T. Hebert and S. Gopal, "The GEM MAP algorithm with 3-D SPECT system response," IEEE Trans. on Medical Imaging 11, 81--90 (1992).  Home/Search   Document Not in Database   Summary   Related Articles   Check

....problem which can be solved using a number of different techniques. The expectation maximization (EM) algorithm, suitable for ML reconstruction [23] has been adopted for MAP estimation with Gaussian priors [24, 25, 26, 27] Extensions of these models to more general MRF priors were proposed in [14, 28, 15, 29]. However, application of the EM algorithm for MAP estimation is difficult and usually suffers from slow convergence. Instead of using EM techniques, we focus on the direct optimization of the MAP equation. We adopt a pixel wise update method known as iterative coordinate descent (ICD) 16, 30] ....

T. Hebert and S. Gopal, "The GEM MAP algorithm with 3-D SPECT system response," IEEE Trans. on Medical Imaging 11, 81--90 (1992).

....Herman, De Pierro, and Gai [8] have modified the EM approach to include Bayesian estimation. A variety of methods have also been proposed for adapting the EM algorithm 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 ....

....to implement or understand in the ML case, it is not directly and simply applicable to MAP estimation when the complete data is taken to be the number of photons emitted from each pixel. This is because there is no closed form solution for the maximization step of the iteration. Hebert and Leahy[9, 10] have developed the GEM algorithm to cope with these e#ects. The GEM algorithm takes the form of coordinate gradient ascent of the MAP EM cost functional with a heuristic step size which can be adjusted to guarantee convergence. De Pierro s majorization method for MAP reconstruction is also ....

T. Hebert and S. Gopal, "The GEM MAP Algorithm with 3-D SPECT System Response," IEEE Trans. Med. Im., vol. 11, no. 1, pp. 81-90, March 1992.

....than filtered backprojection. In particular, the incorporation of the spatially varying or spatially invariant point response reduces noise at resolutions comparable to single pixel 5 ML EM (or filtered backprojection) and offers improved resolution with increased noise at further iterations [5, 44, 45, 46, 47, 48]. 2.7 Summary This background chapter described the nature of some of the most significant artifacts in SPECT imaging attenuation and point response. Building on this background, we will show that the location and type of attenuation artifact depends on the relative 5 Single pixel means ....

....projector using cubic interpolation. A comparison of interpolators for rotation based projectors is given in Section 6.3. One set of projections, referred to as the unblurred projections, were generated with the system point response modeled as a delta function (also termed a single pixel kernel [46]) The second set of projections included the effects of the Gaussian point response model obtained with measurements from the GE camera. The same procedure was repeated using a 0.32mm Gamma1 sampling rate (64 views of 128 bins each equi spaced over 180 degrees) for 17 Gaussians with fwhm ....

T. J. Hebert and S. S. Gopal, "The GEM MAP algorithm with 3-D SPECT system response," IEEE Trans. Med. Imaging, vol. 11, no. 1, pp. 81--90, 1992.

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