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, picture technology and electronic picture processing, electromagnetic wave propagation, electron microscopy, and the computing tools utilized in these kind of domain names.

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

**Example text**

In contrast, the 2D forward representation [Eqs. (24)–(26)] whitens a row i of the image field per iteration. Consequently, the 3D forward regressors L(k) s and F (k) s for the video sequence have dimensions of (NI NJ × NI NJ ) in comparison to the 2D forward regressors Lii s and Li−1i s for the image field, which are of order NJ . Extending the 2D Riccati equations [Eqs. (27) and (28)], the expressions for the 3D forward regressors are given by S (k) S (NK ) = A1 , = A1 − A2 S (k+1) −1 for (k = NK ), A2 , (42) for (NK − 1) k 1 , (43) where (L(k) )T L(k) = S (k) and F (k) = (L(k) )−T A2 .

Respective convergences were observed within p < 15 and m < 20 iterations, implying a computational savings of O(104 ) over the bilateral model [Eq. (37)]. 4. By using the sub-block SNP/VQR [Eqs. (69) and (70)], the number of computations required to generate the 3D error field is significantly reduced from that required in the block SNP/VQR [Eqs. (40) and (41)]. In the (k) (k) reduced model, sub-blocks Lℓ1 ℓ2 and Fℓ1 ℓ2 are of dimensions (NJ × NJ ). For a three-block banded approximation, the total number of floating point operations (flops) required to generate the error field v(i, j, k) with the subblock SNP/VQR is given by 8NI NJ2 for one frame k.

Pi+Li+L 0 UT i,i+L ⎤ ⎡ U T ⎤ ⎡ −1 ⎤ PiJ Uii ii T ⎥ ⎢ 0 ⎥ U Pi+1,J ⎥ ⎢ i,i+1 ⎥ ⎥⎢ ⎥ =⎢ .. ⎥ ⎦⎢ ⎣ ... ⎦ , ⎣ · . ⎦ T 0 PJ J Ui,J (83) .. UJTJ UJ J = PJ−1 J. (84) Theorem 1 shows how the blocks {Uij } of the Cholesky factor U are determined from the blocks {Pij } of the L-banded P . Equations (82) and (83) show that the Cholesky blocks {Uii · · · Ui,i+L } on block row i of U , 1 i (J − L), involve only the (L + 1)2 blocks in the principal submatrix P (i : i + L, i : i + L) that are in the neighborhood of these Cholesky blocks {Uii , .