ADAPTIVE MODELING FOR BIT RATE CONTROL

High-Efficiency Video Coding (HEVC) is the latest video coding standard developed by the Joint Collaborative Team on Video Coding (JCT-VC). An effective rate control mechanism plays a critical role in making the best possible use of the network resources. The coding performance can be maximised through the appropriate allocation of bits under the constraints of a total bit rate budget and the buffer size. Existing rate control strategies generally determine the rate control parameters according to previous encoding results. However, there is no priori-knowledge available when the first frame of a video sequence is encoded or scene changes occur. Consequently, it is challenging to choose appropriate rate control parameters in such cases. In order to address this issue, we investigated deep learning oriented methods and proposed a Convolutional Neural Network (CNN)-based rate control scheme for HEVC intra-coding. As the CNN has the advantage of local perception and the Coding Tree Unit's (CTU's) Quantisation Parameter (QP) value is determined during the CTU level rate control process, we applied the CNN at the CTU level as well to achieve an accurate QP prediction. An improved QP determination model (R-QP model) involving only two model coefficients (µ and v) was suggested to simplify the QP calculation process. A CNN was used to predict the model coefficients, namely µ and v. Our CNN has four convolution layers, two pooling layers and three fully connected layers. Each of the convolution layers contains a Rectified Linear Unit (ReLU). The last fully connected layer outputs the predicted values of µ and v. The images from the UCID dataset and the RAISE dataset were used to train the CNN. In order to obtain a universal model, none of the frames in the HEVC common test sequences were employed as training images. In order to achieve a reasonable bit budget allocation, a CNN-based framework was used to predict the bit consumption for each CTU according to the entire picture content that it contains. At the training stage, the network took the original images and the QP values as inputs, and the corresponding actual bit consumptions were used as the labels. Once the CNN coefficients have been obtained through training, the bit consumption for each CTU under different QP values can be directly predicted from the original images. The predicted bit consumption was subsequently used to readjust the bit budget for each CTU to achieve a more reasonable bit allocation. We implemented the proposed CNN-based rate control scheme in the HEVC reference software HM 16.9. As the priori-knowledge of the previous encoding results had not been considered in the proposed algorithm, only the first frame of each video sequence was encoded. The experimental results showed that our proposed scheme performs better than the default rate control implementation in the HEVC reference software, namely the BDBR is reduced by 1.33% on average while maintaining the same reconstructed picture quality. Compared with the state-of-the-art CNN-based rate control algorithm proposed by Li, our schemes achieved better coding efficiency. It can be concluded that the proposed R-QP model is effective in describing the rate-distortion relationship in HEVC, and the CNN-based bit allocation scheme is appropriate for ensuring that the best use of each bit is made.

Avoiding Distortion in Corporate Valuation Litigation: An Application of Discounted Cash Flow

A domain decomposition method with Lagrange multipliers for the Stokes problem is developed and analysed. A common approach to solve the Stokes problem, termed the Uzawa algorithm, is to decouple the velocity and the pressure. This approach yields the Schur complement system for the pressure Lagrange multiplier which is solved with an iterative solver. Each outer iteration of the Uzawa procedure involves the inversion of a Laplacian in each spatial direction. The objective of this paper is to effectively solve this inner system (the vector Laplacian system) by applying the finite‐element tearing and interconnecting (FETI) method. Previously calculated search directions for the FETI solver are reused in subsequent outer Uzawa iterations. The advantage of the approach proposed in this paper is that pressure is continuous across the entire computational domain. Numerical tests are performed by solving the driven cavity problem. An analysis of the number of outer Uzawa iterations and inner FETI iterations is reported. Results show that the total number of inner iterations is almost numerically scalable since it grows asymptotically with the mesh size and the number of subdomains. Copyright © 2003 John Wiley & Sons, Ltd.

A new version of an iterative scheme of deconvolution originally introduced by Richardson (1972) and [ Lucy (1974) is presented. This algorithm is based on the Maximum Likelihood principle and imposes additional constraints on the solution of the inverse problem. The main idea of the newly presented method is to link the number of iterations with the local difference between the object profile in the input image and the noisy background. If this difference is of the order of the noise level, only very few iterations are performed, whereas if this difference is much greater than this level, the number of iterations attains its maximum assigned value. Thus, the number of iterations is used as a regularizer for the restoration. Due to this adaptive approach, the background noise is highly suppressed and the probability of restoration artefacts is seriously diminished. What is more, the quality of restored images (described by the Kullback-Leibler distance between deconvolved and original profile) for the adaptive iterative scheme increases in comparison with the original approach, whereas the mean number of iterations per one pixel is substantially reduced. Some examples of the deconvolution of one- and two-dimensional profiles presenting advantages of the new algorithm are described. Photometric fidelity of both methods is also compared and the predominance of the adaptive approach is confirmed.

For engineering design optimization, the full-space formulation offers the potential for greater efficiency than the more commonly used reduced-space formulation. This potential is greater when the numerical model involves discretized partial differential equations or coupled disciplines. However, the full-space formulation results in a larger optimization problem with at least a factor of two increase in the number of optimization variables and equality constraints. Using Newton-type methods to solve such problems involves solving a large-scale and, often, ill-conditioned Karush–Kuhn–Tucker linear system at each optimization iteration. This can be time-consuming to solve even with a Krylov solver. If the number of iterations is reduced, the full-space formulation could be applied to a broader class of problems. This paper presents an inexact quasi-Newton algorithm with an adaptive extension for solving large-scale equality-constrained optimization problems. The new algorithm inexactly solves the Karush–Kuhn–Tucker system using new inexactness criteria that are derived to ensure a descent direction. The adaptive extension chooses the stopping condition of the Krylov solver by also taking its convergence rate into account. The paper presents results of numerical experiments applying this algorithm to three types of problems: six constrained optimization problems from the widely used CUTEst test suite, a bar thickness optimization problem, and a two-dimensional topology optimization problem. For all problems, the new algorithm consistently shows a roughly 50% reduction in the total number of Krylov solver iterations and a minimum of roughly 15% reduction in the optimization time. Moreover, the proposed approach for selecting the Krylov solver tolerance shows an improvement in all cases, whereas the existing forcing-parameter approach shows an increase in the number of Krylov iterations in some cases. These results indicate that this new method for selecting solver tolerances is effective and robust, and a good choice in algorithms that use a Krylov solver for solving the Karush–Kuhn–Tucker linear system.

Recent works in the boundary element method (BEM) community have been devoted to the derivation of fast techniques to perform the matrix-vector product needed in the iterative solver. Fast BEMs are now very mature. However, it has been shown that the number of iterations can significantly hinder the overall efficiency of fast BEMs. The derivation of robust preconditioners is now inevitable to increase the size of the problems that can be considered. Analytical preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead of discretization. The main contribution of this paper is to propose new analytical preconditioners to treat Neumann exterior scattering problems in 2D and 3D elasticity. These preconditioners are local approximations of the adjoint Neumann-to-Dirichlet map. We propose three approximations with different orders. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). An analytical spectral study confirms the expected behavior of the preconditioners, i.e., a better eigenvalue clustering especially in the elliptic part contrary to the standard CFIE of the first-kind. We provide various 2D numerical illustrations of the efficiency of the method for smooth and non smooth geometries. In particular, the number of iterations is shown to be independent of the density of discretization points per wavelength which is not the case for the standard CFIE. In addition, it is less sensitive to the frequency.

This paper presents a new version of the fast decoupled loadflow in that a more broad range of power systems can be solved. The key lies in the different way in which the resistances are ignored and in a different iteration scheme. In the standard algorithm the resistances are ignored while building the B-prime loadflow matrix; this paper shows it is preferable that the resistances are ignored in the B double-prime matrix instead of the B-prime matrix. For normal test systems there is hardly any difference in the number of iterations, however, the new algorithm iterates faster if one or more problematic R/X ratios are present. An iteration scheme with strict successive P and Q iterations prevents cycling convergence behaviour which can be found in some low voltage systems. In this paper the advantages of the new version (to be indicated with the BX scheme) are demonstrated with runs on IEEE test systems with both uniformly and nonuniformly scaled resistances or reactances. R-scaling up to 3 is always possible, sometimes values up to 5 can be used. X-scaling of at least 0.1 is possible without losing convergence and with iteration counts which are significantly lower than with the standard scheme.

A New Rate Control Scheme in HDTV Systems

Atmospheric tomography, i.e., the reconstruction of the turbulence profile in the atmosphere, is a challenging task for adaptive optics (AO) systems for the next generation of extremely large telescopes. Within the AO community, the solver of first choice is the so-called Matrix Vector Multiplication (MVM) method, which directly applies the (regularized) generalized inverse of the system operator to the data. For small telescopes this approach is feasible, however, for larger systems such as the European Extremely Large Telescope (ELT), the atmospheric tomography problem is considerably more complex, and the computational efficiency becomes an issue. Iterative methods such as the Finite Element Wavelet Hybrid Algorithm (FEWHA) are a promising alternative. FEWHA is a wavelet-based reconstructor that uses the well-known iterative preconditioned conjugate gradient (PCG) method as a solver. The number of floating point operations and the memory usage are decreased significantly by using a matrix-free representation of the forward operator. A crucial indicator for the real-time performance are the number of PCG iterations. In this paper, we propose an augmented version of FEWHA, where the number of iterations is decreased by 50% using an augmented Krylov subspace method. We demonstrate that a parallel implementation of augmented FEWHA allows the fulfilment of the real-time requirements of the ELT.

In this paper, a novel rate control scheme for low delay video coding of High Efficiency Video Coding (HEVC) is proposed. The proposed scheme is developed by considering a new temporal prediction structure of HEVC. In the proposed scheme, the relationship between bit rate and quantization step is exploited firstly to formulate an accurate quadratic rate-quantization (R-Q) model. Secondly, a method of determining the quantization parameters (QPs) for the first frames within a group of pictures is proposed. Thirdly, an accurate frame-level bit allocation method is proposed for HEVC. Finally, based on the proposed R-Q model and the target bit allocated for the frame, the QPs are predicted for coding tree units by using rate-distortion (R-D) optimization. We compare our scheme against that of three other state-of-the-art rate control schemes. Experimental results show that the proposed rate control scheme can increase the Bjøntegaard delta peak signal-to-noise ratio by 0.65 dB and 0.09 dB on average compared with the JCTVC-I0094 and JCTVC-M0036 schemes, respectively, both of which have been implemented in an HEVC test model encoder; furthermore, the proposed scheme achieves a similar R-D performance to Wang's scheme, as well as obtaining the smallest bit rate mismatch error of all the schemes.

This work proposes a new rotation mode CORDIC algorithm, which considerably reduces the iteration number. It is achieved by combining several design techniques. Particularly, a new table-lookup recoding scheme for rotation angles and variable scale factors is developed to reduce the iteration numbers for rotation and scale factor compensation. By addressing the MSB parts of the residual rotation angles to a lookup table, two micro rotation angles are retrieved that in combination best matches the MSB parts. We also combine the leading-one bit detection operations for residual rotation angles, to skip unnecessary rotations. The resulting problems of variable scale factors are then solved by our previous fast decomposition and compensation algorithm (C.C. Li and S.G. Chen, in Proceedings of 1996 IEEE International Symposium Circuits and Systems, May 1996, Atlanta, USA, pp. 264–267s C.C. Li and S.G. Chen, in Proceedings of 1997 IEEE International Conference on Acoustic, Speech and Signal Processing, Munich, 1997, Germany, pp. 639–642). To further reduce the iteration number of scale factor compensation, we again apply the mentioned residual recoding technique and the leading-one bit detection scheme to the fast variable scale factor algorithm. Those techniques collectively reduce the iteration number significantly. Simulations show that in average the new design needs only 9.78 iterations to generate results with 22-bit accuracy, including all the iterations for rotations and scale factor compensations. Statistically, the total iteration number is less than n/2 for results with n-bit accuracy. The introduced extra table size is of the same order of magnitude as that for the angle set ltan−1 2−i, i e 0,1,…,nr, required by general CORDIC algorithms. The new recoding scheme can be applied to other elementary function such as division and square-root functions.

We connect the F iteration process with the class of generalized α -nonexpansive mappings. Under some appropriate assumption, we establish some weak and strong convergence theorems in Banach spaces. To show the numerical efficiency of our established results, we provide a new example of generalized α -nonexpansive mappings and show that its F iteration process is more efficient than many other iterative schemes. Our results are new and extend the corresponding known results of the current literature.

High energy consumption, low efficiency and the difficulty of modeling the platform injection-production system are the main issues appeared on the offshore petroleum platform. For addressing these problems, fuzzy control can be easily used to resolved the control model problem, this paper designs the improved fuzzy controller to online adjust the scaling factor by analyzing the influence of the quantization factor and scaling factor of fuzzy controller on the system dynamic performance. To testify the effectiveness of the improved fuzzy controller, we apply it on the experiment device of production wells. The results show that the improved fuzzy controller has better control performance than the conventional controller.

We extended the Davidson method, which was used to solve the standard eigenvalue problem, to solve the generalized eigenvalue problem and proposed the corresponding block iterative algorithm. Through theoretical analysis and numerical calculation, we found that the block iterative algorithm was doomed to converge after finite iterations if the process of iteration was not divergent. If the dimension of the matrix is n, the number of the eigenvalues and corresponding eigenvectors to be calculated is k, the size of the initial subspace is r(r≥k), the number of iteration is m, then they will fit in with the equation n=r+km. The positive integer root m could be obtained by regulating the size of the subspace.

Solution of large-scale nonlinear optimization problems and systems of nonlinear equations continues to be a difficult problem. One of the main classes of algorithms for solving these problems is the class of Newton–Krylov methods. In this article the number of iterations of a Krylov subspace method needed to guarantee at least a linear convergence of the respective Newton–Krylov method is studied. The problem is especially complicated if the matrix of the linear system to be solved is nonsymmetric. In the article, explicit estimates for the number of iterations for the Krylov subspace methods are obtained.