在過去近十年中，關於訊號分離的研究，受到了許多學者的注目。尤其盲訊號源的領域更是被受重視。所謂的盲訊號，意指任何關於源訊號以及混合程序的資訊都是未知的情況，在解決這類問題時，我們唯一可依賴的只有收錄到的混合訊號。然而，本論文欲解決的問題是在不知道源訊號個數的情況下，一個稀疏欠定的卷積盲訊號源分離。我們的演算法分為兩個階段，先估計混合矩陣然後才利用此矩陣分離源訊號。 在估計混合矩陣時，首先定義了兩個特徵參數，包括了level-ratio以及phase-difference，然後利用KNN Graph方式，去除資料中的離群樣本，並用K-Means演算法對其餘的資料分群，我們提出將K-Means演算法和貝氏資訊準則作組合以達到估測源訊號個數的目的。 由於利用K-Means演算法所得到的混合矩陣之行向量中存在著排列的問題。我們偵測源訊號之方位(Direction of Arrival, DOA)，參考每個行向量所對應到的角度進而解決排列問題，達到估計混合矩陣的目的。此外，我們對此混合矩陣，進行相位之補償，已獲得更精確之混合矩陣估計。得到混合矩陣後，再應用最大後驗機率所推導出的最小L1範數之欠定線性最佳化問題分離源訊號。 此外，實驗模擬的部分，我們將提出的方法與傳統方法作比較，這裡採用的傳統方法是利用階層式分群法估測混合矩陣，加上解最小L1範數的一個演算法。並且，也證實了此演算法在殘響環境下仍然保持著它的可行性。 During the past decade, much attention has been given to the separation of source signals, in particular for the blind case where both the sources and the mixing process are unknown and only recordings of the mixtures are available. In this paper, the problem which we want to solve is a sparse under-determined convolution blind source separation (BSS) problem. We consider the case where the number of sources is unknown. We propose a two-step BSS algorithm. The mixing matrix estimation is the first step. In the second step, the estimated matrix estimation is used to separate source signals. In the mixing matrix estimation, we first define two features called level-ratio and phase-difference. Next, we eliminate outliers by KNN Graph and use K-Means clustering to obtain the separated clusters. A DOA detection method is then used to solve the permutation problem, and provides a phase compensation technique for mixing matrix estimation. This paper is based on maximum a posterior approach. After obtaining precise mixing matrix, we solve an optimization problem so that L1 norm is minimized. Beside, the proposed method combines the K-Means algorithm and Bayesian information criterion (BIC) to achieve the goal of source number estimation. About the experiments, we make a performance comparison between the proposed method and the baseline method, which uses a hierarchical clustering to estimate mixing matrix and separating source signals by solving L1 norm minimization, too. Furthermore, we demonstrate the proposed method also work well in reverberation environment.
