By Peter W. Hawkes

ISBN-10: 0123739071

ISBN-13: 9780123739070

Advances in Imaging and Electron Physics merges long-running serials-Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The sequence gains prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photo technological know-how and electronic photo processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in a majority of these domain names.

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**Extra info for Advances in Imaging and Electron Physics, Vol. 145**

**Example text**

The simplified model is referred to as sub-block SNP/VQR and is considered next. C. Sub-Block SNP/VQR To derive the sub-block SNP/VQR, we expand Eqs. (40) and (41) at the sub-block level with L(k) and F (k) approximated by the M-block banded approximations given in (67) and (68). Below we present the resulting expressions for M1 = M2 = 3. Frame (k = 1): ∀(1 ℓ1 NI ), ℓ1 (1) τ =max(1,ℓ1 −3) Frame (2 k NK ): min(ℓ1 +3,NI ) τ =ℓ1 ∀(1 ℓ1 (1) Lℓ1 τ Xτ(1) = vℓ1 . (69) NI ), ℓ1 (k) Fℓ1 τ Xτ(k−1) + (k) τ =max(1,ℓ1 −3) (k) Lℓ1 τ Xτ(k) = vℓ1 .

1995). The forward sweep recursively computes the predictor estimate (Ψi+1|i ) and the filter estimate (Ψi+1|i+1 ) using the KBF: (a) Predictor update. Ψi+1|i = Γ Ψi|i with Ψ1|0 = 0. (57) (b) Filter update. Ψi+1|i+1 = Ψi+1|i + K(Zi+1 − GΨi+1|i ), (58) for 1 i (NI − 1). It may be noted that the Kalman gain K and the filter covariance matrix Pi+1|i+1 can be expressed in terms of the steady-state value of the predictor covariance matrix using Eqs. (55) and (56) with Pi+1|i = P (p) . Both Kalman gain Ki and the filter covariance matrix Pi+1|i+1 converge and do not need any further updating during the KBF iterations.

1979; Bini and Meini, 1999; Yagle, 2001; Corral, 2002) impose some kind of structure on P . , 1979; Bini and Meini, 1999; Yagle, 2001) assume P to be Toeplitz. Unlike existing approaches for matrix inversion, the algorithms presented in this section do not impose any additional constraint on the structure of P ; in particular, the algorithms in this section do not require P to be Toeplitz. Exploiting the earlier results for GMRFs, we show that the matrix P , whose inverse A is an L-block banded matrix, is completely defined by the blocks within its Lblock band.