Tone reservation for peak to average power ratio is considered. The selection of the tone is based on the channel condition. The subcarrier with the worst channel condition is chosen to be our peak reduction carrier to effectively lower the signal PAPR and increase the efficiency of subcarrier transmission. In searching the proper modulation level of the peak reduction carriers, a modified algorithm to recursively adapt this modulation level is proposed. The adjustment is to ensure that a certain percentage of the reduction of the PAPR is achieved. The percentage is reduced in every iteration until the goal is achieved.

Motion compensation is used to reduce the displaced frame difference (DFD) during video coding. To increase the accuracy of the point correspondence during the compensation, a three-parameter motion model is considered. The matching error can be significantly reduced as compared with that of the two-parameter block matching. To derive the parameters, a partial full search method is used. The full search is used when the zoom value is set at one. Otherwise, the gradient-based algorithm is used. Since the DFD is a nonlinear function of the image gradients and the motion parameters, a linearized model is considered. To eliminate the linearization error, Wiener filtering is used to smoothen the DFD to improve the convergence condition of the iterative gradient search. To make the gradient-based search more robust to the gradient variation, several gradient estimation methods are also compared.

Discrete formulation of the surface interpolation problem usually leads to a large sparse linear system. The convergence rate for solving this problem with iterative method is very slow. To improve this condition, wavelet representation for multigrid computation is proposed. With wavelet transforms, the linear system to be solved will be transformed into a new system equation. This new system processes the low frequency and high frequency components more directly and more efficiently. By employing the multigrid computation structure among these different frequency components, a multi-frequency band computation structure which combines the advantages of the wavelet transform and the multigrid method is built. This structure not only avoids the transfer between the adjacent grids and results in a simple structure for implementation but also manipulates the different frequency components more effectively and results in a higher convergence rate for solving linear equation system.

A robust approach to recover the shape of an object from shading information is presented. The scheme is derived based on the perturbation method that minimizes a cost function for computing a surface height from a single image given the imaging model and light direction. To describe the desired solution variables as a linear combination of a set of basis functions, the Ritz method is applied in our approach to discretize the cost function associated with the regularized shape from shading problem. This kind of discretization is simple and the concept of signal representation by a set of weighted basis functions can be clearly stated. To enhance the robustness of alternative scheme, two new constraints are added into the cost function. They constrain the behavior of high-order change rate between the variables, and bound the variables more tightly. Thus, the changes of variables will be more regular. Hence, new constraints strengthen the relations between the input image and the reconstructed surface height. After finding the weighting coefficients using a perturbation method, the solution of the SFS problem will finally be decided.

Discrete formulation of the surface interpolation problem usually leads to a large sparse linear equation system. Due to the poor convergence condition of the equation system, the convergence rate of solving this problem with iterative method is very slow. To improve this condition, a multiresolution basis transfer scheme based on the wavelet transform is proposed. By applying the wavelet transform, the original interpolation basis is transformed into two sets of bases with larger supports while the admissible solution space remains unchanged. With this basis transfer, a new set of nodal variables results and an equivalent equation system with better convergence condition can be solved. The basis transfer can be easily implemented by using an QMF matrix pair associated with the chosen interpolation basis. The consequence of the basis transfer scheme can be regarded as a preconditioner to the subsequent iterative computation method. The effect of the transfer is that the interpolated surface is decomposed into its low-frequency and high-frequency portions in the frequency domain. It has been indicated that the convergence rate of the interpolated surface is dominated by the low-frequency portion. With this frequency domain decomposition, the low-frequency portion of the interpolated surface can be emphasized. As compared with other acceleration methods, this basis transfer scheme provides a more systematical approach for fast surface interpolation. The easy implementation and high flexibility of the proposed algorithm also make it applicable to various regularization problems.>