Effective pattern recognition and find-density-peaks clustering based blind identification for underdetermined speech mixing systems

Abstract

In order to achieve high-efficiency blind identification (BI) for underdetermined speech mixing systems without recovery degradation, this paper proposes a novel BI scheme based on effective pattern recognition and the find-density-peaks (FDP) clustering algorithm. To lower BI’s computational complexity, a 3-step effective pattern recognition procedure is proposed, which consists of voiced-sound pattern sifting, spectrum correction based harmonic representation and phase uniformity based single-active-source (SAS) pattern recognition. Furthermore, a 5-step FDP clustering procedure is summarized and utilized to determine the souce number and estimate all the columns of the mixing matrix. Our experimental results showed that, the proposed 3-step effective pattern recognition procedure can condense the original 56383 TF patterns into only 194 effective SAS patterns, which considerably alleviates the computational burden of BI. Moreover, by means of FDP clustering, not only the source number can be intuitively and readily determined, but also the mixing matrix can be estimated with a higher recovery SNR than the existing BI schemes. Due to harmonic-like components are of wide applications, our proposed BI scheme possesses a vast potential in other harmonics-related blind-signal-separation (BSS) fields such as mechanical vibration analysis, channel estimation in communication.

Appendix A: Dataflow of ratio-based spectrum correction

Given the hanning-windowed STFT spectrograms of M mixtures X_m(t₀,kΔf), m = 1,...,M,Δf = f_s/L (denoting X_m(t₀,k) for simplicity) at some moment t = t₀, the results of spectrum correction (i.e., the outputs $\hat {f_{m}}, \hat {d_{m}}, \hat {\phi _{m}}$) are acquired by the following steps:

• Step 1 Collect all the large-amplitude peak indices k^∗ of X_m(t₀,k). For each index k^∗, calculate the amplitude ratio v_p between X_m(t₀,k^∗) and its sub-peak neighbor, i.e.,

  $$\begin{array}{@{}rcl@{}} v =\frac{ |X_{m}(t_{0}, k^{*}) |}{\max \{ | X_{m}(t_{0}, k^{*}-1)|, | X_{m}(t_{0}, k^{*}+ 1) |\} }. \end{array} $$

  (16)

  Further, a variable u can be calculated as

  $$\begin{array}{@{}rcl@{}} u=(2-v )/(1+v ). \end{array} $$

  (17)

• Step 2 Estimate the aforementioned frequency offset $\hat {\delta }$ as

  $$ \hat{\delta} = \left\{ \begin{array}{rl} u, ~&\text{if} \ |X_{m}(t_{0}, k^{*}+ 1)|> |X_{m}(t_{0}, k^{*}-1)|\\ -u,~&\text{else} \end{array}\right., $$

  (18)

  then, the frequency estimate is $\hat f_{m}=(k^{*}+\hat {\delta }) f_{s}/L$.

• Step 3 Acquire the amplitude estimate $\hat {d}_{m}$ and phase estimate $\hat {\phi }_{m}$ as

  $$\begin{array}{@{}rcl@{}} \hat{d}_{m}= 2 \pi \hat{\delta}(1-\hat{\delta}^{2}) |X_{m}(t_{0}, k_{p})| / \sin (\pi\hat{\delta}). \end{array} $$

  (19)
  $$\begin{array}{@{}rcl@{}} \hat\phi_{m}=\text{ang}[X_{m}(t_{0}, k^{*})]- \pi\hat{\delta}(L-1)/L, \end{array} $$

  (20)

  where ang(⋅) refers to the angle operation.