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A novel weighted least squares PET image reconstruction method using adaptive variable index sets

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Abstract

In this paper, we present a novel image reconstruction method based on weighted least squares (WLS) objective function for positron emission tomography (PET). Unlike a usual WLS algorithm, the proposed method, which we call it SA-WLS, combines the SAGE algorithm with WLS algorithm. It minimized the WLS objective function using single coordinate descent (SCD) method in a sequence of small “hidden” data spaces (HDS). Although SA-WLS used a strategy to update parameter sequentially just like common SCD method, the use of these small HDS makes it converge much faster and produce the reconstructed images with greater contrast and detail than the usual WLS method. In order to decrease further the actual CPU time per iteration, the adaptive variable index sets were introduced to modify SA-WLS (MSA-WLS). Instead of optimizing each pixel, this MSA-WLS method sequentially optimizes many pixels located in an index set at one time. The index sets were automatically modified during each iteration step. MSA-WLS gathers the virtue of simultaneously and sequentially updating the parameters so that it achieves a good compromise between the convergence rate and the computational cost in PET reconstruction problem. Details of these algorithms were presented and the performances were evaluated by a simulated head phantom.

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... The corresponding estimation is called the penalized WLS estimation (PWLS). Many investigators approach the PWLS estimate using iterative algorithms, which include, for example, the expectation-maximization (EM) algorithm [2][3], the gradient-based algorithm [4]–[8] and the coordinate-descent based algorithm [1][9]–[11] (the latter two are similar to some extent). All of them start with an initial guess and then perform image updating iteratively until reaching some specified stopping criterions. ...
... The coordinate-descent algorithm usually offers more convergent rate than the EM or gradient-based algorithms. However, as pointed out in [3][11], this is likely at the cost of computational time. ...
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... Other ML-algorithms have also been utilized. These are, for example, ordered subsets separable surrogates (OSSPS) [165], paraboloidal surrogates coordinate ascent [166], several different weighted least-squares (WLS) methods [167][168][169][170], coordinate-ascent algorithms [171,172] and conjugate-gradient (CG) algorithms [161,173,174]. ...
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... In WLS, the Coordinate Descent (CD) algorithm is one of the recommended methods. Using a WLS approach to reconstruct PET images was to account for errors due to accidental coincidences and detector inefficiency (Zhu et al., 2004;Zhu et al., 2006). Recent challenges in PET image reconstruction include additional exact quantitation, TOF imaging, system modelling, motion rectification and dynamic reconstruction. ...
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  • Riddell