R. E. Carson, Y. Yan, B. Chodkowski, T. K. Yap, and M. E. Daube-Witherspoon, \Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Trans. on Medical Imaging, vol. 13, no. 3, pp. 526-537, September 1994.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....to reduce variance of the ordinary least squares estimator. The quantitative study of estimator bias and variance has been useful for characterizing statistical performance for many statistical signal processing applications including: tomographic reconstruction [7] 8] 9] functional imaging [10], non linear and morphological ltering [11] 12] and spectral estimation of time series [13] 14] However, the plane parameterized by the bias and variance b and 2 is not useful for studying fundamental tradeo s since an estimator can always be found which makes both the bias and ....

R. E. Carson, Y. Yan, B. Chodkowski, T. K. Yap, and M. E. Daube-Witherspoon, \Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Trans. on Medical Imaging, vol. 13, no. 3, pp. 526-537, September 1994.

....response if we could avoid performing extensive numerical simulations. The remainder of this paper is devoted to approximations suitable for likelihood based estimators in tomography. C. Linearized Local Impulse Response In the context of emission tomography, several investigators have observed [13,14,36,37] that the ensemble mean of a likelihood based estimator is approximately equal to the value that one obtains by applying the estimator to noiseless data: E [ Y ) Y ( 4 = 7) Here Y ( E [Y ] Z yf(y; dy (8) denotes the mean of the measurement vector, ....

R. E. Carson, Y. Yan, B. Chodkowski, T. K. Yap, and M. E. Daube-Witherspoon, "Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Tr. Med. Im., vol. 13, no. 3, pp. 526--537, Sept. 1994.

....= 13) This approximation is simply the value produced by applying the estimator (1) to noise free data. This approach requires minimal computation, and works surprisingly well for penalized likelihood objectives. It has been used extensively by investigators in emission tomography [14] 15] [20]. Apparently, the principal source of bias in penalizedlikelihood estimators is the regularizing penalty that one includes in Phi, so (13) allows one to examine the effects of the penalty separately from the effects of noise. However, the approximation (13) is certainly not always adequate, as ....

....with more than 1M counts, the difference was smaller than 1 . Note the asymptotic property: better agreement between simulations and predictions for higher SNR. Many authors have reported that the 0th order mean approximation (13) is reasonably accurate for maximumlikelihood estimators [14] 15] [20]; we have found similar results for penalized likelihood estimators such as (25) This is fortuitous since the 2nd order expressions for mean are considerably more expensive to compute since p = 128 Delta 64 and N = 192 Delta 96 are very large in this example. Figure 3 displays a ....

R. E. Carson, Y. Yan, B. Chodkowski, T. K. Yap, and M. E. Daube-Witherspoon, "Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Tr. Med. Im., vol. 13, no. 3, pp. 526--537, Sept. 1994.

....variant blur in the sinogram space. While spatially variant sinogram blurring models have been considered previously [6] 7] these models were used for sinogram restoration in conjunction with filtered backprojection rather than as part of a statistical reconstruction method. Carson et al. [1] model these blurring effects in a similar manner to that described here, except that they restrict blurring to the radial direction in the sinogram and apparently do not model the depth dependent geometric sensitivities. Our purpose in this paper is to develop the factored matrix representation ....

R.E. Carson, Y. Yan, B.A. Chodkowski, T.K. Yap, and M.E. Daube-Witherspoon. Precision and accuracy of regional radioactivity quantitation using the maxmum likelihood EM reconstruction algorithm. IEEE Transactions on Medical Imaging, 13(3):526--537, September 1994.

....to reduce variance of the ordinary least squares estimator. The quantitative study of estimator bias and variance has been useful for characterizing statistical performance for many statistical signal processing applications including: tomographic reconstruction [7] 8] 9] functional imaging [10], non linear and morphological filtering [11] 12] and spectral estimation of time series [13] 14] However, the plane parameterized by the bias and variance b and oe 2 is not useful for studying fundamental tradeoffs since an estimator can always be found which makes both the bias and ....

R. E. Carson, Y. Yan, B. Chodkowski, T. K. Yap, and M. E. Daube-Witherspoon, "Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Trans. on Medical Imaging, vol. 13, no. 3, pp. 526--537, September 1994.

....response if we could avoid performing extensive numerical simulations. The remainder of this paper is devoted to approximations suitable for likelihood based estimators in tomography. C. Linearized Local Impulse Response In the context of emission tomography, several investigators have observed [13, 14, 37, 38] that the ensemble mean IEEE TRANSACTIONS ON IMAGE PROCESSING, EDICS 2.3, TO APPEAR. VERSION January 23, 1996 4 of a likelihood based estimator is approximately equal to the value that one obtains by applying the estimator to noiseless data: E [ Y ) Y ( 4 = 7) ....

R. E. Carson, Y. Yan, B. Chodkowski, T. K. Yap, and M. E. Daube-Witherspoon, "Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Tr. Med. Im., vol. 13, no. 3, pp. 526--537, Sept. 1994.

....the CRC approximation. Three points of interest were selected as shown in Fig. 4(b) Since several investigators have observed that the ensemble mean of ML and MAP estimators are approximately equal to the reconstruction that is obtained by applying the estimator to the expectation of the data [2, 4, 5, 9, 37], we measured the CRC from reconstructions of two noiseless data sets: i) the original phantom sinogram, and (ii) the sinogram of the phantom after perturbation of a single voxel. Fig. 5 shows a comparison of the measured and theoretically predicted CRCs for each point of interest. The ....

R. Carson, Y. Yan, B. Chodkowski, T. Yap, and M. DaubeWitherspoon, "Precision and accuracy of regional radioactivity quantitation using the maximum likelihood EM reconstruction algorithm," IEEE Transactions on Medical Imaging, vol. 13, no. 3, pp. 526--537, Sept. 1994.

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