Methodologically, there are many different signal processing methods that perform high-efficiency signal decomposition, such as independent component analysis (ICA) [12] and wavelet decomposition [13]. ICA contributes to the applications of blind signal separations based on statistical characteristics of the signals, which reflect linear combinations of different signal sources. Wavelet decomposition offers simultaneous interpretation of the signal in both time and frequency that allows local, transient, intermittent components to be calculated. However, such traditional signal processing method is based on linear assumption. The components derived by wavelet decomposition are often obscured due to the inherent averaging. In 1998, Huang et al. proposed the innovative algorithm of EMD signal decomposition, in which the components are decomposed adaptively to the nature of signals but not the base of transformation [14]. Theoretically, each intrinsic mode function (IMF) decomposed by EMD reflects the response actuated by the corresponding activity of a particular underlying physiological mechanism. In practices, the unpredictable intermittent turbulences damage the consistencies of IMFs. This phenomenon is noted as mode mixing. Recently, an ensemble empirical mode decomposition (EEMD) has been introduced which is considered as an enhanced algorithm of EMD, which solves the problem of mode mixing in the original EMD [1]. In this pilot study, it is assumed that the reflected waves of BP can be derived as a particular intrinsic component (i.e., IMF) by EEMD. Hence, a new EEMD-based calculation of RI can be achieved. Moreover, EEMD also works to decompose the cardiac oscillations from ECG and BP in the new application of multimodal analysis. Phase shift between the cardiac oscillations of ECG and BP is considered to be a phase delay between the driving signal (i.e., ECG) and the output signal (i.e., BP) of the cardiovascular system. It is considered as a new assessment of systemic impedance of the cardiovascular system which is the second EEMD-based assessment presented in this study.
solution manual mathematical methods and algorithms for signal processing
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@articleBłaszczyk2007,abstract = The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.,author = Błaszczyk, Jacek, Karbowski, Andrzej, Malinowski, Krzysztof,journal = International Journal of Applied Mathematics and Computer Science,keywords = dynamic optimization; object-oriented numerical computations; large-scale optimization; nonlinear interior-point methods; performance data analysis; automatic differentiation; sequential quadratic programming,language = eng,number = 4,pages = 515-537,title = Object library of algorithms for dynamic optimization problems: benchmarking SQP and nonlinear interior point methods,url = ,volume = 17,year = 2007,
TY - JOURAU - Błaszczyk, JacekAU - Karbowski, AndrzejAU - Malinowski, KrzysztofTI - Object library of algorithms for dynamic optimization problems: benchmarking SQP and nonlinear interior point methodsJO - International Journal of Applied Mathematics and Computer SciencePY - 2007VL - 17IS - 4SP - 515EP - 537AB - The main purpose of this paper is to describe the design, implementation and possibilities of our object-oriented library of algorithms for dynamic optimization problems. We briefly present library classes for the formulation and manipulation of dynamic optimization problems, and give a general survey of solver classes for unconstrained and constrained optimization. We also demonstrate methods of derivative evaluation that we used, in particular automatic differentiation. Further, we briefly formulate and characterize the class of problems solved by our optimization classes. The solution of dynamic optimization problems with general constraints is performed by transformation into structured large-scale nonlinear programming problems and applying methods for nonlinear optimization. Two main algorithms of solvers for constrained dynamic optimization are presented in detail: the sequential quadratic programming (SQP) exploring the multistage structure of the dynamic optimization problem during the solution of a sequence of quadratic subproblems, and the nonlinear interior-point method implemented in a general-purpose large-scale optimizer IPOPT. At the end, we include a typical numerical example of the application of the constrained solvers to a large-scale discrete-time optimal control problem and we use the performance profiles methodology to compare the efficiency and robustness of different solvers or different options of the same solver. In conclusions, we summarize our experience gathered during the library development.LA - engKW - dynamic optimization; object-oriented numerical computations; large-scale optimization; nonlinear interior-point methods; performance data analysis; automatic differentiation; sequential quadratic programmingUR - ER -
Abstract:Deep learning has been widely used in different fields such as computer vision and speech processing. The performance of deep learning algorithms is greatly affected by their hyperparameters. For complex machine learning models such as deep neural networks, it is difficult to determine their hyperparameters. In addition, existing hyperparameter optimization algorithms easily converge to a local optimal solution. This paper proposes a method for hyperparameter optimization that combines the Sparrow Search Algorithm and Particle Swarm Optimization, called the Hybrid Sparrow Search Algorithm. This method takes advantages of avoiding the local optimal solution in the Sparrow Search Algorithm and the search efficiency of Particle Swarm Optimization to achieve global optimization. Experiments verified the proposed algorithm in simple and complex networks. The results show that the Hybrid Sparrow Search Algorithm has the strong global search capability to avoid local optimal solutions and satisfactory search efficiency in both low and high-dimensional spaces. The proposed method provides a new solution for hyperparameter optimization problems in deep learning models.Keywords: deep learning; hyperparameter optimization; Hybrid Sparrow Search; global optimizationMSC:90C26
The ImageM application proposes an integrated user interface that facilitates the processing and the analysis of multi-dimensional images within the Matlab environment. It provides a user-friendly visualization of multi-dimensional images, a collection of image processing algorithms and methods for analysis of images, the management of spatial calibration, and facilities for the analysis of multi-variate images. ImageM can also be run on the open source alternative software to Matlab, Octave.
Matlab (The Mathworks, Natick, MA), is an efficient software solution for image and signal processing that provides native support for multi-dimensional arrays, a large number of image processing methods, and a great facility for adding custom developments. However, it lacks many features for facilitating the interactive interpretation of image data, such as a user-friendly visualization of multidimensional images, or the management of image meta-data (e.g. spatial calibration), thus limiting its application to bio-image analysis. 2ff7e9595c
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