Statistical Reconstruction Technique Research Articles

Cone-beam breast CT using an offset detector: effect of detector offset and image reconstruction algorithm

Objective. A dedicated cone-beam breast computed tomography (BCT) using a high-resolution, low-noise detector operating in offset-detector geometry has been developed. This study investigates the effects of varying detector offsets and image reconstruction algorithms to determine the appropriate combination of detector offset and reconstruction algorithm. Approach. Projection datasets (300 projections in 360°) of 30 breasts containing calcified lesions that were acquired using a prototype cone-beam BCT system comprising a 40 × 30 cm flat-panel detector with 1024 × 768 detector pixels were reconstructed using Feldkamp–Davis–Kress (FDK) algorithm and served as the reference. The projection datasets were retrospectively truncated to emulate cone-beam datasets with sinograms of 768 768 and 640 768 detector pixels, corresponding to 5 cm and 7.5 cm lateral offsets, respectively. These datasets were reconstructed using the FDK algorithm with appropriate weights and an ASD-POCS-based Fast, total variation-Regularized, Iterative, Statistical reconstruction Technique (FRIST), resulting in a total of 4 offset-detector reconstructions (2 detector offsets × 2 reconstruction methods). Signal difference-to-noise ratio (SDNR), variance, and full-width at half-maximum (FWHM) of calcifications in two orthogonal directions were determined from all reconstructions. All quantitative measurements were performed on images in units of linear attenuation coefficient (1/cm). Results. The FWHM of calcifications did not differ (P > 0.262) among reconstruction algorithms and detector formats, implying comparable spatial resolution. For a chosen detector offset, the FRIST algorithm outperformed FDK in terms of variance and SDNR (P < 0.0001). For a given reconstruction method, the 5 cm offset provided better results. Significance. This study indicates the feasibility of using the compressed sensing-based, FRIST algorithm to reconstruct sinograms from offset-detectors. Among the reconstruction methods and detector offsets studied, FRIST reconstructions corresponding to a 30 cm × 30 cm with 5 cm lateral offset, achieved the best performance. A clinical prototype using such an offset geometry has been developed and installed for clinical trials.

Sparse-view, short-scan, dedicated cone-beam breast computed tomography: image quality assessment

The purpose of this study is to quantify the impact of sparse-view acquisition in short-scan trajectories, compared to 360-degrees full-scan acquisition, on image quality measures in dedicated cone-beam breast computed tomography (BCT). Projection data from 30 full-scan (360-degrees; 300 views) BCT exams with calcified lesions were selected from an existing clinical research database. Feldkamp-Davis-Kress (FDK) reconstruction of the full-scan data served as the reference. Projection data corresponding to two short-scan trajectories, 204 and 270-degrees, which correspond to the minimum and maximum angular range achievable in a cone-beam BCT system were selected. Projection data were retrospectively sampled to provide 225, 180, and 168 views for 270-degrees short-scan, and 170 views for 204-degrees short-scan. Short-scans with 180 and 168 views in 270-degrees used non-uniform angular sampling. A fast, iterative, total variation-regularized, statistical reconstruction technique (FIRST) was used for short-scan image reconstruction. Image quality was quantified by variance, signal-difference to noise ratio (SDNR) between adipose and fibroglandular tissues, full-width at half-maximum (FWHM) of calcifications in two orthogonal directions, as well as, bias and root-mean-squared-error (RMSE) computed with respect to the reference full-scan FDK reconstruction. The median values of bias (8.6 × 10−4–10.3 × 10−4 cm−1) and RMSE (6.8 × 10−6–9.8 × 10−6 cm−1) in the short-scan reconstructions, computed with the full-scan FDK as the reference were close to, but not zero (P < 0.0001, one-sample median test). The FWHM of the calcifications in the short-scan reconstructions did not differ significantly from the reference FDK reconstruction (P > 0.118), except along the superior-inferior direction for the short-scan reconstruction with 168 views in 270-degrees (P = 0.046). The variance and SDNR from short-scan reconstructions were significantly improved compared to the full-scan FDK reconstruction (P < 0.0001). This study demonstrates the feasibility of the short-scan, sparse-view, compressed sensing-based iterative reconstruction. This study indicates that shorter scan times and reduced radiation dose without sacrificing image quality are potentially feasible.

Cone-beam breast computed tomography using ultra-fast image reconstruction with constrained, total-variation minimization for suppression of artifacts

Compressed sensing based iterative reconstruction algorithms for computed tomography such as adaptive steepest descent-projection on convex sets (ASD-POCS) are attractive due to their applicability in incomplete datasets such as sparse-view data and can reduce radiation dose to the patients while preserving image quality. Although IR algorithms reduce image noise compared to analytical Feldkamp-Davis-Kress (FDK) algorithm, they may generate artifacts, particularly along the periphery of the object. One popular solution is to use finer image-grid followed by down-sampling. This approach is computationally intensive but may be compensated by reducing the field of view. Our proposed solution is to replace the algebraic reconstruction technique within the original ASD-POCS by ordered subsets-simultaneous algebraic reconstruction technique (OS-SART) and with initialization using FDK image. We refer to this method as Fast, Iterative, TV-Regularized, Statistical reconstruction Technique (FIRST). In this study, we investigate FIRST for cone-beam dedicated breast CT with large image matrix. The signal-difference to noise ratio (SDNR), the difference of the mean value and the variance of adipose and fibroglandular tissues for both FDK and FIRST reconstructions were determined. With FDK serving as the reference, the root-mean-square error (RMSE), bias, and the full-width at half-maximum (FWHM) of microcalcifications in two orthogonal directions were also computed. Our results suggest that FIRST is competitive to the finer image-grid method with shorter reconstruction time. Images reconstructed using the FIRST do not exhibit artifacts and outperformed FDK in terms of image noise. This suggests the potential of this approach for radiation dose reduction in cone-beam breast CT.

Radiation dose reduction on mutidetector abdominal CT using adaptive statistical iterative reconstruction technique in children

Objective To investigate the feasibility to reduce radiation doses on pediatric mutidetector abdominal CT using the adaptive statistical iterative reconstruction technique (ASIR) associated with automated tube current modulation technique (ATCM). Methods Thirty patients underwent abdominal CT with ATCM and the follow-up scan with ATCM cooperated with 40% ASIR.ATCM was used with age-dependent noise index (NI) settings:NI=9 for 0—5 year old and NI=11 for﹥5 years old for simple ATCM group,NI=11 for 0—5 year old and NI=15 for>5 years old for ATCM cooperated with 40% ASIR group (AISR group).Two radiologists independently evaluated images for diagnostic quality and image noise with subjectively image quality score and image noise score using a 5-point scale.Interobserver agreement was assessed by Kap pa test.The volume CT dose indexes (CTDIvol) for the two groups were recorded.Statistical significance for the CTDIvol value was analyzed by pair-sample t test. Results The average CTDIvol for the ASIR group was (1.38±0.64) mGy,about 60% lower than (3.56±1.23) mGy for the simple ATCM group,and the CTDIvol of two groups had statistically significant differences. (t=33.483,P<0.05).The subjective image quality scores for the simple ATCM group were 4.43±0.57 and 4.37±0.61,Kap pa=0.878,P<0.01 (ASIR group: 4.70±0.47 and 4.60±0.50,Kap pa=0.783,P<0.01),by two observers.The image noise score for the simple ATCM group were 4.03±0.56 and 3.83±0.53,Kappa=0.572,P<0.01 (ASIR group:4.20±0.48 and 4.10±0.48,Kappa=0.748,P<0.01),by two observers.All images had acceptable diagnostic image quality. Conclusion Lower radiation dose can be achieved by elevating NI with ASIR in pediatric CT abdominal studies,while maintaining diagnostically acceptable images. Key words: Radiation dosage; Children; Comparative study

Three-dimensional photon counting integral imaging reconstruction using penalized maximum likelihood expectation maximization

Recent works have demonstrated that three-dimensional (3D) object reconstruction is possible from integral images captured in severely photon starved conditions. In this paper we propose an iterative approach to implement a maximum likelihood expectation maximization estimator with several types of regularization for 3D reconstruction from photon counting integral images. We show that the proposed algorithms outperform the previously reported approaches for photon counting 3D integral imaging reconstruction. To the best of our knowledge, this is the first report on using iterative statistical reconstruction techniques for 3D photon counting integral imaging.

Regularized versus non-regularized statistical reconstruction techniques

Abstract An important feature of positron emission tomography (PET) and single photon emission computer tomography (SPECT) is the stochastic property of real clinical data. Statistical algorithms such as ordered subset-expectation maximization (OSEM) and maximum a posteriori (MAP) are a direct consequence of the stochastic nature of the data. The principal difference between these two algorithms is that OSEM is a non-regularized approach, while the MAP is a regularized algorithm. From the theoretical point of view, reconstruction problems belong to the class of ill-posed problems and should be considered using regularization. Regularization introduces an additional unknown regularization parameter into the reconstruction procedure as compared with non-regularized algorithms. However, a comparison of non-regularized OSEM and regularized MAP algorithms with fixed regularization parameters has shown very minor difference between reconstructions. This problem is analyzed in the present paper. To improve the reconstruction quality, a method of local regularization is proposed based on the spatially adaptive regularization parameter. The MAP algorithm with local regularization was tested in reconstruction of the Hoffman brain phantom.

A gridded monthly upper-air data set from 1918 to 1957

Significant efforts have been devoted in recent years towards extending observation-based three-dimensional atmospheric data sets back in time. Such data sets form an important basis for a better understanding of the climate system. Here we present a new monthly three-dimensional global data set that is based on historical upper-air data and surface data. We use statistical reconstruction techniques, calibrated using ERA-40 data, to obtain gridded data from the numerous, but scattered and heterogeneous historical upper-air observations. In contrast to previous work, in which we used hemispheric principal components on both the predictor and the predictand side to reconstruct spatially complete fields back to 1880, we restrict the procedure to places and times where upper-air observations are available. Each grid column (consisting of four variables at six levels) is then reconstructed independently using only predictor variables in the vicinity (i.e., only local stationarity is required rather than stationary large-scale patterns). The product, termed REC2, is a gridded, global monthly data set of geopotential height, temperature, and u and v wind from 850 to 100 hPa back to 1918. The data set is sparse (i.e., many grid cells are empty), but provides an alternative to large-scale reconstructions as it allows for non-stationary teleconnections. We show the results of several validation experiments, compare our new data set with a number of existing data sets, and demonstrate that it is suitable for analysing large-scale climate variability on interannual time-scales.

Reduced space optimal interpolation of daily rain gauge precipitation in Switzerland

The coarse spacing of automatic rain gauges complicates near‐real‐time spatial analyses of precipitation. We test the possibility of improving such analyses by considering, in addition to the in situ measurements, the spatial covariance structure inferred from past observations with a denser network. To this end, a statistical reconstruction technique, reduced space optimal interpolation (RSOI), is applied over Switzerland, a region of complex topography. RSOI consists of two main parts. First, principal component analysis (PCA) is applied to obtain a reduced space representation of gridded high‐resolution precipitation fields available for a multiyear calibration period in the past. Second, sparse real‐time rain gauge observations are used to estimate the principal component scores and to reconstruct the precipitation field. In this way, climatological information at higher resolution than the near‐real‐time measurements is incorporated into the spatial analysis. PCA is found to efficiently reduce the dimensionality of the calibration fields, and RSOI is successful despite the difficulties associated with the statistical distribution of daily precipitation (skewness, dry days). Examples and a systematic evaluation show substantial added value over a simple interpolation technique that uses near‐real‐time observations only. The benefit is particularly strong for larger‐scale precipitation and prominent topographic effects. Small‐scale precipitation features are reconstructed at a skill comparable to that of the simple technique. Stratifying the reconstruction method by the types of weather type classifications yields little added skill. Apart from application in near real time, RSOI may also be valuable for enhancing instrumental precipitation analyses for the historic past when direct observations were sparse.

Rekonstruktion dynamischer Objekteigenschaften für CT

Nondestructive evaluation techniques are mainly used for two purposes. One of these tasks is quality control in the production process. The second task is concerned with the problem of aging constructions and material degradation to ensure the safe operation of industrial installations. In both cases NDE provides a snapshot of the actual system situation. Dynamic effects are almost neglected. But for system monitoring and process control it is necessary to investigate the dynamics of the system. The paper deals with special statistical reconstruction techniques that are capable to record the dynamic behavior of systems based on nondestructive evaluation techniques.

Structural and Transport Properties of Alumina Porous Membranes from Process-Based and Statistical Reconstruction Techniques

We study the structural and transport properties of two model porous membranes made by compaction of spherical monosize γ-alumina particles. A ballistic deposition process of spherical particles has been employed as a process-based representation method for accurately simulating the pore structure of the membranes. Comparison between the computed and experimental permeability values obtained in the Knudsen regime shows very good agreement for both membranes and indicates that sufficient representation of the original pore structure is achieved with the random sphere packs. In a further step, a medium with the same porosity and autocorrelation function as the sphere pack has been stochastically reconstructed. Comparison between the structural properties of the random sphere pack system (process-based model) and the stochastically reconstructed medium (statistical model) shows nearly identical correlation functions and pore chord length distributions but widely different mass chord length distributions. This is reflected to a significant difference in the prediction of a dynamic property like the Knudsen permeability by a factor of about 4. The results suggest that matching of the porosity and the two-point correlation function alone is not always adequate when pursuing an accurate representation of the structure of a porous material. In such cases, higher order statistical properties of the material contained in the chord length distribution of both pore and solid phase should be satisfied as well. It is also found that proper account of the formation process in the reconstruction of a porous material (process-based model) leads to representations of its structure more accurate than those of statistical reconstruction models.

A clinical perspective of accelerated statistical reconstruction.

Although the potential benefits of maximum likelihood reconstruction have been recognised for many years, the technique has only recently found widespread popularity in clinical practice. Factors which have contributed to the wider acceptance include improved models for the emission process, better understanding of the properties of the algorithm and, not least, the practicality of application with the development of acceleration schemes and the improved speed of computers. The objective in this article is to present a framework for applying maximum likelihood reconstruction for a wide range of clinically based problems. The article draws particularly on the experience of the three authors in applying an acceleration scheme involving use of ordered subsets to a range of applications. The potential advantages of statistical reconstruction techniques include: (a) the ability to better model the emission and detection process, in order to make the reconstruction converge to a quantitative image, (b) the inclusion of a statistical noise model which results in better noise characteristics, and (c) the possibility to incorporate prior knowledge about the distribution being imaged. The great flexibility in adapting the reconstruction for a specific model results in these techniques having wide applicability to problems in clinical nuclear medicine.

Diameter-based analysis of the branching geometry of four mammalian bronchial trees

A diameter-based classification technique, which we have previously used to analyse human bronchial geometry (Phillips et al., Respir. Physiol. 98: 193–217, 1994) is applied also to the partial measurements of the dimensions of dog, rat and hamster conducting airways, made by Raabe et al. (Tracheobronchial Geometry: Human, Dog, Rat, Hamster, 1976). The local branching patterns are characterised by means of three parameters, which reflect the asymmetry and the degree of expansion at each bifurcation, and the ratio of the length of each branch to its diameter. The mean values of these parameters as functions of diameter, calculated from the raw morphometric data, are shown for the four species. A statistical reconstruction technique is then used to estimate from the incomplete measurements of Raabe and coworkers some geometrical properties of the whole system of conducting airways, which are likely to influence transport processes in the lung. These include the distribution of the total airway volume between branches of different diameters, the mean and variance of the total lengths of different pathways through the bronchial tree, and a simple model for the variation of flow velocity with airway diameter. Our results show significant differences between the branching structures of all four species. In particular, the human differs from the others in branching much more symmetrically, and in that branches of a given diameter are typically much longer than in the other species; together, these observations imply that the human bronchial tree is geometrically very different from those of the other species.

A diameter-based reconstruction of the branching pattern of the human bronchial tree Part I. Description and application

We propose an analysis of the branching pattern of the conducting airways of the human bronchial tree, based on classifying airways by diameter rather than by some essentially topological measure of their position in the whole lung. A diameter-based statistical reconstruction technique is applied to the partial measurements of airway dimensions made by Raabe et al. (1976), to quantify some aspects of bronchial geometry likely to influence transport processes in the lung. We give predictions for the total number of airways with each diameter, and for the partitioning of the total bronchial wall area and airway volume between airways of different diameters. We also consider the variability of the lengths of different pathways through the bronchial tree, and using a simple model for the distribution of air flow in the lung, we predict how the average flor velocity depends on airway diameter. Comparison of these results with equivalent predictions derived from Weibel's symmetrical lung model shows qualitative differences, which probably result from Weibel's use of extrapolation techniques to compensate for the lack of data on smaller conducting airways. Comparison with the predictions of Horsfield and Cumming's asymmetrical lung model shows generally good agreement, although there are significant differences relating to the asymmetry of bifurcations and to the diameter-dependence of the flow velocity in the smallest conducting airways.