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. This sequence gains prolonged articles at the physics of electron units (especially semiconductor devices), particle optics at low and high energies, microlithography, photograph technological know-how and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kinds of domain names.

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

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I (80) Since the Cholesky factor U is an upper triangular matrix, its inverse U −1 is also an upper triangular matrix with the following structure: ⎡ U −1 −1 U11 ⎢ 0 ⎢ ⎢ 0 ⎢ =⎢ ⎢ · ⎢ ⎣ 0 0 ∗ −1 U22 0 · · · ∗ ∗ −1 U33 .. ∗ ∗ ∗ .. · · 0 0 · · · · UI−1 −1I −1 0 ∗ ∗ ∗ ⎤ ⎥ ⎥ ⎥ ⎥ ⎥, · ⎥ ⎥ ∗ ⎦ UI−1 I (81) where the lower diagonal entries in U −1 are all zero blocks 0. More importantly, the main diagonal entries in U −1 are block inverses of the corresponding blocks in U . These features are used next to derive three important theorems for L-block banded matrices where we show how to obtain: 1.

The state matrices Γi and Πi are variant matrices and vary from one row i to another. Once the 2D regressors {Lii , Lii−1 } reach the steady-state values {Lii∞ , Lii−1∞ } after a few rows, these matrices become invariant with respect to the rows. In the following algorithm, we assume steady-state condition such that the state matrices {Γi , Πi } reach the invariant values {Γ, Π }. The state and observation noise are assumed to be white and Gaussian, given by Vi ∼ N(0, Σw = σw2 I ) and Ξi ∼ N(0, Σr = σr2 I ), where N denotes the Gaussian distribution with its mean and covariance matrix shown within the brackets.

The same lookup table is also constructed at the decoder. The online computations of the 3D forward regressor blocks are avoided with this approach but at the expense of an additional approximation as the field interactions are quantized to the values included in the lookup table. 263. The most time-consuming operation in the standardized codecs is the block-based motion estimation, which has a computational complexity of O(NI NJ (2R + 1)2 ) per frame for an (NI × NJ ) frame with the search range of ±R pixels.