J A Fessler and A O Hero, "Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction", Tech. Rep. 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, 48109-2122, Feb. 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....to more general Markov random field priors. These methods include the Generalized EM (GEM) algorithm proposed by Hebert and Leahy[9, 10] the one step late (OSL) method proposed by Green[11] and a more general form of De Pierro s method[12] Most recently, Fessler and Hero have proposed SAGE [13], a collection of methods designed to minimize the complete data with each pixel update in EM reconstruction. For the transmission problem, the EM methods are more di#cult to apply because there is not such an obvious choice for the complete data space[14] Ollinger used the EM approach to solve ....

J. A. Fessler and A. O. Hero, "Space-Alternating Generalized EM Algorithm for Penalized Maximum-Likelihood Reconstruction," University of Michigan, Technical Report No. 286, Feb. 1994.

....shown convergence for a linesearch modification of OSL [32] and Mumcuoglu et al. have adapted the conjugate gradient method [42] We show in Section VI that an intrinsically monotonic SAGE algorithm converges faster than even a line search accelerated EM algorithm. This paper is condensed from [43], in which we compare SAGE to many alternative algorithms and show that the convergence rate of SAGE is comparable to even fast nonmonotonic methods such as [40,41] Just as one can force a nonmonotonic algorithm to be monotonic by adding a line search, one can also often accelerate monotonic ....

....a line search, one can also often accelerate monotonic methods by over relaxation. Thus, for meaningful comparisons, one should first decide whether or not monotonicity is required. In this paper, we focus solely on monotonic (intrinsic or forced) algorithms. Additional comparisons can be found in [43]. The organization of this paper is as follows. Section II describes the general structure of the SAGE method. Section III introduces new complete data spaces and hidden data spaces for Poisson data, and gives several algorithms for unpenalized maximum likelihood. Section IV presents PML ....

[Article contains additional citation context not shown here]

J A Fessler and A O Hero, "Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction", Tech. Rep. 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, 48109-2122, Feb. 1994.

No context found.

J A Fessler and A O Hero. Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction. Technical Report 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor,

....small changes in data results in big changes in the reconstruction. Some form of regularization is required. Methods to regularize the ML problem are: stopping the iterations before convergence [118] post smoothing the image [104] and adding a roughness 35 penalty term to the log likelihood [43]. The final methods are called penalized likelihood (PL) methods. They can also be viewed as maximum a posteriori probability (MAP) estimation with a Gauss Markov (or Gibbs) prior [53] where the log prior corresponds to the penalty function. 3.2 Penalized Likelihood PL methods have some distinct ....

J. A. Fessler and A. O. Hero, "Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction," Technical Report 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, 48109-2122, February 1994.

.... thus one needs to include a line search [60] Although conjugate gradient methods have rapid convergence for quadratic optimization, usually one needs some form of preconditioner and enforcing non negativity of the solution is possible but di#cult [68] Space alternating generalized EM (SAGE) [40 42] is a generalized EM type algorithm which updates parameters sequentially by alternating between small hidden data spaces [41] As SAGE uses separate hidden data spaces for each parameter, not only the maximization is simplified but convergence rate is also improved compared to EM. SAGE was shown ....

....sequentially by alternating between small hidden data spaces [41] As SAGE uses separate hidden data spaces for each parameter, not only the maximization is simplified but convergence rate is also improved compared to EM. SAGE was shown to converge faster than many other monotonic algorithms [40] due to its sequential nature. Moreover, sequential updates of SAGE can handle non negativity constraints easily. The recently developed paraboloid surrogates algorithm of Fessler and Erdogan [28,38] which uses optimum curvatures for the parabolic surrogate functions at each iteration, was shown ....

[Article contains additional citation context not shown here]

J. A. Fessler and A. O. Hero, "Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction," Technical Report 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, 48109-2122, February 1994.

....i.e. j Phi( 0; j 0 j Phi( 0; j = 0 ; and if Phi is strictly concave in a neighborhood of , then is a fixed point of (7) and using continuity one can prove local convergence of the iteration (7) to . For reasons of convergence rate [25,26,27], we usually use = 0:6. This under relaxation improves the odds that (7) will yield an increase in Phi. With = 0:6 we have never observed a decrease in Phi over a full iteration, although we have observed small decreases with = 1. Fortuitously, using 1 not only improves the convergence ....

J. A. Fessler and A. O. Hero. Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction. Technical Report 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, 48109-2122, Feb. 1994.

....shown convergence for a line search modification of OSL [32] and Mumcuoglu et al. have adapted the conjugate gradient method [42] We show in Section VI that an intrinsically monotonic SAGE algorithm converges faster than even a line search accelerated EM algorithm. This paper is condensed from [43], in which we compare SAGE to many alternative algorithms and show that the convergence rate of SAGE is comparable to even fast nonmonotonic methods such as [40,41] Just as one can force a nonmonotonic algorithm to be monotonic by adding a line search, one can also often accelerate monotonic ....

....a line search, one can also often accelerate monotonic methods by over relaxation. Thus, for meaningful comparisons, one should first decide whether or not monotonicity is required. In this paper, we focus solely on monotonic (intrinsic or forced) algorithms. Additional comparisons can be found in [43]. The organization of this paper is as follows. Section II describes the general structure of the SAGE method. Section III introduces new complete data spaces and hiddendata spaces for Poisson data, and gives several algorithms for unpenalized maximum likelihood. Section IV presents PML ....

[Article contains additional citation context not shown here]

J A Fessler and A O Hero, "Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction ", Tech. Rep. 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, 48109-2122, Feb. 1994.

.... the effect caused by the mismatch while keeping the benefit of high resolution MRI anatomical information[1] A joint Penalized Maximum Likelihood (JPML) objective function, is used with an joint Space Alternating Generalized Expectation Maximization algorithm (JSAGE) derived upon on SAGE algorithm[5] for SPECT reconstruction. The objective function incorporates statistical distributions of both SPECT acquisition and MRI region measurement, so that the SPECT pixel intensity and functional region are jointly estimated from both SPECT and MRI data. In [1] our computer simulation results showed ....

....domination of mismatched labels extracted from MRI over the SPECT reconstruction. To favor region contiguity prior, we choose U 2 as: U 2 (l) p X k=1 X j2Nk kj (l) 6) where kj is the same as defined in equation (5) B. Reconstruction Algorithm We apply an iterative SAGE algorithm[5], with slight modification for our JPML objective, because it converges fast and ensures a monotonic increase in objective function. To maximize the function Phi joint ( l) with SAGE, the conditional expectation of the likelihood the SAGE algorithm can be straightforwardly modified to jointly ....

J.A. Fessler and A.O. Hero, "Space-Alternating Generalized EM Algorithms for Penalized Maximum-Likelihood Image Reconstruction", Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor, MI, Tech. Rep. 286, Feb. 1994.

No context found.

J A Fessler and A O Hero. Space-alternating generalized EM algorithms for penalized maximum-likelihood image reconstruction. Technical Report 286, Comm. and Sign. Proc. Lab., Dept. of EECS, Univ. of Michigan, Ann Arbor,

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