A Zero-attracting Quaternion-valued Least Mean Square Algorithm for Sparse System Identification

Recently, quaternion-valued signal processing has received more and more attention. In this paper, the quaternion-valued sparse system identification problem is studied for the first time and a zero-attracting quaternion-valued least mean square (LMS) algorithm is derived by considering the l1 norm of the quaternion-valued adaptive weight vector. By incorporating the sparsity information of the system into the update process, a faster convergence speed is achieved, as verified by simulation results

Channel Equalization and Beamforming for Quaternion-Valued Wireless Communication Systems

Quaternion-valued wireless communication systems have been studied in the past. Although progress has been made in this promising area, a crucial missing link is lack of effective and efficient quaternion-valued signal processing algorithms for channel equalization and beamforming. With most recent developments in quaternion-valued signal processing, in this work, we fill the gap to solve the problem by studying two quaternion-valued adaptive algorithms: one is the reference signal based quaternion-valued least mean square (QLMS) algorithm and the other one is the quaternion-valued constant modulus algorithm (QCMA). The quaternion-valued Wiener solution for possible block-based calculation is also derived. Simulation results are provided to show the working of the system

Quaternion-Valued Adaptive Signal Processing and Its Applications to Adaptive Beamforming and Wind Profile Prediction

Quaternion-valued signal processing has received more and more attentions in the past ten years due to the increasing need to process three or four-dimensional signals, such as colour images, vector-sensor arrays, three-phase power systems, dual-polarisation based wireless communica- tion systems, and wind profile prediction. One key operation involved in the derivation of all kinds of adaptive signal processing algorithms is the gradient operator. Although there are some derivations of this operator in literature with different level of details in the quaternion domain, it is still not fully clear how this operator can be derived in the most general case and how it can be applied to various signal processing problems. In this study, we will give a detailed derivation of the quaternion-valued gradient operator with associated properties and then apply it to different areas. In particular, it will be employed to derive the quaternion-valued LMS (QLMS) algorithm and its sparse versions for adaptive beamforming for vector sensor arrays, and another one is its application to wind profile prediction in combination with the classic computational fluid dynamics (CFD) approach. For the adaptive beamforming problem for vector sensor arrays, we consider the crossed- dipole array and the problem of how to reduce the number of sensors involved in the adap- tive beamforming process, so that reduced system complexity and energy consumption can be achieved, whereas an acceptable performance can still be maintained, which is particularly use- ful for large array systems. The quaternion-valued steering vector model for crossed-dipole arrays will be employed, and a reweighted zero attracting (RZA) QLMS algorithm is then pro- posed by introducing a RZA term to the cost function of the original QLMS algorithm. The RZA term aims to have a closer approximation to the l0 norm so that the number of non-zero valued coefficients can be reduced more effectively in the adaptive beamforming process. For wind profile prediction, it can be considered as a signal processing problem and we can solve it using traditional linear and non-linear prediction techniques, such as the proposed QLMS algorithm and its enhanced frequency-domain multi-channel version. On the other hand,it using traditional linear and non-linear prediction techniques, such as the proposed QLMS algorithm and its enhanced frequency-domain multi-channel version. On the other hand,wind flow analysis is also a classical problem in the CFD field, which employs various simulation methods and models to calculate the speed of wind flow at different time. It is accurate but time-consuming with high computational cost. To tackle the problem, a combined approach based on synergies between the statistical signal processing approach and the CFD approach is proposed. There are different ways of combining the signal processing approach and the CFD approach to obtain a more effective and efficient method for wind profile prediction. In the combined method, the signal processing part employs the QLMS algorithm, while for the CFD part, large eddy simulation (LES) based on the Smagorinsky subgrid-scale (SGS) model will be employed so that more efficient wind profile prediction can be achieved

Adaptive Beamforming for Vector-Sensor Arrays Based on Reweighted Zero-Attracting Quaternion-Valued LMS Algorithm

In this work, reference signal based adaptive beamforming for vector sensor arrays consisting of crossed dipoles is studied. In particular, we focus on how to reduce the number of sensors involved in the adaptation so that reduced system complexity and energy consumption can be achieved while an acceptable performance can still be maintained, which is especially useful for large array systems. As a solution, a reweighted zero attracting quaternion-valued least mean square algorithm is proposed. Simulation results show that the algorithm can work effectively for beamforming while enforcing a sparse solution for the weight vector where the corresponding sensors with zerovalued coefficients can be removed from the system

Properties and Applications of a Restricted HR Gradient Operator

For quaternionic signal processing algorithms, the gradients of a quaternion-valued function are required for gradient-based methods. Given the non-commutativity of quaternion algebra, the definition of the gradients is non-trivial. The HR gradient operator provides a viable framework and has found a number of applications. However, the applications so far have been mainly limited to real-valued quaternion functions and linear quaternion-valued functions. To generalize the operator to nonlinear quaternion functions, we define a restricted version of the HR operator. The restricted HR gradient operator comes in two versions, the left and the right ones. We then present a detailed analysis of the properties of the operators, including several different product rules and chain rules. Using the new rules, we derive explicit expressions for the derivatives of a class of regular nonlinear quaternion-valued functions, and prove that the restricted HR gradients are consistent with the gradients in real domain

A computational model of visual attention.

Visual attention is a process by which the Human Visual System (HVS) selects most important information from a scene. Visual attention models are computational or mathematical models developed to predict this information. The performance of the state-of-the-art visual attention models is limited in terms of prediction accuracy and computational complexity. In spite of significant amount of active research in this area, modelling visual attention is still an open research challenge. This thesis proposes a novel computational model of visual attention that achieves higher prediction accuracy with low computational complexity. A new bottom-up visual attention model based on in-focus regions is proposed. To develop the model, an image dataset is created by capturing images with in-focus and out-of-focus regions. The Discrete Cosine Transform (DCT) spectrum of these images is investigated qualitatively and quantitatively to discover the key frequency coefficients that correspond to the in-focus regions. The model detects these key coefficients by formulating a novel relation between the in-focus and out-of-focus regions in the frequency domain. These frequency coefficients are used to detect the salient in-focus regions. The simulation results show that this attention model achieves good prediction accuracy with low complexity. The prediction accuracy of the proposed in-focus visual attention model is further improved by incorporating sensitivity of the HVS towards the image centre and the human faces. Moreover, the computational complexity is further reduced by using Integer Cosine Transform (ICT). The model is parameter tuned using the hill climbing approach to optimise the accuracy. The performance has been analysed qualitatively and quantitatively using two large image datasets with eye tracking fixation ground truth. The results show that the model achieves higher prediction accuracy with a lower computational complexity compared to the state-of-the-art visual attention models. The proposed model is useful in predicting human fixations in computationally constrained environments. Mainly it is useful in applications such as perceptual video coding, image quality assessment, object recognition and image segmentation

Internationales Kolloquium über Anwendungen der Informatik und Mathematik in Architektur und Bauwesen : 20. bis 22.7. 2015, Bauhaus-Universität Weimar

The 20th International Conference on the Applications of Computer Science and Mathematics in Architecture and Civil Engineering will be held at the Bauhaus University Weimar from 20th till 22nd July 2015. Architects, computer scientists, mathematicians, and engineers from all over the world will meet in Weimar for an interdisciplinary exchange of experiences, to report on their results in research, development and practice and to discuss. The conference covers a broad range of research areas: numerical analysis, function theoretic methods, partial differential equations, continuum mechanics, engineering applications, coupled problems, computer sciences, and related topics. Several plenary lectures in aforementioned areas will take place during the conference. We invite architects, engineers, designers, computer scientists, mathematicians, planners, project managers, and software developers from business, science and research to participate in the conference

Flight Mechanics/Estimation Theory Symposium, 1990

This conference publication includes 32 papers and abstracts presented at the Flight Mechanics/Estimation Theory Symposium on May 22-25, 1990. Sponsored by the Flight Dynamics Division of Goddard Space Flight Center, this symposium features technical papers on a wide range of issues related to orbit-attitude prediction, determination and control; attitude sensor calibration; attitude determination error analysis; attitude dynamics; and orbit decay and maneuver strategy. Government, industry, and the academic community participated in the preparation and presentation of these papers

Nonlinear probabilistic estimation of 3-D geometry from images

Thesis (Ph. D.)--Massachusetts Institute of Technology, Program in Media Arts & Sciences, 1997.Includes bibliographical references (p. 159-164).by Ali Jerome Azarbayejani.Ph.D