Multiscale methods for shape constraints in deconvolution: Confidence statements for qualitative features

We derive multiscale statistics for deconvolution in order to detect qualitative features of the unknown density. An important example covered within this framework is to test for local monotonicity on all scales simultaneously. We investigate the moderately ill-posed setting, where the Fourier transform of the error density in the deconvolution model is of polynomial decay. For multiscale testing, we consider a calibration, motivated by the modulus of continuity of Brownian motion. We investigate the performance of our results from both the theoretical and simulation based point of view. A major consequence of our work is that the detection of qualitative features of a density in a deconvolution problem is a doable task, although the minimax rates for pointwise estimation are very slow.

Noisy kriging-based optimization methods: A unified implementation within the DiceOptim package

Kriging-based optimization relying on noisy evaluations of complex systems has recently motivated contributions from various research communities. Five strategies have been implemented in the DiceOptim package. The corresponding functions constitute a user-friendly tool for solving expensive noisy optimization problems in a sequential framework, while offering some flexibility for advanced users. Besides, the implementation is done in a unified environment, making this package a useful device for studying the relative performances of existing approaches depending on the experimental setup. An overview of the package structure and interface is provided, as well as a description of the strategies and some insight about the implementation challenges and the proposed solutions. The strategies are compared to some existing optimization packages on analytical test functions and show promising performances.

Dose Reduction in Standard Head CT: First Results from a New Scanner Using Iterative Reconstruction and a New Detector Type in Comparison with Two Previous Generations of Multi-slice CT

PURPOSE Computed tomography (CT) accounts for more than half of the total radiation exposure from medical procedures, which makes dose reduction in CT an effective means of reducing radiation exposure. We analysed the dose reduction that can be achieved with a new CT scanner [Somatom Edge (E)] that incorporates new developments in hardware (detector) and software (iterative reconstruction). METHODS We compared weighted volume CT dose index (CTDIvol) and dose length product (DLP) values of 25 consecutive patients studied with non-enhanced standard brain CT with the new scanner and with two previous models each, a 64-slice 64-row multi-detector CT (MDCT) scanner with 64 rows (S64) and a 16-slice 16-row MDCT scanner with 16 rows (S16). We analysed signal-to-noise and contrast-to-noise ratios in images from the three scanners and performed a quality rating by three neuroradiologists to analyse whether dose reduction techniques still yield sufficient diagnostic quality. RESULTS CTDIVol of scanner E was 41.5 and 36.4 % less than the values of scanners S16 and S64, respectively; the DLP values were 40 and 38.3 % less. All differences were statistically significant (p < 0.0001). Signal-to-noise and contrast-to-noise ratios were best in S64; these differences also reached statistical significance. Image analysis, however, showed "non-inferiority" of scanner E regarding image quality. CONCLUSIONS The first experience with the new scanner shows that new dose reduction techniques allow for up to 40 % dose reduction while still maintaining image quality at a diagnostically usable level.

Coronary artery stents: influence of adaptive statistical iterative reconstruction on image quality using 64-HDCT

OBJECTIVE: The assessment of coronary stents with present-generation 64-detector row computed tomography (HDCT) scanners is limited by image noise and blooming artefacts. We evaluated the performance of adaptive statistical iterative reconstruction (ASIR) for noise reduction in coronary stent imaging with HDCT. METHODS AND RESULTS: In 50 stents of 28 patients (mean age 64 ± 10 years) undergoing coronary CT angiography (CCTA) on an HDCT scanner the mean in-stent luminal diameter, stent length, image quality, in-stent contrast attenuation, and image noise were assessed. Studies were reconstructed using filtered back projection (FBP) and ASIR-FBP composites. ASIR resulted in reduced image noise vs. FBP (P < 0.0001). Two readers graded the CCTA stent image quality on a 4-point Likert scale and determined the proportion of interpretable stent segments. The best image quality for all clinical images was obtained with 40 and 60% ASIR with significantly larger luminal area visualization compared with FBP (+42.1 ± 5.4% with 100% ASIR vs. FBP alone; P < 0.0001) while the stent length was decreased (-4.7 ± 0.9%,

Statistical Methods and the Meaning of Probabilities. A Philosopher Looks at Statistics

The talk starts out with a short introduction to the philosophy of probability. I highlight the need to interpret probabilities in the sciences and motivate objectivist accounts of probabilities. Very roughly, according to such accounts, ascriptions of probabilities have truth-conditions that are independent of personal interests and needs. But objectivist accounts are pointless if they do not provide an objectivist epistemology, i.e., if they do not determine well-defined methods to support or falsify claims about probabilities. In the rest of the talk I examine recent philosophical proposals for an objectivist methodology. Most of them take up ideas well-known from statistics. I nevertheless find some proposals incompatible with objectivist aspirations.

Impact of a 4th generation iterative reconstruction technique on image quality in low-dose computed tomography of the chest in immunocompromised patients

PURPOSE To determine the image quality of an iterative reconstruction (IR) technique in low-dose MDCT (LDCT) of the chest of immunocompromised patients in an intraindividual comparison to filtered back projection (FBP) and to evaluate the dose reduction capability. MATERIALS AND METHODS 30 chest LDCT scans were performed in immunocompromised patients (Brilliance iCT; 20-40 mAs; mean CTDIvol: 1.7 mGy). The raw data were reconstructed using FBP and the IR technique (iDose4™, Philips, Best, The Netherlands) set to seven iteration levels. 30 routine-dose MDCT (RDCT) reconstructed with FBP served as controls (mean exposure: 116 mAs; mean CDTIvol: 7.6 mGy). Three blinded radiologists scored subjective image quality and lesion conspicuity. Quantitative parameters including CT attenuation and objective image noise (OIN) were determined. RESULTS In LDCT high iDose4™ levels lead to a significant decrease in OIN (FBP vs. iDose7: subscapular muscle 139.4 vs. 40.6 HU). The high iDose4™ levels provided significant improvements in image quality and artifact and noise reduction compared to LDCT FBP images. The conspicuity of subtle lesions was limited in LDCT FBP images. It significantly improved with high iDose4™ levels (> iDose4). LDCT with iDose4™ level 6 was determined to be of equivalent image quality as RDCT with FBP. CONCLUSION iDose4™ substantially improves image quality and lesion conspicuity and reduces noise in low-dose chest CT. Compared to RDCT, high iDose4™ levels provide equivalent image quality in LDCT, hence suggesting a potential dose reduction of almost 80%.

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.

Feasible Dose Reduction in Routine Chest Computed Tomography Maintaining Constant Image Quality Using the Last Three Scanner Generations: From Filtered Back Projection to Sinogram-affirmed Iterative Reconstruction and Impact of the Novel Fully Integrated Detector Design Minimizing Electronic Noise

OBJECTIVE The aim of the present study was to evaluate a dose reduction in contrast-enhanced chest computed tomography (CT) by comparing the three latest generations of Siemens CT scanners used in clinical practice. We analyzed the amount of radiation used with filtered back projection (FBP) and an iterative reconstruction (IR) algorithm to yield the same image quality. Furthermore, the influence on the radiation dose of the most recent integrated circuit detector (ICD; Stellar detector, Siemens Healthcare, Erlangen, Germany) was investigated. MATERIALS AND METHODS 136 Patients were included. Scan parameters were set to a thorax routine: SOMATOM Sensation 64 (FBP), SOMATOM Definition Flash (IR), and SOMATOM Definition Edge (ICD and IR). Tube current was set constantly to the reference level of 100 mA automated tube current modulation using reference milliamperes. Care kV was used on the Flash and Edge scanner, while tube potential was individually selected between 100 and 140 kVp by the medical technologists at the SOMATOM Sensation. Quality assessment was performed on soft-tissue kernel reconstruction. Dose was represented by the dose length product. RESULTS Dose-length product (DLP) with FBP for the average chest CT was 308 mGy*cm ± 99.6. In contrast, the DLP for the chest CT with IR algorithm was 196.8 mGy*cm ± 68.8 (P = 0.0001). Further decline in dose can be noted with IR and the ICD: DLP: 166.4 mGy*cm ± 54.5 (P = 0.033). The dose reduction compared to FBP was 36.1% with IR and 45.6% with IR/ICD. Signal-to-noise ratio (SNR) was favorable in the aorta, bone, and soft tissue for IR/ICD in combination compared to FBP (the P values ranged from 0.003 to 0.048). Overall contrast-to-noise ratio (CNR) improved with declining DLP. CONCLUSION The most recent technical developments, namely IR in combination with integrated circuit detectors, can significantly lower radiation dose in chest CT examinations.

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.

Blind Deconvolution via Lower-Bounded Logarithmic Image Priors

In this work we devise two novel algorithms for blind deconvolution based on a family of logarithmic image priors. In contrast to recent approaches, we consider a minimalistic formulation of the blind deconvolution problem where there are only two energy terms: a least-squares term for the data fidelity and an image prior based on a lower-bounded logarithm of the norm of the image gradients. We show that this energy formulation is sufficient to achieve the state of the art in blind deconvolution with a good margin over previous methods. Much of the performance is due to the chosen prior. On the one hand, this prior is very effective in favoring sparsity of the image gradients. On the other hand, this prior is non convex. Therefore, solutions that can deal effectively with local minima of the energy become necessary. We devise two iterative minimization algorithms that at each iteration solve convex problems: one obtained via the primal-dual approach and one via majorization-minimization. While the former is computationally efficient, the latter achieves state-of-the-art performance on a public dataset.

Fully Adaptive Newton--Galerkin Methods for Semilinear Elliptic Partial Differential Equations

In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both prediction-type adaptive Newton methods and a linear adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples

Impact of Hybrid Iterative Reconstruction on Agatston Coronary Artery Calcium Scores in Comparison to Filtered Back Projection in Native Cardiac CT

PURPOSE To investigate whether the effects of hybrid iterative reconstruction (HIR) on coronary artery calcium (CAC) measurements using the Agatston score lead to changes in assignment of patients to cardiovascular risk groups compared to filtered back projection (FBP). MATERIALS AND METHODS 68 patients (mean age 61.5 years; 48 male; 20 female) underwent prospectively ECG-gated, non-enhanced, cardiac 256-MSCT for coronary calcium scoring. Scanning parameters were as follows: Tube voltage, 120 kV; Mean tube current time-product 63.67 mAs (50 - 150 mAs); collimation, 2 × 128 × 0.625 mm. Images were reconstructed with FBP and with HIR at all levels (L1 to L7). Two independent readers measured Agatston scores of all reconstructions and assigned patients to cardiovascular risk groups. Scores of HIR and FBP reconstructions were correlated (Spearman). Interobserver agreement and variability was assessed with ĸ-statistics and Bland-Altmann-Plots. RESULTS Agatston scores of HIR reconstructions were closely correlated with FBP reconstructions (L1, R = 0.9996; L2, R = 0.9995; L3, R = 0.9991; L4, R = 0.986; L5, R = 0.9986; L6, R = 0.9987; and L7, R = 0.9986). In comparison to FBP, HIR led to reduced Agatston scores between 97 % (L1) and 87.4 % (L7) of the FBP values. Using HIR iterations L1 - L3, all patients were assigned to identical risk groups as after FPB reconstruction. In 5.4 % of patients the risk group after HIR with the maximum iteration level was different from the group after FBP reconstruction. CONCLUSION There was an excellent correlation of Agatston scores after HIR and FBP with identical risk group assignment at levels 1 - 3 for all patients. Hence it appears that the application of HIR in routine calcium scoring does not entail any disadvantages. Thus, future studies are needed to demonstrate whether HIR is a reliable method for reducing radiation dose in coronary calcium scoring.

Computational Comparison of Continuous and Discontinuous Galerkin Time-Stepping Methods for Nonlinear Initial Value Problems

This article centers on the computational performance of the continuous and discontinuous Galerkin time stepping schemes for general first-order initial value problems in R n , with continuous nonlinearities. We briefly review a recent existence result for discrete solutions from [6], and provide a numerical comparison of the two time discretization methods.