Median Root Prior Research Articles

Evaluation of Median Root Prior for Robust In-Beam PET Reconstruction

Dose delivery verification in proton beam radiotherapy is used to ensure the delivery of the dose to the correct location. A positron emission tomography (PET) scanner can be used to detect the secondary radiation during the treatment, so-called in-beam PET. This is a challenging application for PET due to the low counts and limited angular coverage. We propose a maximum a posteriori (MAP) reconstruction with median root prior (MRP) for the reconstruction of in-beam PET data. The proposed method was compared against MAP with total variation (TV) prior and maximum likelihood expectation maximization (MLEM), which have previously been used for this application. The effects of different ring configurations and time-of-flight information were tested with simulations of a geometrical phantom and a realistic patient treatment plan. The results indicate that both MAP methods produced sharper edges than MLEM, allowing more accurate edge localization in the reconstructed images. Even for the partial ring configurations, no elongation was observed with MAP methods. MAP-MRP successfully reduced the noise, whereas MAP-TV resulted in checkerboard artifacts. MAP-MRP was also more stable against the selection of the reconstruction parameters. In conclusion, MAP-MRP offers a simple and robust alternative for the reconstruction of in-beam PET data.

Effects of Regularisation Priors and Anatomical Partial Volume Correction on Dynamic PET Data

Dynamic PET provides temporal information about the tracer uptake. However, each PET frame has usually low statistics, resulting in noisy images. Furthermore, PET images suffer from partial volume effects. The goal of this study is to understand the effects of prior regularisation on dynamic PET data and subsequent anatomical partial volume correction. The Median Root Prior (MRP) regularisation method was used in this work during reconstruction. The quantification and noise in image-domain and time-domain (time-activity curves) as well as the impact on parametric images is assessed and compared with Ordinary Poisson Ordered Subset Expectation Maximisation (OP-OSEM) reconstruction with and without Gaussian filter. This study shows the improvement in PET images and time-activity curves (TAC) in terms of noise as well as in the parametric images when using prior regularisation in dynamic PET data. Anatomical partial volume correction improves the TAC and consequently, parametric images. Therefore, the use of MRP with anatomical partial volume correction is of interest for dynamic PET studies.

Influence of Iterative Reconstruction Algorithms on PET Image Resolution

The aim of the present study was to assess image quality of PET scanners through a thin layer chromatography (TLC) plane source. The source was simulated using a previously validated Monte Carlo model. The model was developed by using the GATE MC package and reconstructed images obtained with the STIR software for tomographic image reconstruction. The simulated PET scanner was the GE DiscoveryST. A plane source consisted of a TLC plate, was simulated by a layer of silica gel on aluminum (Al) foil substrates, immersed in 18F-FDG bath solution (1MBq). Image quality was assessed in terms of the modulation transfer function (MTF). MTF curves were estimated from transverse reconstructed images of the plane source. Images were reconstructed by the maximum likelihood estimation (MLE)-OSMAPOSL, the ordered subsets separable paraboloidal surrogate (OSSPS), the median root prior (MRP) and OSMAPOSL with quadratic prior, algorithms. OSMAPOSL reconstruction was assessed by using fixed subsets and various iterations, as well as by using various beta (hyper) parameter values. MTF values were found to increase with increasing iterations. MTF also improves by using lower beta values. The simulated PET evaluation method, based on the TLC plane source, can be useful in the resolution assessment of PET scanners.

Bayesian image reconstruction for positron emission tomography based on anisotropic median-diffusion

For improving the quality of positron emission tomography (PET) images, the partial differential equation median (PDEmedian) algorithm which incorporates an anisotropic diffusion (AD) filter into the median root prior (MRP) algorithm was proposed. However, due to the shortcomings of the AD filter, the PDEmedian algorithm is difficult to realize. This work aims to solve this problem by introducing a new diffusion model into the PDEmedian. The proposed algorithm shows its positive effects on image reconstruction and denoising. Experimental results present that the new algorithm can preserve sharp edges while reducing noise at the same time. Furthermore, in comparison to other similar reconstruction algorithms, the proposed method is less sensitive to the value of the gradient threshold and the adjustment of the diffusion number.

Effective Anatomical Priors for Emission Tomographic Reconstruction

Bayesian tomographic reconstruction with anatomical side information from other imaging modalities can improve both image quality and quantitation in emission tomography for both single-photon emission computed tomography and positron emission tomography. However, the complexity and sensitivity to registration error between function and anatomical images often limit its clinical applications. To alleviate these challenges, this study proposes two priors, anatomical median root prior (AMRP) and anatomical mean prior (AMP), with a simple scheme of incorporating anatomical information. The priors are based on a simple edge-preserving prior that aims to retain the true intensity edges without blurring, median root prior (MRP), by replacing the median value among neighboring pixels with the median or mean value in a corresponding predefined anatomical region. Digital simulations and Monte Carlo simulations were conducted to evaluate the performance of the proposed methods. As compared to MRP, the proposed priors both showed sharper edges, better uniformity, and more accurate activity recovery with well-aligned anatomical and functional images. In addition, a tolerance study in terms of the misregistration between anatomical and functional images was also performed. Acceptable results were obtained for both priors when misalignment was less than 2 pixels, which can be easily achieved in real applications. The proposed anatomical priors for emission tomographic reconstruction can improve both visual and quantitative performance, and are not sensitive to misregistration errors between anatomical and functional images.

Effects of regularisation priors on dynamic PET Data.

Dynamic PET provides temporal information about tracer uptake. However, each PET frame has usually low statistics, resulting in noisy images. The goal is to study effects of prior regularisation on dynamic PET data. Quantification and noise in image-domain and time-domain as well as impact on parametric images is assessed. Dynamic PET data for the Siemens 3T MR-BrainPET was simulated with time-activity curves (TAC) of [1] F-FDG obtained analytically using realistic values for the kinetic model (Table ​(Table1).1). The total number of true counts was 6x108 and scatter and random fractions were both 35%. The data consists of 23 frames as applied in our clinical protocol. For reconstruction, the Ordinary Poisson Ordered Subset Expectation Maximisation (OP-OSEM) method was used in PRESTO [1], which allows to use several 3D priors [2]. The Median Root Prior (MRP) used a 3x3x3 neighbourhood and a Bayes parameter of 0.1 for all frames. Patlak parametric images were calculated using PMOD software. Table 1 Kinetic values used for simulation of two tissues: White-Matter (WM) and Gray-Matter (GM), extracted from real acquired volunteer data. Figure ​Figure11 shows that the MRP OP-OSEM reduces image noise in WM, GM and AIF: from 50% reduction in low-count frames to 10% reduction in high-count frames (e.g. Frame 24). Furthermore, Patlak parametric images also look smoother for MRP OP-OSEM than for OP-OSEM. Figure 1 a) Reconstructed images without MRP corresponding to Frame 14 (2.77x106 counts); b) Reconstructed images with MRP corresponding to Frame 14 (2.77x106 counts); c) Reconstructed images without MRP corresponding to Frame 24 (119x106 counts); d) Reconstructed ... Figure ​Figure22 shows similar quantification for both reconstruction methods (with similar RCs). OP-OSEM presents higher RCs than MRP OP-OSEM in high-count frames (up to 9%), while in low-count frames MRP OP-OSEM presents higher RCs (up to 9%). This is probably due to the fact that the Bayes parameter is count-dependent. Figure 2 TAC using OP-OSEM reconstruction without and with MRP for two different regions: a) GM and b) AIF. This study shows improvement on PET image quality in terms of noise (up to 50% reduction) as well as in parametric images when using prior regularisation in dynamic PET data. Both OP-OSEM and MRP OP-OSEM show similar quantification, with higher RCs for MRP OP-OSEM in low-count frames.

Towards novel regularization approaches to PET image reconstruction

The purpose of this study is to introduce a novel empirical iterative algorithm for medical image reconstruction, under the short name MRP-ISWLS (Median Root Prior Image Space Weighted Least Squares). Further, we assess the performance of the new algorithm by comparing it to the simultaneous version of known MRP algorithms. All algorithms are compared in terms of cross-correlation and CNRs (Contrast-to-Noise Ratios). As it turns out, MRP-ISWLS presents higher CNRs than the known algorithms for objects of different size. Also MRP-ISWLS has better noise manipulation.

Voxel-based NK1 Receptor Occupancy Measurements with [18F]SPA-RQ and Positron Emission Tomography: A Procedure for Assessing Errors from Image Reconstruction and Physiological Modeling

Receptor occupancy studies with positron emission tomography (PET) are widely used as aids in the drug development process. This study introduces a general procedure for assessing errors that arise from the applied image processing methods in PET receptor occupancy studies using the neurokinin-1 (NK1) receptor occupancy study as an example. The bias and variance among eight combinations of image reconstruction and model calculation methods for estimating voxel-level receptor occupancy results were examined. The tests were performed using a dynamic numerical phantom based on a previous PET drug occupancy study with the NK1 receptor antagonist tracer [(18)F]SPA-RQ. The simplified reference tissue model with basis functions (SRTM BF) was best at estimating receptor occupancy in terms of average bias. On the other hand, median root prior (MRP) image reconstruction produced the lowest variances in the occupancy estimates. These results suggest that SRTM BF and MRP is, in this case, the combination of choice in voxel-based receptor occupancy calculation. In the calculation of regional binding potential values, the commonly used sample mean is not applicable and, e.g., the median could be used instead. This study shows that even this kind of complicated receptor study can be statistically evaluated. The reconstruction methods had an effect on the variance in the voxel-based receptor occupancy calculation. The model calculation methods influenced the average bias. The test method was found useful in assessing the methodological sources of systematic and random error in receptor occupancy estimation with PET.

Median-prior tomography reconstruction combined with nonlinear anisotropic diffusion filtering

Positron emission tomography (PET) is becoming increasingly important in the fields of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation for image reconstruction in emission tomography place conditions on which types of images are accepted as solutions. The recently introduced median root prior (MRP) favors locally monotonic images. MRP can preserve sharp edges, but a steplike streaking effect and much noise are still observed in the reconstructed image, both of which are undesirable. An MRP tomography reconstruction combined with nonlinear anisotropic diffusion interfiltering is proposed for removing noise and preserving edges. Analysis shows that the proposed algorithm is capable of producing better reconstructed images compared with those reconstructed by conventional maximum-likelihood expectation maximization (MLEM), MAP, and MRP-based algorithms in PET image reconstruction.

Fuzzy-rule-based image reconstruction for positron emission tomography

Positron emission tomography (PET) and single-photon emission computed tomography have revolutionized the field of medicine and biology. Penalized iterative algorithms based on maximum a posteriori (MAP) estimation eliminate noisy artifacts by utilizing available prior information in the reconstruction process but often result in a blurring effect. MAP-based algorithms fail to determine the density class in the reconstructed image and hence penalize the pixels irrespective of the density class. Reconstruction with better edge information is often difficult because prior knowledge is not taken into account. The recently introduced median-root-prior (MRP)-based algorithm preserves the edges, but a steplike streaking effect is observed in the reconstructed image, which is undesirable. A fuzzy approach is proposed for modeling the nature of interpixel interaction in order to build an artifact-free edge-preserving reconstruction. The proposed algorithm consists of two elementary steps: (1) edge detection, in which fuzzy-rule-based derivatives are used for the detection of edges in the nearest neighborhood window (which is equivalent to recognizing nearby density classes), and (2) fuzzy smoothing, in which penalization is performed only for those pixels for which no edge is detected in the nearest neighborhood. Both of these operations are carried out iteratively until the image converges. Analysis shows that the proposed fuzzy-rule-based reconstruction algorithm is capable of producing qualitatively better reconstructed images than those reconstructed by MAP and MR P algorithms. The reconstructed images a resharper, with small features being better resolved owing to the nature of the fuzzy potential function.

Pinhole single-photon emission tomography reconstruction based on median root prior

The maximum likelihood expectation maximisation (ML-EM) algorithm can be used to reduce reconstruction artefacts produced by filtered backprojection (FBP) methods in pinhole single-photon emission tomography (SPET). However, ML-EM suffers from noise propagation along iterations, which leads to quantitatively unpleasant reconstruction results. To avoid this increase in noise, the median root prior (MRP) algorithm for pinhole SPET was implemented. Projection data of a line source and Picker's thyroid phantom were collected using a single-head gamma camera with a pinhole collimator. MRP was added to existing pinhole ML-EM reconstruction algorithm and the phantom studies were reconstructed using MRP, ML-EM and FBP for comparison. Coefficients of variation, contrasts and full-widths at half-maximum were calculated and showed a clear reduction in noise without significant loss of resolution or decrease in contrast when MRP was applied. MRP also produced visually pleasing images even with high iteration numbers, free of the checkerboard-type noise patterns which are typical of ML-EM images.

Iterative Image Reconstruction for Clinical PET Using Ordered Subsets, Median Root Prior, and a Web-Based Interface

Purpose: The development, implementation and validation of simple, flexible and efficient iterative image reconstruction (IIR) methods for their take-up in routine clinical positron emission tomography (PET) static or dynamic studies. Procedures: The ordered subsets (OS) technique applied for the acceleration of the maximum likelihood expectation maximization (MLEM) IIR algorithm is here extended to include the weighted least-squares (WLS), image space reconstruction algorithm (ISRA) and the space alternating generalized EM (SAGE). The median root prior (MRP) has been successfully applied as a Bayesian regularization to control the noise level in the reconstructed images. All methods are implemented on distributed Pentium systems and tested using simulated PET data from a brain phantom. A Javascript is used for the initiation of the reconstruction. Results: Taking into consideration the image quality and the time required for the reconstruction, the MRP-OSEM (ordered subsets expectation maximization) seems to provide best results after four to eight iterations, with four subsets and a MRP coefficient of 0.2–0.4. Iterative reconstruction of the transmission images with OS-acceleration and MRP regularization with subsequent calculation of the attenuation correction factors (ACFs) is shown to effectively remove streak artifacts in the emission images, especially along paths of high attenuation. Conclusions: An efficient implementation using distributed processing principles and a web-based interface allows the reconstruction of one frame (with 63 cross-section slices) from a dynamic determination in few minutes. This work showed that regular PC systems can provide fast execution and produce results in clinically meaningful times. This eradicates the argument of the computational burden of the method that prevented the extensive use of IIR in today's modern PET systems. (Mol Imag Biol 2002;4:219–231)

Improvement of brain perfusion SPET using iterative reconstruction with scatter and non-uniform attenuation correction.

Filtered back-projection (FBP) is generally used as the reconstruction method for single-photon emission tomography although it produces noisy images with apparent streak artefacts. It is possible to improve the image quality by using an algorithm with iterative correction steps. The iterative reconstruction technique also has an additional benefit in that computation of attenuation correction can be included in the process. A commonly used iterative method, maximum-likelihood expectation maximisation (ML-EM), can be accelerated using ordered subsets (OS-EM). We have applied to the OS-EM algorithm a Bayesian one-step late correction method utilising median root prior (MRP). Methodological comparison was performed by means of measurements obtained with a brain perfusion phantom and using patient data. The aim of this work was to quantitate the accuracy of iterative reconstruction with scatter and non-uniform attenuation corrections and post-filtering in SPET brain perfusion imaging. SPET imaging was performed using a triple-head gamma camera with fan-beam collimators. Transmission and emission scans were acquired simultaneously. The brain phantom used was a high-resolution three-dimensional anthropomorphic JB003 phantom. Patient studies were performed in ten chronic pain syndrome patients. The images were reconstructed using conventional FBP and iterative OS-EM and MRP techniques including scatter and nonuniform attenuation corrections. Iterative reconstructions were individually post-filtered. The quantitative results obtained with the brain perfusion phantom were compared with the known actual contrast ratios. The calculated difference from the true values was largest with the FBP method; iteratively reconstructed images proved closer to the reality. Similar findings were obtained in the patient studies. The plain OS-EM method improved the contrast whereas in the case of the MRP technique the improvement in contrast was not so evident with post-filtering.

Attenuation correction for PET using count-limited transmission images reconstructed with median root prior

Quantitative PET studies require the computation of the attenuation correction factors (ACFs) for compensating the body attenuation effect in the emission data. Short acquisition times for transmission are desired, because of patient comfort and movement elimination. In practice, long acquisition times are used, due to the statistical noise of count-limited scans. In order to reduce the noise, the median root prior (MRP) iterative reconstruction method was used for reconstruction of short-acquisition-time transmission images. Using these images, the ACFs were generated for correction of emission data. The new approach allows for scan times of 2 min or less, which is desirable for quantitative whole-body PET studies. The new method is object-independent and robust, because no smoothing of the scan data or segmentation of the images are used.

Bayesian image reconstruction for emission tomography based on median root prior.

The aim of the present study was to investigate a new type of Bayesian one-step late reconstruction method which utilizes a median root prior (MRP). The method favours images which have locally monotonous radioactivity concentrations. The new reconstruction algorithm was applied to ideal simulated data, phantom data and some patient examinations with PET. The same projection data were reconstructed with filtered back-projection (FBP) and maximum likelihood-expectation maximization (ML-EM) methods for comparison. The MRP method provided good-quality images with a similar resolution to the FBP method with a ramp filter, and at the same time the noise properties were as good as with Hann-filtered FBP images. The typical artefacts seen in FBP reconstructed images outside of the object were completely removed, as was the grainy noise inside the object. Quantitatively, the resulting average regional radioactivity concentrations in a large region of interest in images produced by the MRP method corresponded to the FBP and ML-EM results but at the pixel by pixel level the MRP method proved to be the most accurate of the tested methods. In contrast to other iterative reconstruction methods, e.g. ML-EM, the MRP method was not sensitive to the number of iterations nor to the adjustment of reconstruction parameters. Only the Bayesian parameter beta had to be set. The proposed MRP method is much more simple to calculate than the methods described previously, both with regard to the parameter settings and in terms of general use. The new MRP reconstruction method was shown to produce high-quality quantitative emission images with only one parameter setting in addition to the number of iterations.

Lymphoid and non-lymphoid cells in the epithelium and lamina propria of intestinal mucosa of pigs.

The jejunum and ileum of 5 day old and adult normal pigs and of 45 day old germ free pigs were used to study the lymphocyte pools in the epithelium and lamina propria by sequential treatments with EDTA, four hours, and 12 hours of collagenase treatment. In adult animals the incubation of the jejunal wall with EDTA resulted in mean (SD) 26.8 (10.9) x 10(6) intraepithelial lymphocytes per g of tissue. The ileal wall gave lower cell yields. After complete digestion of the lamina propria by collagenase a further yield of 35.2 (10.2) x 10(6)/g lymphocytes was achieved. The separation of the gut wall from 5 day old pigs resulted in a 10-fold lower total lymphocyte yield, and the tissue was totally digested after four hours of collagenase treatment. Many eosinophils and mast cells were found in the suspensions from adult animal tissues after the collagenase treatment; 4.7 x 10(6)/g and 4.8 x 10(6)/g, respectively. The suspensions after 12 hour collagenase incubation contained up to 30% plasma cells. Almost all cells isolated by EDTA incubation were CD8+ T cells. After collagenase incubation CD4+ and CD8+ T lymphocytes were found in all animal groups, and in adult animals up to 20% surface Ig+ cells were harvested. When the incorporation of the thymidine analogue bromodesoxyuridine was used to study the lymphocyte production in vivo 3 to 7% lymphocytes in the epithelium were labelled 24 hours later (lamina propria T lymphocytes about 1%). In this study lymphoid as well as non-lymphoid cells have been analysed in mucosal cell suspensions. The absolute cell yield per gram of mucosal tissue is a basis to estimate the pool sizes of intraepithelial and lamina propria lymphocytes.