By Peter W. Hawkes

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 good points prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, snapshot technology and electronic snapshot processing, electromagnetic wave propagation, electron microscopy, and the computing equipment utilized in these types of domain names.

**Read or Download Advances in Imaging and Electron Physics, Vol. 145 PDF**

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

**Example text**

Summary This section presented a practical implementation of the RTS filter based on a noncausal GMRF state model for restoration of a blurred image corrupted by additive noise. We exploit the shift-invariant characteristics of the state matrices in the noncausal GMRP predictive model and use the steady-state solution of the Riccati equation in the RTS filter. The resulting implementation is computationally practical and faster than the competing algorithms. The experimental results outperform the Wiener filter and illustrate the superiority of the noncausal GMRP prediction model used in the RTS filter over a causal prediction model.

The input pixel is replaced by a spatial average of its neighborhood pixels. A (3 × 3) window around the reference pixel X(i, j ) is used as the neighborhood for the spatial averaging filter, which is defined as 1 Xs (i, j ) = 9 1 1 ℓ1 =−1 ℓ2 =−1 z(i + ℓ1 , j + ℓ2 ). (63) 20 ASIF F IGURE 3. 54). (c) RTS with causal prediction. This resembles the RTS algorithm described except for the prediction model, which is one-sided (causal) and is given by x(i, ˆ j ) = βdc x(i − 1, j − 1) + βvc x(i − 1, j ) + βhc x(i, j − 1), (64) where βdc , βvc , and βhc are the diagonal, vertical, and horizontal field interactions of a third-order Markov mesh.

The following corollary simplifies Theorem 3 for matrices with tridiagonal matrix inverses. 1. Given the main and the first upper block diagonal entries {Pii , Pii+1 } of P with a tridiagonal (L = 1) block banded inverse A, any insignificant upper triangular block entry of P can be computed from its significant blocks from the following expression: ∀i, j, 1 i j −2 Pij = J, (i + 2) J: j −1 Pℓ+1ℓ Pℓ+1ℓ+1 T ℓ=i Pj −1j . 1, the following notation is used: J (Aℓ ) = A1 A2 · · · AJ . (95) ℓ=1 Note that in Eq.