本論文提出一新穎之盲訊號源分離技術，此技術分為兩個階段，第一階段進行時頻訊號初步分離，我們提出運用凸非負矩陣分解(convex nonnegative matrix factorization)結合複數表示法(complex representation)來估測混合矩陣，在解源訊號方面我們提出基於頻率之壓縮感測(compressive sensing)架構。在本階段，首先對每個時頻點擷取出能量比(level-ratio)與相位差(phase difference)參數；接著，再將參數以各頻帶為單位進行離群樣本去除(outlier elimination)，並利用凸非負矩陣分解演算法進行參數基底擷取；再來，將擷取出的基底解完排列問題後透過複數表示法轉換成混合矩陣；此混合矩陣將結合提出之壓縮感測架構進行源訊號分離。在此架構下、我們將混合矩陣擴充成測量矩陣，以及事先訓練的全域字典利用正交匹配追蹤演算法(orthogonal matching pursuit)以音框為單位解稀疏係數；將字典乘上稀疏係數便完成訊號分離。在第二階段，我們提出結合隱藏式馬可夫模型(hidden markov model)與上個階段之初步分離訊號，進行基於知識基礎之分離訊號強化。首先將源訊號的基礎音素轉換為梅爾倒頻譜係數(MFCC coefficient)後用以訓練各個音素模型。初步分離訊號代入此隱藏式馬可夫模型辨識後，一個音框對於各音素都會產生不同的對數似然(log likelihood)值，我們選出最大似然值的對應因素當作此音框之音素知識。全域字典根據此音素知識進行擴充以增加適應性，最後回到第一階段之壓縮感測架構完成源訊號分離。實驗結果顯示本論文提出之方法相較於傳統方法，在訊號-干擾比(SIR)上有顯著的提升。;This thesis proposed a novel compressive sensing blind source separation (BSS) technique, there are two phase in this technique. In the first phase we focus on source separation, convex nonnegative matrix factorization (convex NMF) incorporates complex representation is proposed to estimate the mixing matrix, and frequency based compressive sensing (CS) framework is proposed to separate the source. In this phase, extract level-ratio and phase difference as the feature for each time-frequency point first. Next, eliminate the outlier of the band based feature by implementing outlier elimination, and cluster the remains by implementing convex NMF algorithm to get the bases of the features. Then, transform the bases into the mixing matrix by complex representation. The mixing matrix is going to be used for source separation with the proposed compressive sensing framework. In this framework, we use the measurement matrix which extended by the mixing matrix, and pre-trained global dictionary to solve the sparse coefficient with orthogonal match pursuit (OMP) frame by frame. Finally, multiply the global dictionary by the sparse coefficient to finish the source separation. In the second phase, the knowledge based source separation enforcement is implemented by the preliminary separated source with hidden markov model (HMM). Transform the basic factor of the source into MFCC coefficient to train each factor model. After substituting the preliminary separated source into HMM, there are different likelihood produced from each factor in a frame. The maximum log likelihood of the corresponding factor is choosed as the factor knowledge for the frame. We extend the global dictionary by the factor to increase the adaptivity of the dictionary. Finally, we go back to the compressive sensing step in the first phase to finish source separation. Experimental results shows that SIR in proposed method is improved compare to the traditional method.
