In this thesis, first of all, we introduce some background information about the NMF and nuclear medicine. There are many algorithms to solve practical problems, such as PCA, ICA, SVD, VQ, etc. However, these methods cannot make sure that the result of the matrix factorization is non-negative, even the input matrix is positive.
In math, negative values are acceptable, but normally negative values are meaningless in our real life. For example, it is impossible that image data has a negative pixel value. NMF provides a method that the factorization result is non-negative. Because of this, it is used widely to solve many practical problems, such as nuclear imaging. Nuclear imaging is a branch of the nuclear medicine and has been widely used for medical diagnosis. There are many kinds of nuclear imaging, like XCT, PET, NMR, SPECT and so on. The basic theory of these technologies is the same: it utilizes the law of the attenuation or distribution of the nuclear radiation, obtaining the information of the interior of the measured object, and then reconstructs the image with computers. The information acquisition of these technologies, including the physical principle and measurements they rely on, may different, but their data processing techniques are based on the computer information processing and image reconstruction technology.
In nuclear imaging, NMF, which is also called “factor analysis”, is the main way for
the image reconstruction. SPECT is a popular technique for nuclear imaging. There
are two kinds of SPECT: static and dynamic. In both cases, the patient is injected the
tracer (radioisotope). The only difference is the acquisition time. For the static case,
the system will wait until the tracer distribution being stable, while for the dynamic
case the system will collect the data after the injection immediately. We expound the
mathematical models and some reconstruction algorithms of the static and dynamic SPECT. The main problem of the reconstruction is to solve g = Af, but directly using the inverse of A to solve this is not a good choice. One of the common ways is MLEM.
MLEM is based on an assumption that the detected sinogram g follows the Poisson distribution and then using the properties of the Poisson distribution to estimate the imaged volume. MAPEM is very similar to MLEM. MAPEM introduces a prior knowledge to be a constraint so that the estimation will not become worse during the reconstruction process. Specially, in dynamic case, f is a 4D volume (3D plus time) which is hard to reconstruct directly. Therefore, NMF is used to decompose f into two smaller matrices: the expanded coefficients and the time-based functions or factors.
Normally, FADS is used for the dynamic reconstruction of SPECT. The challenge of FADS is the high sensitivity of the initial choice. SIFADS is a way to solve this.
It uses spline-based algorithm to estimate a better initial choice and then runs FADS.
CIFA is another way using clustering methods for the initial choice.
This thesis tried to implement some other ways to optimize the result when using FADS. In medical imaging, we want to focus on the tissues. So we emphasized those voxels within the tissues. Another reason for doing this is that we may use clustering methods for the tissues to distinguish the lesions from a certain tissue. The problem for that is errors may transfer from the coefficients to the factors. Therefore, we attempted to use the blurry mask and the factor orthogonalization function to reduce the errors. In all the experiment results, the coefficients of blood are not very good.
There are some other voxels with large values around the blood. However, since the
blood is everywhere inside the human body, this might not be a problem.
For further work, we would like to develop an automatic way (machine learning) to the data preparation. For example, our segmentation (static mask) is created manually. It is a challenge because people who do the segmentation need to know some knowledge both of the anatomy and computer science. Also, it is hard to make sure the boundary of the tissues, especially for the blood and myocardium. We want to achieve an algorithm that can produce an accurate static mask automatically.
Secondly, we want to improve the running time of the reconstruction. The
ordered-subsets expectation maximization (OSEM) is a variant of MLEM which can
accelerate the reconstruction process [34]. Using HPC is another way to speed up the
processing time [35]. Some parallel techniques such as OpenMP, MPI, and CUDA
may also speedup the running time [36][37]. Combining these two methods may
have a better performance.
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In document
Studies with Dynamic Nuclear Imaging Image Reconstruction Algorithm. Haoran Chang
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