Maximum Likelihood Iterative Algorithm Research Articles

Full-field in vivo imaging of nanoparticles using benchtop cone-beam XFCT system with pixelated photon counting detector

Objective. X-ray fluorescence computed tomography (XFCT) is a promising noninvasive technique for in vivo imaging of high-Z elements (e.g. gadolinium (Gd) or gold (Au)). In this study we upgraded our experimental XFCT system using a flat panel photon counting detector with redesigned pinhole collimation in order to achieve 3D XFCT images during one scan. Approach. Aiming at the characteristics of pinhole-collimated cone-beam XFCT imaging, a new scatter correction algorithm was proposed to estimate the normalized spectrum of scatter background based on K–N formula and realize correction by a weighted least squares method. Then, images were quantitatively reconstructed by a maximum likelihood iterative algorithm with the attenuation correction. Main results. The potential on full-field in vivo XFCT imaging of this new system was investigated. An imaging experiment of a PMMA phantom with the diameter of 35 mm was carried out for quantitative evaluation of the system performance. Results show that 2 mg ml−1 Gd solutions can be successfully reconstructed with a 45 min cone-beam XFCT scan. In vivo XFCT imaging experiments of mice with injection of Gd nanoparticles (GdNPs) were also performed and demonstrated in this paper. A mouse was injected through the tail vein with 20 mg ml−1 NaGdF4 solution and then anesthetized with isoflurane during the cone-beam XFCT scan. Significance. The distribution of the GdNPs inside the mouse can be well reconstructed so that the deposition of NPs in vivo can be clearly observed, which indicates the feasibility of the proposed system for full-field XFCT of small animals and further potential in relevant in vivo research.

Maximum Likelihood Iterative Algorithm for Hammerstein Systems with Hard Nonlinearities

In this paper, we consider several iterative algorithms for Hammerstein systems with hard nonlinearities. The Hammerstein system is first simplified as a polynomial identification model through the key term separation technique, and then the parameters are estimated by using the maximum likelihood (ML) based gradient-based iterative algorithm. Furthermore, an ML least squares auxiliary variable algorithm and an ML bias compensation gradient-based iterative algorithm are developed to identify the saturation system with colored noise. Simulation results are included to illustrate the effectiveness of the proposed algorithms.

Quantitative Imaging of Gd Nanoparticles in Mice Using Benchtop Cone-Beam X-ray Fluorescence Computed Tomography System.

Nanoparticles (NPs) are currently under intensive research for their application in tumor diagnosis and therapy. X-ray fluorescence computed tomography (XFCT) is considered a promising non-invasive imaging technique to obtain the bio-distribution of nanoparticles which include high-Z elements (e.g., gadolinium (Gd) or gold (Au)). In the present work, a set of experiments with quantitative imaging of GdNPs in mice were performed using our benchtop XFCT device. GdNPs solution which consists of 20 mg/mL NaGdF4 was injected into a nude mouse and two tumor-bearing mice. Each mouse was then irradiated by a cone-beam X-ray source produced by a conventional X-ray tube and a linear-array photon counting detector with a single pinhole collimator was placed on one side of the beamline to record the intensity and spatial information of the X-ray fluorescent photons. The maximum likelihood iterative algorithm with scatter correction and attenuation correction method was applied for quantitative reconstruction of the XFCT images. The results show that the distribution of GdNPs in each target slice (containing liver, kidney or tumor) was well reconstructed and the concentration of GdNPs deposited in each organ was quantitatively estimated, which indicates that this benchtop XFCT system provides convenient tools for obtaining accurate concentration distribution of NPs injected into animals and has potential for imaging of nanoparticles in vivo.

Regularization of multiplicative iterative algorithms with nonnegative constraint

This paper studies the regularization of the constrained maximum likelihood iterative algorithms applied to incompatible ill-posed linear inverse problems. Specifically, we introduce a novel stopping rule which defines a regularization algorithm for the iterative space reconstruction algorithm in the case of least-squares minimization. Further we show that the same rule regularizes the expectation maximization algorithm in the case of Kullback–Leibler minimization, provided a well-justified modification of the definition of Tikhonov regularization is introduced. The performances of this stopping rule are illustrated in the case of an image reconstruction problem in the x-ray solar astronomy.

Differential emission measure distributions in X-ray solar flares

X-ray spectrometer RESIK has observed spectra in the four wavelength bands from 3.3 Å to 6.1 Å. This spectral range contains many emission lines of H- and He-like ions for Si, S, Ar and K. These lines are formed in plasma of coronal temperatures ( T > 3 MK). Analysis of their intensities allows studying differential emission measure distributions (DEM) in temperature range roughly between 3 MK and 30 MK. The aim of present study was to check whether any relationship exists between the character of DEM distribution, the event phase and the X-ray flare class. To do this we have calculated and analyzed the DEM distributions for a set of flares belonging to different GOES classes from the range B5.6–X1. The DEM distributions have been calculated using “Withbroe–Sylwester” multiplicative, maximum likelihood iterative algorithm. As the input data we have used absolute fluxes observed by RESIK in several spectral bands (lines + continuum). Respective emission functions have been calculated using the CHIANTI v. 5.2 atomic data package.

First Determinations of Differential Emission Measure Distribution from RESIK X-ray Spectra

RESIK Bragg spectrometer aboard CORONAS-F solar observatory collected spectra of hundreds of solar flares in the unique spectral range between 3.3 A and 6.1 A. The instrument’s absolute and relative calibrations are now finished which allows for the first time to interpret the observations in terms of the differential emission measure (DEM) distribution. With known DEM shape it is possible to derive and study in detail flaring plasma composition and energy balance. Here we report results of using an improved Maximum Likelihood iterative algorithm (WithbroeSylwester) for determination of the DEM distributions for 7 January 2003 flare at 23:30 UT. The study is based on the absolute flux values observed in a number of strong Hand He-like transitions of K xviii, Ar xviii, Ar xvii, S xvi, S xv, Si xiv and Si xiii ions. In this respect, we use line and continuum X-ray emissivities as provided by CHIANTI package from SolarSoft.

The design and performance of a simultaneous transmission and emission tomography system

A commercial three-detector single-photon emission computed tomography (SPECT) system that enables simultaneous acquisition of transmission and emission data without increasing patient scanning time has been designed and manufactured. This system produces a reconstructed attenuation coefficient distribution that can be used to correct for photon attenuation in the emission reconstruction. The three detectors with fan-beam collimators are mounted to the gantry in a triangular arrangement. A transmission line source assembly was mounted at the focal line of one of the detectors and controlled to move in synchrony with the opposing fan-beam collimator. Data from transmission and emission sources at different energies were acquired in one detector, while the other two simultaneously acquired emission data. A transmission source of /sup 153/Gd was used with /sup 99m/Tc-labeled radiopharmaceuticals, and /sup 57/Co was used with /sup 201/Tl. Algorithms were developed to subtract crosstalk between transmission and emission energy windows in all three detectors. A transmission maximum-likelihood iterative algorithm was used to reconstruct the attenuation distribution, which was used in combination with an iterative maximum-likelihood expectation-maximization algorithm to compensate for the attenuation of the projection of the emission distribution. The results in phantom studies displayed greater uniformity of activity with attenuation-corrected reconstruction. This was demonstrated visually and quantitatively by using anterior-to-inferior ratios close to one and low spatial %rms error as a measure of improved uniformity.

Computer-aided lesion detection with statistical model-based features in PET images

Positron emission tomography (PET) with the glucose analog [/sup 18/F] fluorodeoxyglucose is proving to be useful in cancer diagnosis and treatment. However, as in all nuclear medicine imaging technologies, lesion detection with PET is often hindered by limited spatial resolution and low signal-to-noise ratios. Under such conditions, conventional diagnosis by visual inspection usually becomes difficult and potentially inaccurate. In this paper, we propose use of computer-aided lesion detection methods for PET imaging by applying a maximum likelihood ratio test and a composite hypothesis test, assuming that the mean positron emission rate is deterministic or random, respectively. In our approach, different statistical models characterizing the mean positron emission rate, the raw sinogram data and the filtered backprojection (FBP) reconstructed image are used to derive the test criteria. Three methods to estimate the unknown parameters of the test functions from observations are presented. The performance of one of the proposed methods is evaluated and compared with both simulated and experimental phantom data. In the preliminary trials, the methods detect correctly (with a high probability >0.9) lesions of diameter/spl ges/15 mm with lesion-to-background contrast 1.1:1. Under the same conditions, the test lesion could not be detected by visual inspection alone in the images reconstructed by either the FBP or the maximum likelihood iterative algorithms. The methods may also be used for the objective assessment of the quality of images reconstructed from different algorithms.

The direct calculation of parametric images from dynamic PET data using maximum-likelihood iterative reconstruction

The aim of this work is to calculate, directly from projection data, concise images characterizing the spatial and temporal distribution of labelled compounds from dynamic PET data. Conventionally, image reconstruction and the calculation of parametric images are performed sequentially. By combining the two processes, low-noise parametric images are obtained, using a computationally feasible parametric iterative reconstruction (PIR) algorithm. PIR is performed by restricting the pixel time - activity curves to a positive linear sum of predefined time characteristics. The weights in this sum are then calculated directly from the PET projection data, using an iterative algorithm based on a maximum-likelihood iterative algorithm commonly used for tomographic reconstruction. The ability of the algorithm to extract known kinetic components from the raw data is assessed, using data from both a phantom experiment and clinical studies. The calculated parametric images indicate differential kinetic behaviour and have been used to aid in the identification of tissues which exhibit differences in the handling of labelled compounds. These parametric images should be helpful in defining regions of interest with similar functional behaviour, and with FDG Patlak analysis.