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A mesh adaptation method is proposed for solving optimal control problems with non-smooth control. The original optimal control problem (OCP) is transcribed into a nonlinear programming (NLP) problem by using the Runge-Kutta discretization method, in which the NLP can be solved by using standard nonlinear programming codes. The method employs collocations from the dyadic background points, which used for the second-generation wavelet (SGW) translation simultaneously. The SGW is used to approximate the control variables and get the wavelet coefficients once they are obtained. In regions contain discontinuities, the magnitude of the relevant wavelet coefficients is large than other regions. The corresponding dyadic background points are reserved as the collocation points. Furthermore, the approximation error of the control and/or state variables can be predicted by a given threshold. Thus, the accuracy and efficiency can be balanced in a simple way. Finally, the method is demonstrated by three numerical examples from the open literature.

In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing moments. The adaptation is introduced in the predict stage of the filter bank with an adaptation region chosen independently for each pixel, based on the intersection of confidence intervals (ICI) rule. The image denoising results are presented for both synthetic and real-world images. It is shown that the obtained wavelet decompositions perform well, especially for synthetic images that contain periodic patterns, for which the proposed method outperforms the state of the art in image denoising. [ABSTRACT FROM AUTHOR]

Distributed video coding is a new paradigm for video compression in opposition over the existing video coding standards like MPEG-x and H.26x families. These codecs make use of motion estimation algorithms, the main part of the compression process of the video signal. Hence, the compression process demands a high computational cost and high performance of the encoder. The present work proposes a video compression scheme based on the lossy distributed source coding theory. The proposed compressor encodes the odd frames and the even frames separately using turbo codes and the discrete wavelet transform. The decoding process is performed in a iterative manner and explores the statistical dependency of the video frames of the original sequence. This approach gives a great encoding runtime reduction and allows the implementation at devices with limited computation power and memory. Simulation results show the good performance of the proposed codec in comparison with the state of the art video compression standard H.264/AVC. [ABSTRACT FROM PUBLISHER]