Ordered subsets algorithms for transmission tomography

Abstract

The ordered subsets EM (OSEM) algorithm has enjoyed considerable interest for emission image reconstruction due to its acceleration of the original EM algorithm and ease of programming. The transmission EM reconstruction algorithm converges very slowly and is not used in practice. In this paper, we introduce a simultaneous update algorithm called separable paraboloidal surrogates (SPS) that converges much faster than the transmission EM algorithm. Furthermore, unlike the 'convex algorithm' for transmission tomography, the proposed algorithm is monotonic even with nonzero background counts. We demonstrate that the ordered subsets principle can also be applied to the new SPS algorithm for transmission tomography to accelerate 'convergence', albeit with similar sacrifice of global convergence properties as for OSEM. We implemented and evaluated this ordered subsets transmission (OSTR) algorithm. The results indicate that the OSTR algorithm speeds up the increase in the objective function by roughly the number of subsets in the early iterates when compared to the ordinary SPS algorithm. We compute mean square errors and segmentation errors for different methods and show that OSTR is superior to OSEM applied to the logarithm of the transmission data. However, penalized-likelihood reconstructions yield the best quality images among all other methods tested.

Nonconvex regularizations in fluorescence molecular tomography for sparsity enhancement

“…MM algorithms-also known as optimization transfer algorithms and its special case, the separable quadratic surrogates (SQS) algorithm (Erdogan & Fessler 1999), has the desired advantages including avoiding matrix inversions, linearizing an optimization problem, dealing gracefully with inequalities, etc. (Hunter & Lange 2004).…”

“…For example, one may add a nonnegative term to obtain the surrogate function (Prakash et al 2014). In the following, we first follow the SQS routine (Erdogan & Fessler 1999) to majorize the least squares fitting term:…”

Performance evaluation of MAP algorithms with different penalties, object geometries and noise levels

“…Optimization Algorithms 1) Relaxed SPS: Instead of considering the true objective function, the optimization can be transferred to separable paraboloidal surrogates (SPS). Ahn [2] introduced a modification of the original SPS algorithm [3] using relaxation to be able to cope with subsets. This "relaxed SPS" version uses a precomputed denominator related to the Hessian.…”

“…The aim of this study is to propose a new algorithm LBFGS-B-PC which combines preconditioning (PC) with the use of a quasi-Newton optimization algorithm (LBFGS-B [4]). Its performance is evaluated and compared with relaxed SPS [3] and LBFGS-B.…”

Pixel-based subsets for rapid multi-pinhole SPECT reconstruction

“…tomography (PET) images (Hutton et al 1997, Leahy and Byrne 2000, Leahy and Qi 2000, Beekman et al 2002, Qi and Leahy 2006, while they also receive strong interest for reconstruction of x-ray computed tomography (CT) images (Manglos et al 1995, Nuyts et al 1998, Erdogan and Fessler 1999, Beekman and Kamphuis 2001, De Man et al 2001, Kole and Beekman 2005, Zbijewski and Beekman 2006. Compared to analytic methods of reconstruction, iterative methods have been shown to be more robust to statistical noise and allow better modeling of the physical detection process, which can be used to correct for several image-degrading effects.…”