Statistical Reconstruction Research Articles

Development of statistical data reconstruction tools, changed by municipal mergers and dissolutions

Development of statistical data reconstruction tools, changed by municipal mergers and dissolutions

Quantifying the Importance of the Statistical Assumption in Statistical X-ray CT Image Reconstruction

Statistical image reconstruction (SIR) is a promising approach to reducing radiation dose in clinical computerized tomography (CT) scans. Clinical CT scanners use energy-integrating detectors. The CT signal follows a compound Poisson distribution, its probability density function (PDF) does not have an analytical form hence cannot be used in an SIR method. The goal of this work is to quantify the effects of using an approximate statistical assumption in SIR methods for clinical CT applications. We apply a pseudo-Ideal Observer (pIO) to simulated CT projection data of the fanbeam geometry at different dose levels. The simulation models the polychromatic X-ray tube spectrum, the effects of the bowtie filter, and the energy-integrating detectors. The pIO uses a pseudo likelihood function (pLF) to calculate the pseudo likelihood ratio, which is the decision variable used by the pIO in a binary detection task. The pLF is an approximation to the true LF of the underlying data. The pIO has inferior performance than the IO unless the pLF coincides with the LF; this performance difference quantifies the closeness between the pseudo likelihood and the exact one. Using lesion detectability in a signal known exactly, background known exactly binary detection task as a figure-of-merit, our results show that at down to 0.1% of a reference tube current level I0, the pIO that uses a Poisson approximation, or a matched variance Gaussian approximation in either the transmission or the line integral domain, achieves 99% the performance of the IO. The constant variance Gaussian approximation has only 70%-80% of the IO performance. At tube currents lower than 0.1% I0, the performance difference is more substantial. We conclude that at current clinical dose levels, it is important to account for the mean-dependent variance in CT projection data in SIR problem formulation, the exact PDF of the CT signal is not as important.

Information‐theoretic discrepancy based iterative reconstructions (IDIR) for polychromatic x‐ray tomography

X-ray photons generated from a typical x-ray source for clinical applications exhibit a broad range of wavelengths, and the interactions between individual particles and biological substances depend on particles' energy levels. Most existing reconstruction methods for transmission tomography, however, neglect this polychromatic nature of measurements and rely on the monochromatic approximation. In this study, we developed a new family of iterative methods that incorporates the exact polychromatic model into tomographic image recovery, which improves the accuracy and quality of reconstruction. The generalized information-theoretic discrepancy (GID) was employed as a new metric for quantifying the distance between the measured and synthetic data. By using special features of the GID, the objective function for polychromatic reconstruction which contains a double integral over the wavelength and the trajectory of incident x-rays was simplified to a paraboloidal form without using the monochromatic approximation. More specifically, the original GID was replaced with a surrogate function with two auxiliary, energy-dependent variables. Subsequently, the alternating minimization technique was applied to solve the double minimization problem. Based on the optimization transfer principle, the objective function was further simplified to the paraboloidal equation, which leads to a closed-form update formula. Numerical experiments on the beam-hardening correction and material-selective reconstruction were conducted to compare and assess the performance of conventional methods and the proposed algorithms. The authors found that the GID determines the distance between its two arguments in a flexible manner. In this study, three groups of GIDs with distinct data representations were considered. The authors demonstrated that one type of GIDs that comprises "raw" data can be viewed as an extension of existing statistical reconstructions; under a particular condition, the GID is equivalent to the Poisson log-likelihood function. The newly proposed GIDs of the other two categories consist of log-transformed measurements, which have the advantage of imposing linearized penalties over multiple discrepancies. For all proposed variants of the GID, the aforementioned strategy was used to obtain a closed-form update equation. Even though it is based on the exact polychromatic model, the derived algorithm bears a structural resemblance to conventional methods based on the monochromatic approximation. The authors named the proposed approach as information-theoretic discrepancy based iterative reconstructions (IDIR). In numerical experiments, IDIR with raw data converged faster than previously known statistical reconstruction methods. IDIR with log-transformed data exhibited superior reconstruction quality and faster convergence speed compared with conventional methods and their variants. The authors' new framework for tomographic reconstruction allows iterative inversion of the polychromatic data model. The primary departure from the traditional iterative reconstruction was the employment of the GID as a new metric for quantifying the inconsistency between the measured and synthetic data. The proposed methods outperformed not only conventional methods based on the monochromatic approximation but also those based on the polychromatic model. The authors have observed that the GID is a very flexible means to design an objective function for iterative reconstructions. Hence, the authors expect that the proposed IDIR framework will also be applicable to other challenging tasks.

Multi-proxy summer and winter precipitation reconstruction for southern Africa over the last 200 years

This study presents the first consolidation of palaeoclimate proxy records from multiple archives to develop statistical rainfall reconstructions for southern Africa covering the last two centuries. State-of-the-art ensemble reconstructions reveal multi-decadal rainfall variability in the summer and winter rainfall zones. A decrease in precipitation amount over time is identified in the summer rainfall zone. No significant change in precipitation amount occurred in the winter rainfall zone, but rainfall variability has increased over time. Generally synchronous rainfall fluctuations between the two zones are identified on decadal scales, with common wet (dry) periods reconstructed around 1890 (1930). A strong relationship between seasonal rainfall and sea surface temperatures (SSTs) in the surrounding oceans is confirmed. Coherence among decadal-scale fluctuations of southern African rainfall, regional SST, SSTs in the Pacific Ocean and rainfall in south-eastern Australia suggest SST-rainfall teleconnections across the southern hemisphere. Temporal breakdowns of the SST-rainfall relationship in the southern African regions and the connection between the two rainfall zones are observed, for example during the 1950s. Our results confirm the complex interplay between large-scale teleconnections, regional SSTs and local effects in modulating multi-decadal southern African rainfall variability over long timescales.

Quantitative Monte Carlo–Based 90Y SPECT Reconstruction

The evaluation of radiation absorbed doses in tumorous and healthy tissues is of increasing interest for (90)Y microsphere radioembolization of liver malignancies. The objectives of this work were to introduce and validate a new reconstruction method for quantitative (90)Y bremsstrahlung SPECT to improve posttreatment dosimetry. A fast Monte Carlo simulator was adapted for (90)Y and incorporated into a statistical reconstruction algorithm (SPECT-MC). Photon scatter and attenuation for all photons sampled from the full (90)Y energy spectrum were modeled during reconstruction by Monte Carlo simulations. The energy- and distance-dependent collimator-detector response was modeled with precalculated convolution kernels. The National Electrical Manufacturers Association 2007/International Electrotechnical Commission 2008 image quality phantom was used to quantitatively evaluate the performance of SPECT-MC in comparison with those of state-of-the-art clinical SPECT reconstruction and PET. The liver radiation absorbed doses estimated by SPECT, PET, and SPECT-MC were evaluated in 5 patients consecutively treated with radioembolization. In comparison with state-of-the-art clinical (90)Y SPECT reconstruction, SPECT-MC substantially improved image contrast (e.g., from 25% to 88% for the 37-mm sphere) and decreased the mean residual count error in the lung insert (from 73% to 15%) at the cost of higher image noise. Image noise and the mean count error were lower for SPECT-MC than for PET. Image contrast was higher in the larger spheres (diameter of ≥28 mm) but lower in the smaller spheres (≤22 mm) for SPECT-MC than for PET. In the clinical study, mean absorbed dose estimates in liver regions with high absorbed doses were consistently higher for SPECT-MC than for SPECT (P = 0.0625) and consistently higher for SPECT-MC than for PET (P = 0.0625). The quantitative accuracy of (90)Y bremsstrahlung SPECT is substantially improved by Monte Carlo-based modeling of the image-degrading factors. Consequently, (90)Y bremsstrahlung SPECT may be used as an alternative to (90)Y PET.

Evaluation of fixed- and random-effects models and multistage estimation procedures in statistical population reconstruction

Statistical population reconstruction (SPR) using hunter-supplied, age-at-harvest data provides a flexible framework for estimating population parameters and trends over large geographic areas. Early development of the technique assumed natural survival and the vulnerability coefficients that translate hunter effort into harvest mortality are constant over time. We developed random-effects models that relaxed these assumptions to produce more realistic models for cohort analysis. We compared the statistical performance of fixed-effects and random-effects models and the relative benefits of single-stage and 2-stage estimators of abundance with Monte Carlo simulation studies. In single-stage analyses, initial cohort abundance is estimated directly within the likelihood model. In 2-stage analyses, survival and harvest probabilities are estimated using likelihood conditional on total cohort harvest. Annual abundances are then estimated outside the likelihood using Horvitz–Thompson type estimators. Our simulation results indicate random-effects models conditional on total cohort harvest have low bias and yield asymptotic 95% confidence intervals that have near nominal coverage. The other estimation procedures produced confidence intervals for annual abundance that had far-from-nominal coverage. Our new random-effects, 2-stage model is illustrated using 18 years of age-at-harvest data from an elk (Cervus elaphus) herd in the Lower Peninsula of Michigan. Results indicate the multistage estimation process incorporating random effects provides accurate abundance estimates and confidence interval coverage, and we recommend its use. © 2013 The Wildlife Society.

Extended regional climate model projections for Europe until the mid-twentyfirst century: combining ENSEMBLES and CMIP3

This study aims at sharpening the existing knowledge of expected seasonal mean climate change and its uncertainty over Europe for the two key climate variables air temperature and precipitation amount until the mid-twentyfirst century. For this purpose, we assess and compensate the global climate model (GCM) sampling bias of the ENSEMBLES regional climate model (RCM) projections by combining them with the full set of the CMIP3 GCM ensemble. We first apply a cross-validation in order to assess the skill of different statistical data reconstruction methods in reproducing ensemble mean and standard deviation. We then select the most appropriate reconstruction method in order to fill the missing values of the ENSEMBLES simulation matrix and further extend the matrix by all available CMIP3 GCM simulations forced by the A1B emission scenario. Cross-validation identifies a randomized scaling approach as superior in reconstructing the ensemble spread. Errors in ensemble mean and standard deviation are mostly less than 0.1 K and 1.0 % for air temperature and precipitation amount, respectively. Reconstruction of the missing values reveals that expected seasonal mean climate change of the ENSEMBLES RCM projections is not significantly biased and that the associated uncertainty is not underestimated due to sampling of only a few driving GCMs. In contrast, the spread of the extended simulation matrix is partly significantly lower, sharpening our knowledge about future climate change over Europe by reducing uncertainty in some regions. Furthermore, this study gives substantial weight to recent climate change impact studies based on the ENSEMBLES projections, since it confirms the robustness of the climate forcing of these studies concerning GCM sampling.

Regional compensation for statistical maximum likelihood reconstruction error of PET image pixels

In positron emission tomography (PET), there is an increasing interest in studying not only the regional mean tracer concentration, but its variation arising from local differences in physiology, the tissue heterogeneity. However, in reconstructed images this physiological variation is shadowed by a large reconstruction error, which is caused by noisy data and the inversion of tomographic problem. We present a new procedure which can quantify the error variation in regional reconstructed values for given PET measurement, and reveal the remaining tissue heterogeneity. The error quantification is made by creating and reconstructing the noise realizations of virtual sinograms, which are statistically similar with the measured sinogram. Tests with physical phantom data show that the characterization of error variation and the true heterogeneity are possible, despite the existing model error when real measurement is considered.

Accelerating ordered subsets image reconstruction for X-ray CT using spatially nonuniform optimization transfer.

Statistical image reconstruction algorithms in X-ray computed tomography (CT) provide improved image quality for reduced dose levels but require substantial computation time. Iterative algorithms that converge in few iterations and that are amenable to massive parallelization are favorable in multiprocessor implementations. The separable quadratic surrogate (SQS) algorithm is desirable as it is simple and updates all voxels simultaneously. However, the standard SQS algorithm requires many iterations to converge. This paper proposes an extension of the SQS algorithm that leads to spatially nonuniform updates. The nonuniform (NU) SQS encourages larger step sizes for the voxels that are expected to change more between the current and the final image, accelerating convergence, while the derivation of NU-SQS guarantees monotonic descent. Ordered subsets (OS) algorithms can also accelerate SQS, provided suitable "subset balance" conditions hold. These conditions can fail in 3-D helical cone-beam CT due to incomplete sampling outside the axial region-of-interest (ROI). This paper proposes a modified OS algorithm that is more stable outside the ROI in helical CT. We use CT scans to demonstrate that the proposed NU-OS-SQS algorithm handles the helical geometry better than the conventional OS methods and "converges" in less than half the time of ordinary OS-SQS.

Random effects models and multistage estimation procedures for statistical population reconstruction of small game populations.

Recently, statistical population models using age-at-harvest data have seen increasing use for monitoring of harvested wildlife populations. Even more recently, detailed evaluation of model performance for long-lived, large game animals indicated that the use of random effects to incorporate unmeasured environmental variation, as well as second-stage Horvitz-Thompson-type estimators of abundance, provided more reliable estimates of total abundance than previous models. We adapt this new modeling framework to small game, age-at-harvest models with only young-of-the-year and adult age classes. Our Monte Carlo simulation results indicate superior model performance for the new modeling framework, evidenced by lower bias and proper confidence interval coverage. We apply this method to male wild turkey harvest in the East Ozarks turkey productivity region, Missouri, USA, where statistical population reconstruction indicates a relatively stationary population for 1996–2010.

The utility of auxiliary data in statistical population reconstruction

Although statistical population reconstruction (SPR) provides a flexible framework for estimating demographics of harvested populations using age‐at‐harvest data, that information alone is insufficient. Auxiliary data are needed to ensure all model parameters are estimable and to improve the precision and accuracy of the estimates. We examined the influence of two types of auxiliary information, independent estimates of annual abundance and annual harvest mortality from radio‐telemetry studies, on the stability and precision of abundance estimates from SPR. Further, we evaluated whether the timing of auxiliary studies in the reconstruction affected the precision of abundance estimates. Monte Carlo studies simulated auxiliary data with precision levels defined by the coefficients of variation (CV) of 0.05, 0.125, 0.25 and 0.50 corresponding to the three levels of precision suggested by Robson & Regier (1964) for accurate research, accurate management and rough management and a minimal information scenario. For comparable levels of precision, radio‐telemetry studies used to estimate harvest mortality stabilized the reconstructed population trends better than independent abundance surveys. However, independent abundance surveys were superior at improving the precision of reconstructed abundance estimates. We found that the timing of auxiliary studies did not influence the stability of SPR estimates, which has important implications for managers designing studies to collect auxiliary data. Our research highlights that different types and quality of auxiliary studies affects the precision and stability of SPR models differently.

Estimating Monthly Precipitation Reconstruction Uncertainty Beginning in 1900

Abstract Uncertainty estimates are computed for a statistical reconstruction of global monthly precipitation that was developed in an earlier publication. The reconstruction combined the use of spatial correlations with gauge precipitation and correlations between precipitation and related data beginning in 1900. Several types of errors contribute to uncertainty, including errors associated with the reconstruction method and input data errors. This reconstruction includes the use of correlated data for the ocean-area first guess, which contributes to much of the uncertainty over those regions. Errors associated with the input data include random, sampling, and bias errors. Random and bias data errors are mostly filtered out of the reconstruction analysis and are the smallest components of the total error. The largest errors are associated with sampling and the method, which together dominate the total error. The uncertainty estimates in this study indicate that (i) over oceans the reconstruction is most reliable in the tropics, especially the Pacific, because of the large spatial scales of ENSO; (ii) over the high-latitude oceans multidecadal variations are fairly reliable, but many month-to-month variations are not; and (iii) over- and near-land errors are much smaller because of local gauge. The reconstruction indicates that the average precipitation increases early in the twentieth century, followed by several decades of multidecadal variations with little trend until near the end of the century, when precipitation again appears to systematically increase. The uncertainty estimates indicate that the average changes over land are most reliable, while over oceans the average change over the reconstruction period is slightly larger than the uncertainty.

Tomographic reconstruction using prior with adaptively binary neighborhood

Bayesian approaches can be used to improve ill-posed image reconstruction by regularizing the inverse solution using spacial or temporal neighborhood information. This paper proposes a prior with adaptively binary neighborhood (ABN prior) for statistical tomographic reconstruction. With binary weight map adapted to local image features, the proposed prior can lead to improved reconstruction by including relevant pixels belonging to similar structures and excluding those not. A two-step algorithm is also put forward for tomographic reconstruction using the proposed prior. Experiments using both simulated and clinical computerized tomography (CT) data are performed to validate the reconstructions with the proposed ABN prior.

Freshwater outflow of the Baltic Sea and transport in the Norwegian current: A statistical correlation analysis based on a numerical experiment

Based on the results of a numerical ocean model, we investigate statistical correlations between wind forcing, surface salinity and freshwater transport out of the Baltic Sea on one hand, and Norwegian coastal current freshwater transport on the other hand. These correlations can be explained in terms of physics and reveal how the two freshwater transports are linked with wind forcing, although this information proves to be non-sufficient when it comes to the dynamics of the Norwegian coastal current. Based on statistical correlations, the Baltic Sea freshwater transport signal is reconstructed and shows a good correlation but a poor variability when compared with the measured signal, at least when data filtered on a two-daily time scale is used. A better variability coherence is reached when data filtered on a weekly or monthly time scale is used. In the latest case, a high degree of precision is reached for the reconstructed signal. Using the same kind of methods for the case of the Norwegian coastal current, the negative peaks of the freshwater transport signal can be reconstructed based on wind data only, but the positive peaks are under-represented although some of them exist mostly because the meridional wind forcing along the Norwegian coast is taken into account. Adding Norwegian coastal salinity data helps improving the reconstruction of the positive peaks, but a major improvement is reached when adding non-linear terms in the statistical reconstruction. All coefficients used to re-construct both freshwater transport signals are provided for use in European Shelf or climate modeling configurations.

Upgrade to lterative Image Reconstruction (lR) in MDCT lmaging: A Clinical Study for Detailed Parameter Optimization Beyond Vendor Recommendations Using the Adaptive Statistical lterative Reconstruction Environment (ASIR) Part2: The Chest

To compare the image quality in dose-reduced 64-row CT of the chest at different levels of adaptive statistical iterative reconstruction (ASIR) to full-dose baseline examinations reconstructed solely with filtered back projection (FBP) in a realistic upgrade scenario. A waiver of consent was granted by the institutional review board (IRB). The noise index (NI) relates to the standard deviation of Hounsfield units in a water phantom. Baseline exams of the chest (NI = 29; LightSpeed VCT XT, GE Healthcare) were intra-individually compared to follow-up studies on a CT with ASIR after system upgrade (NI = 45; Discovery HD750, GE Healthcare), n = 46. Images were calculated in slice and volume mode with ASIR levels of 0 - 100 % in the standard and lung kernel. Three radiologists independently compared the image quality to the corresponding full-dose baseline examinations (-2: diagnostically inferior, -1: inferior, 0: equal, + 1: superior, + 2: diagnostically superior). Statistical analysis used Wilcoxon's test, Mann-Whitney U test and the intraclass correlation coefficient (ICC). The mean CTDIvol decreased by 53 % from the FBP baseline to 8.0 ± 2.3 mGy for ASIR follow-ups; p < 0.001. The ICC was 0.70. Regarding the standard kernel, the image quality in dose-reduced studies was comparable to the baseline at ASIR 70 % in volume mode (-0.07 ± 0.29, p = 0.29). Concerning the lung kernel, every ASIR level outperformed the baseline image quality (p < 0.001), with ASIR 30 % rated best (slice: 0.70 ± 0.6, volume: 0.74 ± 0.61). Vendors' recommendation of 50 % ASIR is fair. In detail, the ASIR 70 % in volume mode for the standard kernel and ASIR 30 % for the lung kernel performed best, allowing for a dose reduction of approximately 50 %.

Statistical reconstruction of two-phase random media

A robust and efficient algorithm is proposed to reconstruct two-phase composite materials with random morphology, according to given samples or given statistical characteristics. The new method is based on nonlinear transformation of Gaussian random fields, where the correlation of the underlying Gaussian field is determined explicitly rather than through iterative methods. The reconstructed media can meet the binary-valued marginal probability distribution function and the two point correlation function of the reference media. The new method, whose main computation is completed using fast Fourier transform (FFT), is highly efficient and particularly suitable for reconstructing large size random media or a large number of samples. Its feasibility and performance are examined through a series of practical examples with comparisons to other state-of-the-art methods in random media reconstruction.

Statistical reconstruction algorithms for continuous wave electron spin resonance imaging

Electron spin resonance imaging (ESRI) is an important branch of ESR that deals with heterogeneous samples ranging from semiconductor materials to small live animals and even humans. ESRI can produce either spatial images (providing information about the spatially dependent radical concentration) or spectral–spatial images, where an extra dimension is added to describe the absorption spectrum of the sample (which can also be spatially dependent). The mapping of oxygen in biological samples, often referred to as oximetry, is a prime example of an ESRI application. ESRI suffers frequently from a low signal-to-noise ratio (SNR), which results in long acquisition times and poor image quality. A broader use of ESRI is hampered by this slow acquisition, which can also be an obstacle for many biological applications where conditions may change relatively quickly over time. The objective of this work is to develop an image reconstruction scheme for continuous wave (CW) ESRI that would make it possible to reduce the data acquisition time without degrading the reconstruction quality. This is achieved by adapting the so-called “statistical reconstruction” method, recently developed for other medical imaging modalities, to the specific case of CW ESRI. Our new algorithm accounts for unique ESRI aspects such as field modulation, spectral–spatial imaging, and possible limitation on the gradient magnitude (the so-called “limited angle” problem). The reconstruction method shows improved SNR and contrast recovery vs. commonly used back-projection-based methods, for a variety of simulated synthetic samples as well as in actual CW ESRI experiments.

Soft-Tissue Imaging in Low-Dose, C-Arm Cone-Beam CT Using Statistical Image Reconstruction.

C-arm cone-beam CT (CBCT) is an emerging tool for intraoperative imaging, but current embodiments exhibit modest soft-tissue imaging capability and are largely constrained to high-contrast imaging tasks. A major advance in image quality is facilitated by statistical iterative reconstruction techniques. This work adapts a general penalized likelihood (PL) reconstruction approach with variable penalties and regularization to C-arm CBCT and investigates performance in imaging of large (>10 mm), low-contrast (<100 HU) tasks pertinent to soft-tissue surgical guidance. Experiments involved a mobile C-arm for CBCT with phantoms and cadavers presenting soft-tissue structures imaged using 3D filtered backprojection (FBP), quadratic, and non-quadratic PL reconstruction. Polyethylene phantoms with various tissue-equivalent inserts were used to quantity contrast-to-noise / resolution tradeoffs in low-contrast (~40 HU) structures, and the optimal reconstruction parameters were translated to imaging an anthropomorphic head phantom with low-contrasts targets and a cadaveric torso. Statistical reconstruction - especially non-quadratic PL variants - boosted soft-tissue image quality through reduction of noise and artifacts (e.g., a ~2-4 fold increase in contrast-to-noise ratio (CNR) at equivalent spatial resolution). For tasks relating to large, low-contrast tissues, even greater gains were possible using non-quadratic penalties and strong regularization that sacrificed spatial resolution in a manner still consistent with the imaging task. The advances in image quality offered by statistical reconstruction present promise and new challenges for interventional imaging, with high-speed computing facilitating realistic application. Careful investigation of performance relative to specific imaging tasks permits knowledgeable application of such techniques in a manner that overcomes conventional tradeoffs in noise, resolution, and dose and could extend application of CBCT-capable C-arms to soft-tissue interventions in neurosurgery as well as thoracic and abdominal interventions.

Algorithms for Non-Negatively Constrained Maximum Penalized Likelihood Reconstruction in Tomographic Imaging

Image reconstruction is a key component in many medical imaging modalities. The problem of image reconstruction can be viewed as a special inverse problem where the unknown image pixel intensities are estimated from the observed measurements. Since the measurements are usually noise contaminated, statistical reconstruction methods are preferred. In this paper we review some non-negatively constrained simultaneous iterative algorithms for maximum penalized likelihood reconstructions, where all measurements are used to estimate all pixel intensities in each iteration.

Statistical Reconstruction of Material Decomposed Data in Spectral CT

Photon-counting detector technology has enabled the first experimental investigations of energy-resolved computed tomography (CT) imaging and the potential use for K-edge imaging. However, limitations in regards to detecter technology have been imposing a limit to effective count rates. As a consequence, this has resulted in high noise levels in the obtained images given scan time limitations in CT imaging applications. It has been well recognized in the area of low-dose imaging with conventional CT that iterative image reconstruction provides a superior signal to noise ratio compared to traditional filtered backprojection techniques. Furthermore, iterative reconstruction methods also allow for incorporation of a roughness penalty function in order to make a trade-off between noise and spatial resolution in the reconstructed images. In this work, we investigate statistically-principled iterative image reconstruction from material-decomposed sinograms in spectral CT. The proposed reconstruction algorithm seeks to minimize a penalized likelihood-based cost functional, where the parameters of the likelihood function are estimated by computing the Fisher information matrix associated with the material decomposition step. The performance of the proposed reconstruction method is quantitatively investigated by use of computer-simulated and experimental phantom data. The potential for improved K-edge imaging is also demonstrated in an animal experiment.