S. Alenius

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 β 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.

Using local median as the location of the prior distribution in iterative emission tomography image reconstruction

Iterative reconstruction algorithms like MLEM (Maximum Likelihood Expectation Maximization) can be regularized using a weighted roughness penalty term according to certain a priori assumptions of the desired image. In the R?RP (Median Root Prior) algorithm the penalty is set according to the deviance of a pixel from the local median. This allows both noise reduction and edge preservation. The prior distribution is Gaussian located around the median of a neighborhood of the pixel. Non-monotonic details smaller than a given limit are considered as noise and are penalized. Thus, MRP implicitly contains the general description of the characteristics of the desired emission image, and good localization of tissue boundaries is achieved without anatomical data. In contrast to the MLEM method, the number of iterations needs not be restricted and unlike many other Bayesian methods MRP has only one parameter. The penalty term can be applied to various iterative reconstruction algorithms. The assumption that the true pixel value is close to the local median applies to any emission images, including the 3D acquisition and images reconstructed from parametric sinograms.

Generalization of median root prior reconstruction

Penalized iterative algorithms for image reconstruction in emission tomography contain conditions on which kind of images are accepted as solutions. The penalty term has commonly been a function of pairwise pixel differences in the activity in a local neighborhood, such that smooth images are favored. Attempts to ensure better edge and detail preservation involve difficult tailoring of parameter values or the penalty function itself. The previously introduced median root prior (MRP) favors locally monotonic images. MRP preserves sharp edges while reducing locally nonmonotonic noise at the same time. Quantitative properties of MRP are good, because differences in the neighboring pixel values are not penalized as such. The median is used as an estimate for a penalty reference, against which the pixel value is compared when setting the penalty. In order to generalize the class of MRP-type of priors, the standard median was replaced by other order statistic operations, the L and finite-impulse-response median hybrid (FMH) filters. They allow for smoother appearance as they apply linear weighting together with robust nonlinear operations. The images reconstructed using the new MRP-L and MRP-FMH priors are visually more conventional. Good quantitative properties of MRP are not significantly altered by the new priors.

Implementation and evaluation of a 3D one-step late reconstruction algorithm for 3D positron emission tomography brain studies using median root prior

Abstract. A fully three-dimensional (3D) one-step late (OSL), maximum a posteriori (MAP) reconstruction algorithm based on the median root prior (MRP) was implemented and evaluated for the reconstruction of 3D positron emission tomography (PET) studies. The algorithm uses the ordered subsets (OS) scheme for convergence acceleration and data update during iterations. The algorithm was implemented using the software package developed within the EU project PARAPET (www.brunel.ac.uk/~masrppet). The MRP algorithm was evaluated using experimental phantom and real 3D PET brain studies. Various experimental set-ups in terms of activity distribution and counting statistics were considered. The performance of the algorithm was assessed by calculating figures of merit such as: contrast, coefficient of variation, activity ratio between two regions and full width at half of maximum for resolution measurements. The performance of MRP was compared with that of 3D ordered subsets-expectation maximisation (OSEM) and 3D re-projection (3DRP) algorithms. In all the experimental situations considered, MRP showed: (1) convergence to a stable solution, (2) effectiveness in noise reduction, particularly for low statistics data, (3) good preservation of spatial details. Compared with the OSEM and 3DRP algorithms, MRP provides comparable or better results depending on the parameters used for the reconstruction of the images.

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

Abstract. 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 non-uniform 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.

Implementation and evaluation of an ordered subsets reconstruction algorithm for transmission PET studies using median root prior and inter-update median filtering

Abstract. An ordered subsets (OS) reconstruction algorithm based on the median root prior (MRP) and inter-update median filtering was implemented for the reconstruction of low count statistics transmission (TR) scans. The OS-MRP-TR algorithm was evaluated using an experimental phantom, simulating positron emission tomography (PET) whole-body (WB) studies, as well as patient data. Various experimental conditions, in terms of TR scan time (from 1xa0h to 1xa0min), covering a wide range of TR count statistics were evaluated. The performance of the algorithm was assessed by comparing the mean value of the attenuation coefficient (MVAC) of known tissue types and the coefficient of variation (CV) for low-count TR images, reconstructed with the OS-MRP-TR algorithm, with reference values obtained from high-count TR images reconstructed with a filtered back-projection (FBP) algorithm. The reconstructed OS-MRP-TR images were then used for attenuation correction of the corresponding emission (EM) data. EM images reconstructed with attenuation correction generated by OS-MRP-TR images, of low count statistics, were compared with the EM images corrected for attenuation using reference (high statistics) TR data. In all the experimental situations considered, the OS-MRP-TR algorithm showed: (1) a tendency towards a stable solution in terms of MVAC; (2) a difference in the MVAC of within 5% for a TR scan of 1xa0min reconstructed with the OS-MRP-TR and a TR scan of 1xa0h reconstructed with the FBP algorithm; (3) effectiveness in noise reduction, particularly for low count statistics data [using a specific parameter configuration the TR images reconstructed with OS-MRP-TR(1xa0min) had a lower CV than the corresponding TR images of a 1-h scan reconstructed with the FBP algorithm]; (4) a difference of within 3% between the mean counts in the EM images attenuation corrected using the OS-MRP-TR images of 1xa0min and the mean counts in the EM images attenuation corrected using the OS-MRP-TR images of 1xa0h; (5) preservation of good image quality for both TR and EM reconstructed images. In conclusion, the OS-MRP-TR algorithm is particularly suitable for WB PET studies, allowing: (1) the acquisition of a very short TR scan (within 1xa0min), (2) the reconstruction of such TR data in low-noise TR images and (3) the use of the reconstructed OS-MRP-TR images for attenuation correction of corresponding EM data.

Combination of multiple images for flash re-lightning

This paper introduces a novel way to combine multiple images of the same scene in order to improve the visual appearance. Especially, images taken with the flash often contain artifacts such as too strong flash illumination and too dark background. The nature of the ambient lightning can be combined back with other image features. Two or more flash/no-flash images are combined to a spatially adaptive mixture image that represents the essential features of the images. No assumptions are made on which images contribute to the result. The lightning, shadows, and colors are a blind combination of the input images. The new method uses the principal component analysis (PCA) to find an optimal fusing factors for the images in order to compute the resulting image. The images are decomposed and processed using PCA to find out the local adaptive principal component. Image decomposition prior to PCA makes it possible for both coarse and fine image features to be fused. Also other camera parameters than the flash can be varied. For instance, if images with multiple focus settings are fused by the new APC (adaptive principal combination) method, the resulting mixture image depicts an extended depth of focus.

Improving the visual quality of median root prior images in PET and SPECT reconstruction

The median root prior (MRP) iterative reconstruction algorithm favors locally monotonic images. MRP preserves sharp edges while reducing noise at the same time. Quantitative properties of MRP are good, because a sufficiently high number of iterations can be run. In order to make the visual quality of MRP images more conventional, the standard median was replaced by other order statistic operations, the L- and FMH-filters. They allow for smoother appearance as they apply linear weighting together with nonlinear operations. The images reconstructed using the new MRP-L and MRP-FMH priors are visually more appealing. Good quantitative properties of MRP are not significantly altered by the new priors.

Transmission images and attenuation correction with short acquisitions using median root prior reconstruction in PET

Quantitative PET studies require computing of the attenuation correction factors (ACF) 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 algorithm was used for reconstruction of short 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 scan data or segmentation of the image are used.