J. Fessler, "Mean and variance of implicitely defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Transactions on Image Processing, vol. 5, pp. 493--506, 1996.  Home/Search Document Not in Database Summary Related Articles Check |
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Scatter Correction for Positron Emission Mammography - Jinyi Qi And (2001) (Correct)
.... s are independent, we first focus on noise from s and assume y noisefree (i.e. y = y = Px s) We can approximate x(y, s) using a first order Taylor series expansion at the point s = s: x(y, s) # x(y, s) # s x(y, s) s s) 5) This approximation is similar to that presented in [6]. From (5) we have the following expression for the covariance of noise in the reconstruction caused by the noise in the estimated scatter sinogram #( x) ## s x(y, s)#( s) # s x(y, s) # (6) where #( s) is the covariance matrix of the estimated scatter sinogram. To compute # s x(y, s) ....
....expression for the covariance of noise in the reconstruction caused by the noise in the estimated scatter sinogram #( x) ## s x(y, s)#( s) # s x(y, s) # (6) where #( s) is the covariance matrix of the estimated scatter sinogram. To compute # s x(y, s) we follow the idea presented in [6]. We restrict our attention to the situations where the solution of (3) satisfies 0= # #x j [L(y x, s) #U(x) # # # x= x(y,s) j=1, M. 7) While this assumption precludes inequality constraints, it should work fine here because of the uniform background. Differentiating (7) with ....
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J. Fessler, "Mean and variance of implicitely defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Transactions on Image Processing, vol. 5, pp. 493--506, 1996.
A Theoretical Study of the Contrast Recovery and Variance of MAP .. - Qi, Leahy (1999) (4 citations) (Correct)
....large numbers of iterations is time consuming. These methods also require explicit update equations, so that they are inapplicable to numerical optimization methods such as gradient or coordinate wise ascent which involve line searches. An alternative approach was proposed by Fessler and Rogers [9, 10] who analyzed the mean, variance, and spatial resolution at a fixed point of the objective function. The resolution and noise properties are computed at the fixed point using partial derivatives and truncated Taylor series approximations. These results are independent of the particular optimizing ....
....can be pre solved [11] Here, we analyze the resolution and variance properties of MAP reconstruction methods. Because several fast convergent algorithms have been developed for MAP reconstruction [12, 13, 14] and penalized weighted least squares [15, 16, 17] we have adopted the approach in [9, 10] and investigate the properties of the MAP estimator at a fixed point of the objective function rather than as a function of iteration. The resolution is characterized by the local impulse response contrast recovery coefficient (CRC) We derive simplified approximate equations for local impulse ....
[Article contains additional citation context not shown here]
J. Fessler, "Mean and variance of implicitely defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Transactions on Image Processing, vol. 5, no. 3, pp. 493--506, March 1996.
Fast computation of the covariance of MAP reconstructions of PET .. - Qi, Leahy (Correct)
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J. Fessler, "Mean and variance of implicitely defined biased estimators (such as penalized maximum likelihood): Applications to tomography," IEEE Transactions on Image Processing, vol. 5, no. 3, pp. 493--506, March 1996.
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