Sparse Component Analysis (SCA) Based on Adaptive Time—Frequency Thresholding for Underdetermined Blind Source Separation (UBSS)
Abstract
:1. Introduction
2. The UBSS–SCA-Based Method
3. Mixed Signal Generation
4. Mixing Matrix Estimation
4.1. The Proposed Adaptive Time–Frequency Thresholding (ATFT) Method
- Let .
- The threshold of ATFT, , is obtained from the norm of the result of all mixtures and was computed by
- 3.
- According to Equation (5), the thresholding operation is defined as
4.2. Single Source Point (SSP) Detection
Algorithm 1: Mixing matrix estimation procedure using the proposed ATFT method |
Input: The mixed signal, .
|
4.3. Clustering
Algorithm 2: The procedure of mixing matrix estimation using hierarchical clustering |
Input: The extracted SSP vectors, .
|
5. Source Recovery Estimation
Algorithm 3: Source recovery estimation |
Input: The mixed signal, , and the estimated mixing matrix, .
|
6. Numerical Simulations
6.1. The Performance of Mixing Matrix Estimation
6.2. The Performance of Source Recovery Estimation
7. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
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References | Mixing System | Single-Source Point Detection | Limitations |
---|---|---|---|
[25] | Two mixtures of three sources from two guitars and one voice | Time–frequency ratio of the mixtures (TIFROM) | Low estimation accuracy for noisy and insufficiently sparse sources |
[24] | Three, four and five mixtures each for four to seven speech utterances | Compared the absolute directions of the real and imaginary parts of the TF points in the mixing signals | Limited application, requires real-valued entries in the mixing matrix |
[26] | Three mixtures of four sets of sources consisting of the genres of music, speech, instruments and various sounds | An SSD algorithm that recognises the TF points occupied by a single source for each source. | Loses efficiency when the mixing matrix is complex and not real |
[27] | Two mixtures of three speech signals | Extracts prior information from the complex-valued mixing matrix at the receiver’s end | Too much computation or poor robustness |
[16] | Three mixtures of four speech sources | Sparse coding | Has a fixed parameter to select the STFT coefficients before SSP detection |
[28] | Two mixtures of four speech signals | An SSP detection technique based on the transformation matrix | The selection of the peak value used to determine the number of source signals is greatly affected by noise |
[29] | Two mixtures of two sets of sources consisting of three male and female speech signals | Calculates the mixing ratio | Sensitive to noise in real-world systems |
[13] | Three mixtures of six flutes | Calculating the mixing ratio | Sensitive to noise |
Database | Zhen’s Method | ATFT Method |
---|---|---|
Bioacoustic signals | 2.3321 | 1.9218 |
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Hassan, N.; Ramli, D.A. Sparse Component Analysis (SCA) Based on Adaptive Time—Frequency Thresholding for Underdetermined Blind Source Separation (UBSS). Sensors 2023, 23, 2060. https://doi.org/10.3390/s23042060
Hassan N, Ramli DA. Sparse Component Analysis (SCA) Based on Adaptive Time—Frequency Thresholding for Underdetermined Blind Source Separation (UBSS). Sensors. 2023; 23(4):2060. https://doi.org/10.3390/s23042060
Chicago/Turabian StyleHassan, Norsalina, and Dzati Athiar Ramli. 2023. "Sparse Component Analysis (SCA) Based on Adaptive Time—Frequency Thresholding for Underdetermined Blind Source Separation (UBSS)" Sensors 23, no. 4: 2060. https://doi.org/10.3390/s23042060