PolyU IR Collection:
http://hdl.handle.net/10397/980
2014-12-20T08:54:14ZNear-field beamformer design problems
http://hdl.handle.net/10397/6863
Title: Near-field beamformer design problems
Authors: Li, Zhibao
Abstract: This thesis is concerned with the near-field beamformer design problems in reverberant environment and the microphone array placement design problems. Firstly, we study the influence of room acoustics on the design of broadband beamformer. We introduce the image source method to estimate the room impulse responses, and establish several optimization models for the broadband beamformer design. We also study the barrier beamformer design problem, and introduce the space-time conservation element and solution element method to estimate the corresponding barrier impulse responses. Secondly, we study the time-domain beamformer design problem in the reverberant environment. We formulate the beamformer design problem as a linear system, and convert it into the least squares problem, whereas it has large scale and bad condition in the reverberant environment. Thus we introduce the Tikhonov regularization technique to improve the condition of the original problem. Moreover, we analyze the effectiveness of beamformer design as the filter length increases. With considering the nondirectional background noise of speech enhancement, the indoor LCMV beamformer problem is studied in the next. We use the estimated room impulse responses to formulate the model of indoor LCMV beamformer design, then construct a relaxed optimization problem to solve the filter coeffcients approximately. Moreover, post-filtering technique combining with indoor LCMV beamformer is studied to further improve the speech quality, and it is found that the MSIG post-filter combining with indoor LCMV beamformer has the best performance. Then we study the microphone array placement design problem, and formulate a composite optimization model for it. With the help of infinite length technique, we convert the subproblem on the solving of filter coefficients into the performance limit estimation problem. Moreover, we develop a hybrid descent method with genetic algorithm to solve the problem of microphone array placement design, the descent method can find the best solution around the current placement, and the genetic technique can jump out from the local solution. Finally, we study the microphone array placement design problem in reverberant environment. We introduce the LCMV framework combining with the infinite length technique to evaluate the effectiveness of placement design. And we also introduce the hybrid descent method to find the optimal array placement design eventually.
Description: xxii, 158 p. : ill. ; 30 cm.; PolyU Library Call No.: [THS] LG51 .H577P AMA 2014 Li2014-01-01T00:00:00ZOptimal design of distributed microphone array
http://hdl.handle.net/10397/6773
Title: Optimal design of distributed microphone array
Authors: Gao, Mingjie
Abstract: This thesis concentrates on the study of distributed broadband beamforming system and source localization problem. The main contributions of this thesis consist of the following four parts. 1. For the design of distributed broadband beamforming system, each microphone is equipped with wireless communications capability. It is designed such that the error between the actual response and the desired response is minimized which is then formulated as a minimax optimization problem. Since we find that the performance of the optimized designs is very sensitive to the perturbations in microphone locations, we first use sensor network technology which solved by semi-definite programming method to estimate the microphone locations, and then incorporate it into the design process. We propose a suitable robust formulation as a remedy to regain the performance. The minimax optimization problem is transformed into a semi-definite programming problem so that interior point algorithms can be applied. We illustrate the proposed method by several designs and demonstrate that this approach is essential to regain accuracy in the optimized designs. 2. The broadband beamforming design problem is formulated as a non-strictly convex semi-infinite programming problem. The approach to solve it is that adding a small perturbation quadratic function to the objective function to make it strictly convex. We demonstrate that the solution of the per-turbation semi-infinite programming problem approximates the solution of the original problem as the perturbation going to 0. The new exchange algorithm is applied successfully to the filter design problem. 3. We present a new method to solve the source localization problem with time-difference information. Fist we formulate a mixed SDP-SOCP relaxation model and then state how to obtain the exact solution from the solutions of the mixed SDP-SOCP relaxation model and the second order polynomial equation. The estimator properties for the true source location under noises is proposed. We also give bi-level method to solve the source localization problem that formulated only as a semi-definite programming. Then a mixed SDP-SOCP relaxation model for source localization combined with sensor network localization problem is studied, also we give some statistical analyses for it. Many illustrated examples demonstrate those approaches can be applied successfully and some comparisons are presented. 4. We obtain a representation for the solution of the mixed SDP-SOCP model and the characterization such that the mixed SDP-SOCP model has an exact relaxation in two-dimensional case. We derive the geometry of the localizable region for the proposed mixed model. The characterization shows that the source localization with some time-difference information can be solved exactly by the mixed SDP-SOCP relaxation model in a larger region than the triangle region determined by three points.
Description: xiv, 163 p. : ill. ; 30 cm.; PolyU Library Call No.: [THS] LG51 .H577P AMA 2013 Gao2013-01-01T00:00:00ZSome nonlinear spectral properties of higher order tensors
http://hdl.handle.net/10397/6495
Title: Some nonlinear spectral properties of higher order tensors
Authors: Song, Yisheng
Abstract: The main purposes of this thesis focus on the nonlinear spectral properties of higher order tensor with the help of the spectral theory and fixed point theory of nonlinear positively homogeneous operator as well as the constrained minimization theory of homogeneous polynomial. The main contributions of this thesis are as follows. We obtain the Fredholm alternative theorems of the eigenvalue (included E-eigenvalue, H-eigenvalue, Z-eigenvalue) of a higher order tensor A. Some relationship between the Gelfand formula and the spectral radius are discussed for the spectra induced by such several classes of eigenvalues of a higher order tensor. This content is mainly based on the paper 5 in Underlying Papers. We show that the eigenvalue problem of a nonnegative tensor A can be viewed as the fixed point problem of the Edelstein Contraction with respect to Hilbert's projective metric. Then by means of the Edelstein Contraction Theorem, we deal with the existence and uniqueness of the positive eigenvalue-eigenvector of such a tensor, and give an iteration sequence for finding positive eigenvalue of such a tensor, i.e., a nonlinear version of the famous Krein-Rutman Theorem. This content is mainly based on the paper 2 in Underlying Papers. We introduce the concept of eigenvalue to the additively homogeneous mapping pairs (f, g), and establish existence and uniqueness of such a eigenvalue under the boundedness of some orbits of f, g in the Hilbert semi-norm. In particular, the nonlinear Perron-Frobenius property for nonnegative tensor pairs (A, B) is given without involving the calculation of the tensor inversion. Moreover, we also present the iteration methods for finding generalized H-eigenvalue of nonnegative tensor pairs (A, B). This content is mainly based on the paper 1 in Underlying Papers. We introduce the concepts of Pareto H-eigenvalue and Pareto Z-eigenvalue of higher order tensor for studying constrained minimization problem and show the necessary and sufficient conditions of such eigenvalues. We obtain that a symmetric tensor has at least one Pareto H-eigenvalue (Pareto Z-eigenvalue). What is more, the minimum Pareto H-eigenvalue (or Pareto Z-eigenvalue) of a symmetric tensor is exactly equal to the minimum value of constrained minimization problem of homogeneous polynomial deduced by such a tensor, which gives an alternative methods for solving the minimum value of constrained minimization problem. In particular, a symmetric tensor A is copositive if and only if every Pareto H-eigenvalue (Z.eigenvalue) of A is non-negative. This content is mainly based on the papers 3 and 4 in Underlying Papers.
Description: 101 p. ; 30 cm.; PolyU Library Call No.: [THS] LG51 .H577P AMA 2013 Song2013-01-01T00:00:00ZSpectral hypergraph theory
http://hdl.handle.net/10397/6477
Title: Spectral hypergraph theory
Authors: Hu, Shenglong
Abstract: The main subject of this thesis is the study of a few basic problems in spectral hypergraph theory based on Laplacian-type tensors. These problems are hypergraph analogues of some important problems in spectral graph theory. As some foundations, we study some new problems of tensor determinant and non-negative tensor partition. Then two classes of Laplacian-type tensors for uniform hypergraphs are proposed. One is called Laplacian, and the other one Laplace-Beltrami tensor. We study the H-spectra of uniform hypergraphs through their Laplacian, and the Z-spectra of even uniform hypergraphs through their Laplace-Beltrami tensors. All the H{204}-eigenvalues of the Laplacian can be computed out through the developed partition method. Spectral component, an intrinsic notion of a uniform hypergraph, is introduced to characterize the hypergraph spectrum. Many fundamental properties of the spectrum are connected to the underlying hypergraph structures. Basic spectral hypergraph theory based on Laplacian-type tensors are built. With the theory, we study algebraic connectivity, edge connectivity, vertex connectivity, edge expansion, and spectral invariance of the hypergraph.
Description: xii, 107 p. : ill. ; 30 cm.; PolyU Library Call No.: [THS] LG51 .H577P AMA 2013 HuS2013-01-01T00:00:00Z