Advances in Imaging and Electron Physics, Vol. 145 by Peter W. Hawkes

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

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Pj i+1 · Pjj Pj i 40 ASIF The Cholesky factorization of A = U T U results in the Cholesky factor U , that is an upper triangular matrix. To indicate that the matrix U is the upper triangular Cholesky factor of A, we work often with the notation U = chol(A). 1 shows that the Cholesky factor of the L-block banded matrix A has exactly L nonzero block diagonals above the main diagonal. 1. A positive definite and symmetric matrix A = U T U is L-block banded if and only if (iff) the constituent blocks Uij in its upper triangular Cholesky factor U are Uij = 0 for (j − i) > L, 1 (J − L).

I+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. The steady-state values of the Kalman gain and filter covariance matrix are denoted by K and P (f ) .

Conditional replenishment leads to considerable reduction in the number of code vectors transmitted. Although not implemented in our codec, conditional replenishment can be coupled with motion compensation schemes to provide better tradeoffs between video quality and compression ratio than conditional replenishment alone. Part III (Decoder) of Figure 5 represents the SNP/VQR decoder, which ∗ } by inverting reconstructs the video sequence from the VQ blocks {v1∗ , . . , vN the steps of the encoder (part I of Figure 5) in the reverse order.

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