the sum of a subspace of centered functions for μμ and its orthogonal in HH. This decomposition leads to a special case of ANOVA kernels, for which the functional ANOVA representation of the best predictor can be elegantly derived, either in an interpolation or regularization framework. The proposed kernels appear to be particularly convenient for analyzing the effect of each (group of) variable(s) and computing sensitivity indices without recursivity.

Kernels and Designs for Modelling Invariant Functions: From Group Invariance to Additivity

We focus on kernels incorporating different kinds of prior knowledge on functions to be approximated by Kriging. A recent result on random fields with paths invariant under a group action is generalised to combinations of composition operators, and a characterisation of kernels leading to random fields with additive paths is obtained as a corollary. A discussion follows on some implications on design of experiments, and it is shown in the case of additive kernels that the so-called class of “axis designs” outperforms Latin hypercubes in terms of the IMSE criterion.

On ANOVA Decompositions of Kernels and Gaussian Random Field Paths

The FANOVA (or “Sobol’-Hoeffding”) decomposition of multivariate functions has been used for high-dimensional model representation and global sensitivity analysis. When the objective function f has no simple analytic form and is costly to evaluate, computing FANOVA terms may be unaffordable due to numerical integration costs. Several approximate approaches relying on Gaussian random field (GRF) models have been proposed to alleviate these costs, where f is substituted by a (kriging) predictor or by conditional simulations. Here we focus on FANOVA decompositions of GRF sample paths, and we notably introduce an associated kernel decomposition into 4 d 4d terms called KANOVA. An interpretation in terms of tensor product projections is obtained, and it is shown that projected kernels control both the sparsity of GRF sample paths and the dependence structure between FANOVA effects. Applications on simulated data show the relevance of the approach for designing new classes of covariance kernels dedicated to high-dimensional kriging.

Effects of long-term feeding of genetically modified corn (event MON810) on the performance of lactating dairy cows

A long-term study over 25 months was conducted to evaluate the effects of genetically modified corn on performance of lactating dairy cows. Thirty-six dairy cows were assigned to two feeding groups and fed with diets based on whole-crop silage, kernels and whole-crop cobs from Bt-corn (Bt-MON810) or its isogenic not genetically modified counterpart (CON) as main components. The study included two consecutive lactations. There were no differences in the chemical composition and estimated net energy content of Bt-MON810 and CON corn components and diets. CON feed samples were negative for the presence of Cry1Ab protein, while in Bt-MON810 feed samples the Cry1Ab protein was detected. Cows fed Bt-MON810 corn had a daily Cry1Ab protein intake of 6.0 mg in the first lactation and 6.1 mg in the second lactation of the trial. Dry matter intake (DMI) was 18.8 and 20.7 kg/cow per day in the first and the second lactation of the trial, with no treatment differences. Similarly, milk yield (23.8 and 29.0 kg/cow per day in the first and the second lactation of the trial) was not affected by dietary treatment. There were no consistent effects of feeding MON810 or its isogenic CON on milk composition or body condition. Thus, the present long-term study demonstrated the compositional and nutritional equivalence of Bt-MON810 and its isogenic CON.

Diagnostic accuracy of coronary in-stent restenosis using 64-slice computed tomography: comparison with invasive coronary angiography

OBJECTIVES: This study sought to evaluate the diagnostic accuracy of coronary binary in-stent restenosis (ISR) with angiography using 64-slice multislice computed tomography coronary angiography (CTCA) compared with invasive coronary angiography (ICA). BACKGROUND: A noninvasive detection of ISR would result in an easier and safer way to conduct patient follow-up. METHODS: We performed CTCA in 81 patients after stent implantation, and 125 stented lesions were scanned. Two sets of images were reconstructed with different types of convolution kernels. On CTCA, neointimal proliferation was visually evaluated according to luminal contrast attenuation inside the stent. Lesions were graded as follows: grade 1, none or slight neointimal proliferation; grade 2, neointimal proliferation with no significant stenosis (<50%); grade 3, neointimal proliferation with moderate stenosis (> or =50%); and grade 4, neointimal proliferation with severe stenosis (> or =75%). Grades 3 and 4 were considered binary ISR. The diagnostic accuracy of CTCA compared with ICA was evaluated. RESULTS: By ICA, 24 ISRs were diagnosed. Sensitivity, specificity, positive predictive value, and negative predictive value were 92%, 81%, 54%, and 98% for the overall population, whereas values were 91%, 93%, 77%, and 98% when excluding unassessable segments (15 segments, 12%). For assessable segments, CTCA correctly diagnosed 20 of the 22 ISRs detected by ICA. Six lesions without ISR were overestimated as ISR by CTCA. As the grade of neointimal proliferation by CTCA increases, the median value of percent diameter stenosis increased linearly. CONCLUSIONS: Binary ISR can be excluded with high probability by CTCA, with a moderate rate of false-positive results.

Calibration of a portal imaging device for high-precision dosimetry: a Monte Carlo study

Today electronic portal imaging devices (EPID's) are used primarily to verify patient positioning. They have, however, also the potential as 2D-dosimeters and could be used as such for transit dosimetry or dose reconstruction. It has been proven that such devices, especially liquid filled ionization chambers, have a stable dose response relationship which can be described in terms of the physical properties of the EPID and the pulsed linac radiation. For absolute dosimetry however, an accurate method of calibration to an absolute dose is needed. In this work, we concentrate on calibration against dose in a homogeneous water phantom. Using a Monte Carlo model of the detector we calculated dose spread kernels in units of absolute dose per incident energy fluence and compared them to calculated dose spread kernels in water at different depths. The energy of the incident pencil beams varied between 0.5 and 18 MeV. At the depth of dose maximum in water for a 6 MV beam (1.5 cm) and for a 18 MV beam (3.0 cm) we observed large absolute differences between water and detector dose above an incident energy of 4 MeV but only small relative differences in the most frequent energy range of the beam energy spectra. It is shown that for a 6 MV beam the absolute reference dose measured at 1.5 cm water depth differs from the absolute detector dose by 3.8%. At depth 1.2 cm in water, however, the relative dose differences are almost constant between 2 and 6 MeV. The effects of changes in the energy spectrum of the beam on the dose responses in water and in the detector are also investigated. We show that differences larger than 2% can occur for different beam qualities of the incident photon beam behind water slabs of different thicknesses. It is therefore concluded that for high-precision dosimetry such effects have to be taken into account. Nevertheless, the precise information about the dose response of the detector provided in this Monte Carlo study forms the basis of extracting directly the basic radiometric quantities photon fluence and photon energy fluence from the detector's signal using a deconvolution algorithm. The results are therefore promising for future application in absolute transit dosimetry and absolute dose reconstruction.

Improved sampling for gradient-domain metropolis light transport

We present a generalized framework for gradient-domain Metropolis rendering, and introduce three techniques to reduce sampling artifacts and variance. The first one is a heuristic weighting strategy that combines several sampling techniques to avoid outliers. The second one is an improved mapping to generate offset paths required for computing gradients. Here we leverage the properties of manifold walks in path space to cancel out singularities. Finally, the third technique introduces generalized screen space gradient kernels. This approach aligns the gradient kernels with image structures such as texture edges and geometric discontinuities to obtain sparser gradients than with the conventional gradient kernel. We implement our framework on top of an existing Metropolis sampler, and we demonstrate significant improvements in visual and numerical quality of our results compared to previous work.

Reducing CT radiation dose with iterative reconstruction algorithms: the influence of scan and reconstruction parameters on image quality and CTDIvol

OBJECTIVES In this phantom CT study, we investigated whether images reconstructed using filtered back projection (FBP) and iterative reconstruction (IR) with reduced tube voltage and current have equivalent quality. We evaluated the effects of different acquisition and reconstruction parameter settings on image quality and radiation doses. Additionally, patient CT studies were evaluated to confirm our phantom results. METHODS Helical and axial 256 multi-slice computed tomography scans of the phantom (Catphan(®)) were performed with varying tube voltages (80-140kV) and currents (30-200mAs). 198 phantom data sets were reconstructed applying FBP and IR with increasing iterations, and soft and sharp kernels. Further, 25 chest and abdomen CT scans, performed with high and low exposure per patient, were reconstructed with IR and FBP. Two independent observers evaluated image quality and radiation doses of both phantom and patient scans. RESULTS In phantom scans, noise reduction was significantly improved using IR with increasing iterations, independent from tissue, scan-mode, tube-voltage, current, and kernel. IR did not affect high-contrast resolution. Low-contrast resolution was also not negatively affected, but improved in scans with doses <5mGy, although object detectability generally decreased with the lowering of exposure. At comparable image quality levels, CTDIvol was reduced by 26-50% using IR. In patients, applying IR vs. FBP resulted in good to excellent image quality, while tube voltage and current settings could be significantly decreased. CONCLUSIONS Our phantom experiments demonstrate that image quality levels of FBP reconstructions can also be achieved at lower tube voltages and tube currents when applying IR. Our findings could be confirmed in patients revealing the potential of IR to significantly reduce CT radiation doses.

Lung Nodule Detection by Microdose CT Versus Chest Radiography (Standard and Dual-Energy Subtracted).

OBJECTIVE The purpose of this study was to investigate the feasibility of microdose CT using a comparable dose as for conventional chest radiographs in two planes including dual-energy subtraction for lung nodule assessment. MATERIALS AND METHODS We investigated 65 chest phantoms with 141 lung nodules, using an anthropomorphic chest phantom with artificial lung nodules. Microdose CT parameters were 80 kV and 6 mAs, with pitch of 2.2. Iterative reconstruction algorithms and an integrated circuit detector system (Stellar, Siemens Healthcare) were applied for maximum dose reduction. Maximum intensity projections (MIPs) were reconstructed. Chest radiographs were acquired in two projections with bone suppression. Four blinded radiologists interpreted the images in random order. RESULTS A soft-tissue CT kernel (I30f) delivered better sensitivities in a pilot study than a hard kernel (I70f), with respective mean (SD) sensitivities of 91.1% ± 2.2% versus 85.6% ± 5.6% (p = 0.041). Nodule size was measured accurately for all kernels. Mean clustered nodule sensitivity with chest radiography was 45.7% ± 8.1% (with bone suppression, 46.1% ± 8%; p = 0.94); for microdose CT, nodule sensitivity was 83.6% ± 9% without MIP (with additional MIP, 92.5% ± 6%; p < 10(-3)). Individual sensitivities of microdose CT for readers 1, 2, 3, and 4 were 84.3%, 90.7%, 68.6%, and 45.0%, respectively. Sensitivities with chest radiography for readers 1, 2, 3, and 4 were 42.9%, 58.6%, 36.4%, and 90.7%, respectively. In the per-phantom analysis, respective sensitivities of microdose CT versus chest radiography were 96.2% and 75% (p < 10(-6)). The effective dose for chest radiography including dual-energy subtraction was 0.242 mSv; for microdose CT, the applied dose was 0.1323 mSv. CONCLUSION Microdose CT is better than the combination of chest radiography and dual-energy subtraction for the detection of solid nodules between 5 and 12 mm at a lower dose level of 0.13 mSv. Soft-tissue kernels allow better sensitivities. These preliminary results indicate that microdose CT has the potential to replace conventional chest radiography for lung nodule detection.

On degeneracy and invariances of random fields paths with applications in Gaussian process modelling

We study pathwise invariances and degeneracies of random fields with motivating applications in Gaussian process modelling. The key idea is that a number of structural properties one may wish to impose a priori on functions boil down to degeneracy properties under well-chosen linear operators. We first show in a second order set-up that almost sure degeneracy of random field paths under some class of linear operators defined in terms of signed measures can be controlled through the two first moments. A special focus is then put on the Gaussian case, where these results are revisited and extended to further linear operators thanks to state-of-the-art representations. Several degeneracy properties are tackled, including random fields with symmetric paths, centred paths, harmonic paths, or sparse paths. The proposed approach delivers a number of promising results and perspectives in Gaussian process modelling. In a first numerical experiment, it is shown that dedicated kernels can be used to infer an axis of symmetry. Our second numerical experiment deals with conditional simulations of a solution to the heat equation, and it is found that adapted kernels notably enable improved predictions of non-linear functionals of the field such as its maximum.