KEYWORDS: Sensors, Collimators, Single photon emission computed tomography, Reconstruction algorithms, Expectation maximization algorithms, Image processing, Monte Carlo methods, Heart, Signal to noise ratio, Spatial resolution
Single photon emission computerized tomographic (SPECT) images often suffer from low resolution and low count
density. To improve spatial resolution of SPECT it is possible to use a pinhole collimator; however, this further reduces
the system sensitivity. A potential solution to this problem is to use coded apertures, which offers increased sensitivity
by using multiple pinholes, at the cost of increased image reconstruction time.
A generic reconstruction algorithm has been developed which allows for arbitrary acquisition geometry via affine
transforms (translation and rotation). The reconstruction process uses a (Siddon) ray projector, the expectation
maximization (EM) algorithm and a 1 to n pinhole position matrix. Iteration times scale as a function of the number of
pinholes in the collimator. Resolution recovery has also been incorporated into the reconstruction algorithm.
The algorithm developed allows for the investigation of optimal imaging settings for small animal imaging. Simulated
acquisitions of an ex-vivo rat heart with 1, 5 and 8 pinholes, over 360 degree acquisition, showing that multi-pinhole
imaging can be successfully applied to rat cardiac imaging. Further refinement of the acquisition parameters, such as
image overlap, collimator pinhole configuration and geometrical imaging configuration, will predict the theoretical
settings for quantitative cardiac multi-pinhole SPECT imaging.
Yi-Hwa Liu, Zakir Sahul, Christopher Weyman, William Ryder, Donald Dione, Lawrence Dobrucki, Choukri Mekkaoui, Matthew Brennan, Xiaoyue Hu, Christi Hawley, Albert Sinusas
We have developed a new single photon emission computerized tomography (SPECT) hotspot quantification
method incorporating extra cardiac activity correction and hotspot normal limit estimation. The method was validated
for estimation accuracy of myocardial tracer focal uptake in a chronic canine model of myocardial infarction (MI). Dogs
(n = 4) at 2 weeks post MI were injected with Tl-201 and a
Tc-99m-labeled hotspot tracer targeted at matrix
metalloproteinases (MMPs). An external point source filled with
Tc-99m was used for a reference of absolute
radioactivity. Dual-isotope (Tc-99m/Tl-201) SPECT images were acquired simultaneously followed by an X-ray CT
acquisition. Dogs were sacrificed after imaging for myocardial gamma well counting. Images were reconstructed with
CT-based attenuation correction (AC) and without AC (NAC) and were quantified using our quantification method.
Normal limits for myocardial hotspot uptake were estimated based on 3 different schemes: maximum entropy,
meansquared-error minimization (MSEM) and global minimization. Absolute myocardial hotspot uptake was quantified from
SPECT images using the normal limits and compared with well-counted radioactivity on a segment-by-segment basis (n = 12 segments/dog). Radioactivity was expressed as % injected dose (%ID). There was an excellent correlation (r = 0.78-0.92) between the estimated activity (%ID) derived using the SPECT quantitative approach and
well-counting, independent of AC. However, SPECT quantification without AC resulted in the significant underestimation of radioactivity. Quantification using SPECT with AC and the MSEM normal limit yielded the best results compared with well-counting. In conclusion, focal myocardial "hotspot" uptake of a targeted radiotracer can be accurately quantified in
vivo using a method that incorporates SPECT imaging with AC, an external reference, background scatter compensation,
and a suitable normal limit. This hybrid SPECT/CT approach allows for the serial non-invasive quantitative evaluation
of molecular targeted tracers in the heart.
Near-field coded aperture imaging is known to have superior image resolution and count sensitivity over conventional parallel-hole collimated nuclear imaging. There have been several studies in image reconstruction for two-dimensional planar objects using the coded aperture imaging technology. However, coded aperture imaging for three-dimensional (3D) objects has not been extensively investigated. In this paper, a 3D reconstruction method for near-field coded aperture imaging is presented. We first introduce the "out-of-focus" correction factor into the generic expectation maximization (EM) algorithm for 3D near-field coded aperture images with the assumption that the photon emissions of coded aperture projections follow the Poisson statistics. The ordered subset expectation maximization (OSEM) method is then adapted for full 3D coded aperture image reconstruction. A 3D capillary tube phantom filled with 99mTc radioactive solution was used to evaluate the performance of our methods. A dual-head SPECT camera, one head quipped with a coded aperture module and the other with a parallel-hole collimator, was utilized for image acquisitions. Images were reconstructed using the modified EM and OSEM methods associated with the depth-dependent out-of-focus correction. The preliminary phantom results showed that our methods may have potential of reconstructing 3D near-field coded aperture images and also providing superior image resolution as compared to conventional parallel-hole collimated images.
This paper presents recent results of our reconstructions of 3-D data from Drosophila chromosomes as well as our simulations with a refined version of the algorithm used in the former. It is well known that the calibration of the point spread function (PSF) of a fluorescence microscope is a tedious process and involves esoteric techniques in most cases. This problem is further compounded in the case of confocal microscopy where the measured intensities are usually low. A number of techniques have been developed to solve this problem, all of which are methods in blind deconvolution. These are so called because the measured PSF is not required in the deconvolution of degraded images from any optical system. Our own efforts in this area involved the maximum likelihood (ML) method, the numerical solution to which is obtained by the expectation maximization (EM) algorithm. Based on the reasonable early results obtained during our simulations with 2-D phantoms, we carried out experiments with real 3-D data. We found that the blind deconvolution method using the ML approach gave reasonable reconstructions. Next we tried to perform the reconstructions using some 2-D data, but we found that the results were not encouraging. We surmised that the poor reconstructions were primarily due to the large values of dark current in the input data. This, coupled with the fact that we are likely to have similar data with considerable dark current from a confocal microscope prompted us to look into ways of constraining the solution of the PSF. We observed that in the 2-D case, the reconstructed PSF has a tendency to retain values larger than those of the theoretical PSF in regions away from the center (outside of those we considered to be its region of support). This observation motivated us to apply an upper bound constraint on the PSF in these regions. Furthermore, we constrain the solution of the PSF to be a bandlimited function, as in the case in the true situation. We have derived two separate approaches for implementing the constraint. One approach involves the mathematical rigors of Lagrange multipliers. This approach is discussed in another paper. The second approach involves an adaptation of the Gershberg Saxton algorithm, which ensures bandlimitedness and non-negativity of the PSF. Although the latter approach is mathematically less rigorous than the former, we currently favor it because it has a simpler implementation on a computer and has smaller memory requirements. The next section describes briefly the theory and derivation of these constraint equations using Lagrange multipliers.
KEYWORDS: 3D image processing, 3D modeling, 3D image reconstruction, Image restoration, Point spread functions, Data corrections, Luminescence, Expectation maximization algorithms, Laser systems engineering, Microscopy
The image reconstruction method of maximum likelihood estimation (MLE) has been used in the authors' previous work for fluorescence microscopy. By computer simulations, it was previously found that this method worked very well for addressing two dimensional superresolution and three dimensional optical sectioning problems. In this paper, the results of 3D reconstructions with real data will be presented.
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