Abstract
Image reconstruction is a key component in many medical imaging modalities. The problem of image reconstruction can be viewed as a special inverse problem where the unknown image pixel intensities are estimated from the observed measurements. Since the measurements are usually noise contaminated, statistical reconstruction methods are preferred. In this paper we review some non-negatively constrained simultaneous iterative algorithms for maximum penalized likelihood reconstructions, where all measurements are used to estimate all pixel intensities in each iteration.
Highlights
Image reconstruction in medical imaging, in general, considers estimating pixel intensities or attenuations from measurements obtained from an imaging system
Emission and transmission tomography and X-ray CT all fall into this category
In this paper we present and discuss several important simultaneous maximum penalized likelihood (MPL) reconstruction algorithms, where the non-negativity constraint is enforced
Summary
Image reconstruction in medical imaging, in general, considers estimating pixel intensities or attenuations from measurements obtained from an imaging system. When wi = μi we have the weighted least squares model as suggested in [11] Another example in emission (or transmission) tomography is the randoms-precorrected PET scan (assume no scattering to simplify). In this context, the observed measurements are yi = yiPrompt − yiDelay , where yiPrompt and yiDelay (both unavailable directly) denotes the number of coincidences of the prompt and delayed windows respectively. Note that the shifted Poisson approximation matches the first two moments with the true probability model for yi + 2ri when both the prompt and delayed measurements are assumed independent and follow Poisson distributions. In this paper we focus on explaining and summarizing different non-negatively constrained tomographic imaging algorithms. Numerical comparisons of some of these algorithms are available in [26], and will not be given in this paper
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