由於在盲語音分離的應用，線性準平穩源訊號混合的盲識別獲得了巨大的研究興趣。在這個問題上，我們利用準穩態源訊號的時變特性來識別未知的混合系統系數。傳統的方法有二：i)基於張量分解的平行因子分析(PARAFAC);ii)基於對多個矩陣的聯合對角化的聯合對角化算法(JD)。一般來說，PARAFAC和JD 都採用了源聯合的提取方法；即是說，對應所有訊號源的系統係數在升法上是用時進行識別的。 / 在這篇論文中，我利用Khati-Rao(KR)子空間來設計一種新的盲識別算法。在我設計的算法中提出一種與傳統的方法不同的提法。在我設計的算法中，盲識別問題被分解成數個結構上相對簡單的子問題，分別對應不同的源。在超定混合模型，我們提出了一個專門的交替投影算法(AP)。由此產生的算法，不但能從經驗發現是非常有競爭力的，而且更有理論上的利落收斂保證。另外，作為一個有趣的延伸，該算法可循一個簡單的方式應用於欠混合模型。對於欠定混合模型，我們提出啟發式的秩最小化算法從而提高算法的速度。 / Blind identification of linear instantaneous mixtures of quasi-stationary sources (BI-QSS) has received great research interest over the past few decades, motivated by its application in blind speech separation. In this problem, we identify the unknown mixing system coefcients by exploiting the time-varying characteristics of quasi-stationary sources. Traditional BI-QSS methods fall into two main categories: i) Parallel Factor Analysis (PARAFAC), which is based on tensor decomposition; ii) Joint Diagonalization (JD), which is based on approximate joint diagonalization of multiple matrices. In both PARAFAC and JD, the joint-source formulation is used in general; i.e., the algorithms are designed to identify the whole mixing system simultaneously. / In this thesis, I devise a novel blind identification framework using a Khatri-Rao (KR) subspace formulation. The proposed formulation is different from the traditional formulations in that it decomposes the blind identication problem into a number of per-source, structurally less complex subproblems. For the over determined mixing models, a specialized alternating projections algorithm is proposed for the KR subspace for¬mulation. The resulting algorithm is not only empirically found to be very competitive, but also has a theoretically neat convergence guarantee. Even better, the proposed algorithm can be applied to the underdetermined mixing models in a straightforward manner. Rank minimization heuristics are proposed to speed up the algorithm for the underdetermined mixing model. The advantages on employing the rank minimization heuristics are demonstrated by simulations. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lee, Ka Kit. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 72-76). / Abstracts also in Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Settings of Quasi-Stationary Signals based Blind Identification --- p.4 / Chapter 2.1 --- Signal Model --- p.4 / Chapter 2.2 --- Assumptions --- p.5 / Chapter 2.3 --- Local Covariance Model --- p.7 / Chapter 2.4 --- Noise Covariance Removal --- p.8 / Chapter 2.5 --- Prewhitening --- p.9 / Chapter 2.6 --- Summary --- p.10 / Chapter 3 --- Review on Some Existing BI-QSS Algorithms --- p.11 / Chapter 3.1 --- Joint Diagonalization --- p.11 / Chapter 3.1.1 --- Fast Frobenius Diagonalization [4] --- p.12 / Chapter 3.1.2 --- Pham’s JD [5, 6] --- p.14 / Chapter 3.2 --- Parallel Factor Analysis --- p.16 / Chapter 3.2.1 --- Tensor Decomposition [37] --- p.17 / Chapter 3.2.2 --- Alternating-Columns Diagonal-Centers [12] --- p.21 / Chapter 3.2.3 --- Trilinear Alternating Least-Squares [10, 11] --- p.23 / Chapter 3.3 --- Summary --- p.25 / Chapter 4 --- Proposed Algorithms --- p.26 / Chapter 4.1 --- KR Subspace Criterion --- p.27 / Chapter 4.2 --- Blind Identification using Alternating Projections --- p.29 / Chapter 4.2.1 --- All-Columns Identification --- p.31 / Chapter 4.3 --- Overdetermined Mixing Models (N > K): Prewhitened Alternating Projection Algorithm (PAPA) --- p.32 / Chapter 4.4 --- Underdetermined Mixing Models (N <K) --- p.34 / Chapter 4.4.1 --- Rank Minimization Heuristic --- p.34 / Chapter 4.4.2 --- Alternating Projections Algorithm with Huber Function Regularization --- p.37 / Chapter 4.5 --- Robust KR Subspace Extraction --- p.40 / Chapter 4.6 --- Summary --- p.44 / Chapter 5 --- Simulation Results --- p.47 / Chapter 5.1 --- General Settings --- p.47 / Chapter 5.2 --- Overdetermined Mixing Models --- p.49 / Chapter 5.2.1 --- Simulation 1 - Performance w.r.t. SNR --- p.49 / Chapter 5.2.2 --- Simulation 2 - Performance w.r.t. the Number of Available Frames M --- p.49 / Chapter 5.2.3 --- Simulation 3 - Performance w.r.t. the Number of Sources K --- p.50 / Chapter 5.3 --- Underdetermined Mixing Models --- p.52 / Chapter 5.3.1 --- Simulation 1 - Success Rate of KR Huber --- p.53 / Chapter 5.3.2 --- Simulation 2 - Performance w.r.t. SNR --- p.54 / Chapter 5.3.3 --- Simulation 3 - Performance w.r.t. M --- p.54 / Chapter 5.3.4 --- Simulation 4 - Performance w.r.t. N --- p.56 / Chapter 5.4 --- Summary --- p.56 / Chapter 6 --- Conclusion and Future Works --- p.58 / Chapter A --- Convolutive Mixing Model --- p.60 / Chapter B --- Proofs --- p.63 / Chapter B.1 --- Proof of Theorem 4.1 --- p.63 / Chapter B.2 --- Proof of Theorem 4.2 --- p.65 / Chapter B.3 --- Proof of Observation 4.1 --- p.65 / Chapter B.4 --- Proof of Proposition 4.1 --- p.66 / Chapter C --- Singular Value Thresholding --- p.67 / Chapter D --- Categories of Speech Sounds and Their Impact on SOSs-based BI-QSS Algorithms --- p.69 / Chapter D.1 --- Vowels --- p.69 / Chapter D.2 --- Consonants --- p.69 / Chapter D.1 --- Silent Pauses --- p.70 / Bibliography --- p.72
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328543 |
| Date | January 2012 |
| Contributors | Lee, Ka Kit., Chinese University of Hong Kong Graduate School. Division of Electronic Engineering. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (ix, 76 leaves) : ill. (some col.) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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