
-
Previous Article
Optimal recycling price strategy of clothing enterprises based on closed-loop supply chain
- JIMO Home
- This Issue
-
Next Article
Retailer's willingness to adopt blockchain technology based on private demand information
Online First articles are published articles within a journal that have not yet been assigned to a formal issue. This means they do not yet have a volume number, issue number, or page numbers assigned to them, however, they can still be found and cited using their DOI (Digital Object Identifier). Online First publication benefits the research community by making new scientific discoveries known as quickly as possible.
Readers can access Online First articles via the “Online First” tab for the selected journal.
Two-level optimization approach with accelerated proximal gradient for objective measures in sparse speech reconstruction
1. | School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University of Technology, Perth, Australia |
2. | Faculty of Engineering and Physical Sciences, University of Southampton Malaysia (UoSM), Iskandar Puteri, Johor, Malaysia |
Compressive speech enhancement makes use of the sparseness of speech and the non-sparseness of noise in time-frequency representation to perform speech enhancement. However, reconstructing the sparsest output may not necessarily translate to a good enhanced speech signal as speech distortion may be at risk. This paper proposes a two level optimization approach to incorporate objective quality measures in compressive speech enhancement. The proposed method combines the accelerated proximal gradient approach and a global one dimensional optimization method to solve the sparse reconstruction. By incorporating objective quality measures in the optimization process, the reconstructed output is not only sparse but also maintains the highest objective quality score possible. In other words, the sparse speech reconstruction process is now quality sparse speech reconstruction. Experimental results in a compressive speech enhancement consistently show score improvement in objectives measures in different noisy environments compared to the non-optimized method. Additionally, the proposed optimization yields a higher convergence rate with a lower computational complexity compared to the existing methods.
References:
[1] |
A. Beck and M. Teboulle,
A fast iterative shrinkage-thresholding algorithm for linear inverse problem, SIAM Journal on Imaging Sciences, 2 (2009), 183-202.
doi: 10.1137/080716542. |
[2] |
J. Benesty and Y. Huang, A Perspective on Single-Channel Frequency-Domain Speech Enhancement, San Rafael: Morgan and Claypool Publishers, 2010.
doi: 10.2200/S00344ED1V01Y201104SAP008. |
[3] |
S. F. Boll,
Supression of acoustic noise in speech using spectral subtraction, IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-27 (1979), 113-120.
|
[4] |
O. Burdakov, Y. Dai and N. Huang,
Stabilized Barzilai-Borwein method, J. Comp. Math., 37 (2019), 916-936.
doi: 10.4208/jcm.1911-m2019-0171. |
[5] |
E. J. Candés, J. Romberg and T. Tao,
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[6] |
E. J. Candes and T. Tao,
Near-optimal signal recovery from random projections: universal encoding strategies, IEEE Transactions on Information Theory, 52 (2006), 5406-5425.
doi: 10.1109/TIT.2006.885507. |
[7] |
E. J. Candes and M. B. Wakin, An introduction to compressive sampling, IEEE Signal Processing Magazine, (2008), 21-30. |
[8] |
H. H. Dam and A. Cantoni,
Interior point method for optimum zero-forcing beamforming with per-antenna power constraints and optimal step size, Signal Processing, 106 (2015), 10-14.
doi: 10.1016/j.sigpro.2014.06.028. |
[9] |
H. H. Dam and S. Nordholm,
Accelerated gradient with optimal step size for second-order blind signal separation, Multidimens. Syst. Signal Process., 29 (2018), 903-919.
doi: 10.1007/s11045-017-0478-8. |
[10] |
T. Esch and P. Vary, Efficient musical noise suppression for speech enhancement system, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, (2009), 4409-4412.
doi: 10.1109/ICASSP.2009.4960607. |
[11] |
P. K. Ghosh, A. Tsiartas and S. Narayanan,
Robust voice activity detection using long-term signal variability, IEEE Transactions on Audio, Speech and Language Processing, 19 (2011), 600-613.
doi: 10.1109/TASL.2010.2052803. |
[12] |
S. J. Kim, K. Koh, M. Lustig, S. Boyd and D. Gorinevsky,
An interior-point method for large-scale $l_1$-regularized least squares, IEEE Journal of Selected Topics in Signal Processing, 1 (2007), 606-617.
|
[13] |
H. Li, C. Fang and Z. Lin, Accelerated first-order optimization algorithms for machine learning, Proceedings of the IEEE, (2020), 1-16. |
[14] |
P. C. Loizou, Speech Enhancement: Theory and Practice, CRC press, Boca Raton, 2013.
doi: 10.1201/9781420015836.![]() ![]() |
[15] |
S. Y. Low,
Compressive speech enhancement in the modulation domain, Speech Communication, 102 (2018), 87-99.
doi: 10.1016/j.specom.2018.08.003. |
[16] |
S. Y. Low, D. S. Pham and S. Venkatesh,
Compressive speech enhancement, Speech Communication, 55 (2013), 757-768.
doi: 10.1016/j.specom.2013.03.003. |
[17] |
R. Martin,
Noise power spectral density estimation based on optimal smoothing and minimum statistics, IEEE Transactions on Speech and Audio Processing, 9 (2001), 504-512.
doi: 10.1109/89.928915. |
[18] |
R. Miyazaki, H. Saruwatari, T. Inoue, K. Shikano and K. Kondo, Musical-noise-free speech enhancement: Theory and evaluation, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (2012), 4565-4568.
doi: 10.1109/ICASSP.2012.6288934. |
[19] |
M. Nazih, K. Minaoui and P. Comon, Using the proximal gradient and the accelerated proximal gradient as a canonical polyadic tensor decomposition algorithms in difficult situations, Signal Processing, 171 (2020), 107472.
doi: 10.1016/j.sigpro.2020.107472. |
[20] |
N. Parikh and S. Boyd,
Proximal Algorithms, Foundation and Trends in Optimization, 1 (2013), 123-231.
|
[21] |
A. W. Rix, J. G. Beerends, M. P. Hollier and A. P. Hekstra,
Perceptual evaluation of speech quality (PESQ) - a new method for speech quality assessment of telephone networks and codecs, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), 2 (2001), 749-752.
doi: 10.1109/ICASSP.2001.941023. |
[22] |
M. Schmidt, Least squares optimization with l1-norm regularization, Technical Report CSP542B, 2005. |
[23] |
Y. Shi, S. Y. Low and K. F. C. Yiu,
Hyper-parameterization of sparse reconstruction for speech enhancement, Applied Acoustics, 138 (2018), 72-79.
doi: 10.1016/j.apacoust.2018.03.020. |
[24] |
C. H. Taal, R. C. Hendriks, R. Heusdens and J. Jensen, A short-time objective intelligibility measure for time-frequency weighted noisy speech, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, (2010), 4214-4217.
doi: 10.1109/ICASSP.2010.5495701. |
[25] |
R. Tibshirani,
Regression shrinkage and selection via the lasso, J. Roy. Statist. Soc. Ser. B, 58 (1996), 267-288.
doi: 10.1111/j.2517-6161.1996.tb02080.x. |
[26] |
M. Torcoli, An improved measure of musical noise based on spectral kurtosis, 019 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), (2019), 90-94.
doi: 10.1109/WASPAA.2019.8937195. |
[27] |
D. Wu, W. Zhu and M. N. S. Swamy, A compressive sensing method for noise reduction of speech and audio signals, 2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS), (2011), 1-4.
doi: 10.1109/MWSCAS.2011.6026662. |
[28] |
Z. Zhang, Y. Xu, J. Yang, X. Li and D. Zhang,
A Survey of Sparse Representation: Algorithms and Applications, IEEE Access, 3 (2015), 490-530.
|
show all references
References:
[1] |
A. Beck and M. Teboulle,
A fast iterative shrinkage-thresholding algorithm for linear inverse problem, SIAM Journal on Imaging Sciences, 2 (2009), 183-202.
doi: 10.1137/080716542. |
[2] |
J. Benesty and Y. Huang, A Perspective on Single-Channel Frequency-Domain Speech Enhancement, San Rafael: Morgan and Claypool Publishers, 2010.
doi: 10.2200/S00344ED1V01Y201104SAP008. |
[3] |
S. F. Boll,
Supression of acoustic noise in speech using spectral subtraction, IEEE Transactions on Acoustics, Speech and Signal Processing, ASSP-27 (1979), 113-120.
|
[4] |
O. Burdakov, Y. Dai and N. Huang,
Stabilized Barzilai-Borwein method, J. Comp. Math., 37 (2019), 916-936.
doi: 10.4208/jcm.1911-m2019-0171. |
[5] |
E. J. Candés, J. Romberg and T. Tao,
Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information, IEEE Transactions on Information Theory, 52 (2006), 489-509.
doi: 10.1109/TIT.2005.862083. |
[6] |
E. J. Candes and T. Tao,
Near-optimal signal recovery from random projections: universal encoding strategies, IEEE Transactions on Information Theory, 52 (2006), 5406-5425.
doi: 10.1109/TIT.2006.885507. |
[7] |
E. J. Candes and M. B. Wakin, An introduction to compressive sampling, IEEE Signal Processing Magazine, (2008), 21-30. |
[8] |
H. H. Dam and A. Cantoni,
Interior point method for optimum zero-forcing beamforming with per-antenna power constraints and optimal step size, Signal Processing, 106 (2015), 10-14.
doi: 10.1016/j.sigpro.2014.06.028. |
[9] |
H. H. Dam and S. Nordholm,
Accelerated gradient with optimal step size for second-order blind signal separation, Multidimens. Syst. Signal Process., 29 (2018), 903-919.
doi: 10.1007/s11045-017-0478-8. |
[10] |
T. Esch and P. Vary, Efficient musical noise suppression for speech enhancement system, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing, (2009), 4409-4412.
doi: 10.1109/ICASSP.2009.4960607. |
[11] |
P. K. Ghosh, A. Tsiartas and S. Narayanan,
Robust voice activity detection using long-term signal variability, IEEE Transactions on Audio, Speech and Language Processing, 19 (2011), 600-613.
doi: 10.1109/TASL.2010.2052803. |
[12] |
S. J. Kim, K. Koh, M. Lustig, S. Boyd and D. Gorinevsky,
An interior-point method for large-scale $l_1$-regularized least squares, IEEE Journal of Selected Topics in Signal Processing, 1 (2007), 606-617.
|
[13] |
H. Li, C. Fang and Z. Lin, Accelerated first-order optimization algorithms for machine learning, Proceedings of the IEEE, (2020), 1-16. |
[14] |
P. C. Loizou, Speech Enhancement: Theory and Practice, CRC press, Boca Raton, 2013.
doi: 10.1201/9781420015836.![]() ![]() |
[15] |
S. Y. Low,
Compressive speech enhancement in the modulation domain, Speech Communication, 102 (2018), 87-99.
doi: 10.1016/j.specom.2018.08.003. |
[16] |
S. Y. Low, D. S. Pham and S. Venkatesh,
Compressive speech enhancement, Speech Communication, 55 (2013), 757-768.
doi: 10.1016/j.specom.2013.03.003. |
[17] |
R. Martin,
Noise power spectral density estimation based on optimal smoothing and minimum statistics, IEEE Transactions on Speech and Audio Processing, 9 (2001), 504-512.
doi: 10.1109/89.928915. |
[18] |
R. Miyazaki, H. Saruwatari, T. Inoue, K. Shikano and K. Kondo, Musical-noise-free speech enhancement: Theory and evaluation, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), (2012), 4565-4568.
doi: 10.1109/ICASSP.2012.6288934. |
[19] |
M. Nazih, K. Minaoui and P. Comon, Using the proximal gradient and the accelerated proximal gradient as a canonical polyadic tensor decomposition algorithms in difficult situations, Signal Processing, 171 (2020), 107472.
doi: 10.1016/j.sigpro.2020.107472. |
[20] |
N. Parikh and S. Boyd,
Proximal Algorithms, Foundation and Trends in Optimization, 1 (2013), 123-231.
|
[21] |
A. W. Rix, J. G. Beerends, M. P. Hollier and A. P. Hekstra,
Perceptual evaluation of speech quality (PESQ) - a new method for speech quality assessment of telephone networks and codecs, 2001 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.01CH37221), 2 (2001), 749-752.
doi: 10.1109/ICASSP.2001.941023. |
[22] |
M. Schmidt, Least squares optimization with l1-norm regularization, Technical Report CSP542B, 2005. |
[23] |
Y. Shi, S. Y. Low and K. F. C. Yiu,
Hyper-parameterization of sparse reconstruction for speech enhancement, Applied Acoustics, 138 (2018), 72-79.
doi: 10.1016/j.apacoust.2018.03.020. |
[24] |
C. H. Taal, R. C. Hendriks, R. Heusdens and J. Jensen, A short-time objective intelligibility measure for time-frequency weighted noisy speech, 2010 IEEE International Conference on Acoustics, Speech and Signal Processing, (2010), 4214-4217.
doi: 10.1109/ICASSP.2010.5495701. |
[25] |
R. Tibshirani,
Regression shrinkage and selection via the lasso, J. Roy. Statist. Soc. Ser. B, 58 (1996), 267-288.
doi: 10.1111/j.2517-6161.1996.tb02080.x. |
[26] |
M. Torcoli, An improved measure of musical noise based on spectral kurtosis, 019 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA), (2019), 90-94.
doi: 10.1109/WASPAA.2019.8937195. |
[27] |
D. Wu, W. Zhu and M. N. S. Swamy, A compressive sensing method for noise reduction of speech and audio signals, 2011 IEEE 54th International Midwest Symposium on Circuits and Systems (MWSCAS), (2011), 1-4.
doi: 10.1109/MWSCAS.2011.6026662. |
[28] |
Z. Zhang, Y. Xu, J. Yang, X. Li and D. Zhang,
A Survey of Sparse Representation: Algorithms and Applications, IEEE Access, 3 (2015), 490-530.
|



Noise type | SNR | Accelerated Proximal Gradient | Proximal Gradient | Interior Point Method |
Babble noise | 0dB | 3.1307s | 3.3139s | 7.2640s |
5dB | 2.7209s | 2.8722s | 7.0281s | |
10dB | 2.3887s | 2.4476s | 6.8677s | |
15dB | 2.2449s | 2.4057s | 6.8233s | |
20dB | 2.0481s | 2.1050s | 6.6695s | |
Destroyer noise | 0dB | 2.8322s | 2.9187s | 6.9363s |
5dB | 2.4799s | 2.5386s | 6.8301s | |
10dB | 2.2675s | 2.4413s | 6.7417s | |
15dB | 2.1390s | 2.2119s | 6.7070s | |
20dB | 1.8859s | 1.9688s | 6.4216s | |
White noise | 0dB | 3.4491s | 3.5234s | 6.6548s |
5dB | 2.8229s | 2.9723s | 6.9340s | |
10dB | 2.5765s | 2.6288s | 7.2333s | |
15dB | 2.3393s | 2.4726s | 7.0217s | |
20dB | 1.9912s | 2.0732s | 6.5130s |
Noise type | SNR | Accelerated Proximal Gradient | Proximal Gradient | Interior Point Method |
Babble noise | 0dB | 3.1307s | 3.3139s | 7.2640s |
5dB | 2.7209s | 2.8722s | 7.0281s | |
10dB | 2.3887s | 2.4476s | 6.8677s | |
15dB | 2.2449s | 2.4057s | 6.8233s | |
20dB | 2.0481s | 2.1050s | 6.6695s | |
Destroyer noise | 0dB | 2.8322s | 2.9187s | 6.9363s |
5dB | 2.4799s | 2.5386s | 6.8301s | |
10dB | 2.2675s | 2.4413s | 6.7417s | |
15dB | 2.1390s | 2.2119s | 6.7070s | |
20dB | 1.8859s | 1.9688s | 6.4216s | |
White noise | 0dB | 3.4491s | 3.5234s | 6.6548s |
5dB | 2.8229s | 2.9723s | 6.9340s | |
10dB | 2.5765s | 2.6288s | 7.2333s | |
15dB | 2.3393s | 2.4726s | 7.0217s | |
20dB | 1.9912s | 2.0732s | 6.5130s |
Noise type | SNR | Accelerated Proximal Gradient | Proximal Gradient | Interior Point Method |
Babble noise | 0dB | 0.8681s | 0.9342s | 12.7778s |
5dB | 0.7779s | 0.8346s | 12.5931s | |
10dB | 0.7119s | 0.7730s | 12.2826s | |
15dB | 0.6637s | 0.7199s | 12.0663s | |
20dB | 0.6138s | 0.6703s | 11.7910s | |
Destroyer noise | 0dB | 0.8096s | 0.8760s | 12.4143s |
5dB | 0.7330s | 0.7863s | 12.4028s | |
10dB | 0.6709s | 0.7329s | 12.0540s | |
15dB | 0.6263s | 0.6908s | 11.9282s | |
20dB | 0.5950s | 0.6550 | 11.8206s | |
White noise | 0dB | 0.9592s | 1.0401s | 11.9704s |
5dB | 0.8137s | 0.8761s | 12.5119s | |
10dB | 0.7049s | 0.7656s | 12.8533s | |
15dB | 0.6503s | 0.7136s | 12.3004s | |
20dB | 0.6193s | 0.6818s | 11.9545s |
Noise type | SNR | Accelerated Proximal Gradient | Proximal Gradient | Interior Point Method |
Babble noise | 0dB | 0.8681s | 0.9342s | 12.7778s |
5dB | 0.7779s | 0.8346s | 12.5931s | |
10dB | 0.7119s | 0.7730s | 12.2826s | |
15dB | 0.6637s | 0.7199s | 12.0663s | |
20dB | 0.6138s | 0.6703s | 11.7910s | |
Destroyer noise | 0dB | 0.8096s | 0.8760s | 12.4143s |
5dB | 0.7330s | 0.7863s | 12.4028s | |
10dB | 0.6709s | 0.7329s | 12.0540s | |
15dB | 0.6263s | 0.6908s | 11.9282s | |
20dB | 0.5950s | 0.6550 | 11.8206s | |
White noise | 0dB | 0.9592s | 1.0401s | 11.9704s |
5dB | 0.8137s | 0.8761s | 12.5119s | |
10dB | 0.7049s | 0.7656s | 12.8533s | |
15dB | 0.6503s | 0.7136s | 12.3004s | |
20dB | 0.6193s | 0.6818s | 11.9545s |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0328 | 0.7147 | |
Fixed value | 2.0073 | 0.7032 | ||
Fixed value | 2.0241 | 0.7103 | ||
Unprocessed | 1.8938 | 0.7145 | ||
5 dB | Optimized | 2.4100 | 0.8200 | |
Fixed value | 2.3896 | 0.8107 | ||
Fixed value | 2.3996 | 0.8170 | ||
Unprocessed | 2.2203 | 0.8130 | ||
10 dB | Optimized | 2.7702 | 0.8999 | |
Fixed value | 2.7522 | 0.8918 | ||
Fixed value | 2.7639 | 0.8974 | ||
Unprocessed | 2.5434 | 0.8899 | ||
15dB | Optimized | 3.1247 | 0.9504 | |
Fixed value | 3.0937 | 0.9455 | ||
Fixed value | 3.1144 | 0.9489 | ||
Unprocessed | 2.8556 | 0.9423 | ||
20dB | Optimized | 3.4425 | 0.9767 | |
Fixed value | 3.3898 | 0.9731 | ||
Fixed value | 3.4317 | 0.9757 | ||
Unprocessed | 3.1674 | 0.9734 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0328 | 0.7147 | |
Fixed value | 2.0073 | 0.7032 | ||
Fixed value | 2.0241 | 0.7103 | ||
Unprocessed | 1.8938 | 0.7145 | ||
5 dB | Optimized | 2.4100 | 0.8200 | |
Fixed value | 2.3896 | 0.8107 | ||
Fixed value | 2.3996 | 0.8170 | ||
Unprocessed | 2.2203 | 0.8130 | ||
10 dB | Optimized | 2.7702 | 0.8999 | |
Fixed value | 2.7522 | 0.8918 | ||
Fixed value | 2.7639 | 0.8974 | ||
Unprocessed | 2.5434 | 0.8899 | ||
15dB | Optimized | 3.1247 | 0.9504 | |
Fixed value | 3.0937 | 0.9455 | ||
Fixed value | 3.1144 | 0.9489 | ||
Unprocessed | 2.8556 | 0.9423 | ||
20dB | Optimized | 3.4425 | 0.9767 | |
Fixed value | 3.3898 | 0.9731 | ||
Fixed value | 3.4317 | 0.9757 | ||
Unprocessed | 3.1674 | 0.9734 |
SNR | Method s | PESQ | STOI | |
0 dB | Optimized | 2.1629 | 0.7532 | |
Fixed value | 2.1543 | 0.7448 | ||
Fixed value | 2.1456 | 0.7497 | ||
Unprocessed | 1.9271 | 0.7524 | ||
5 dB | Optimized | 2.5370 | 0.8337 | |
Fixed value | 2.5186 | 0.8267 | ||
Fixed value | 2.5283 | 0.8325 | ||
Unprocessed | 2.2955 | 0.8281 | ||
10 dB | Optimized | 2.8704 | 0.9001 | |
Fixed value | 2.8543 | 0.8933 | ||
Fixed value | 2.8677 | 0.8985 | ||
Unprocessed | 2.6132 | 0.8902 | ||
15dB | Optimized | 3.1914 | 0.9468 | |
Fixed value | 3.1611 | 0.9412 | ||
Fixed value | 3.1876 | 0.9455 | ||
Unprocessed | 2.9256 | 0.9382 | ||
20dB | Optimized | 3.4868 | 0.9737 | |
Fixed value | 3.4427 | 0.9696 | ||
Fixed value | 3.4722 | 0.9726 | ||
Unprocessed | 3.2468 | 0.9697 |
SNR | Method s | PESQ | STOI | |
0 dB | Optimized | 2.1629 | 0.7532 | |
Fixed value | 2.1543 | 0.7448 | ||
Fixed value | 2.1456 | 0.7497 | ||
Unprocessed | 1.9271 | 0.7524 | ||
5 dB | Optimized | 2.5370 | 0.8337 | |
Fixed value | 2.5186 | 0.8267 | ||
Fixed value | 2.5283 | 0.8325 | ||
Unprocessed | 2.2955 | 0.8281 | ||
10 dB | Optimized | 2.8704 | 0.9001 | |
Fixed value | 2.8543 | 0.8933 | ||
Fixed value | 2.8677 | 0.8985 | ||
Unprocessed | 2.6132 | 0.8902 | ||
15dB | Optimized | 3.1914 | 0.9468 | |
Fixed value | 3.1611 | 0.9412 | ||
Fixed value | 3.1876 | 0.9455 | ||
Unprocessed | 2.9256 | 0.9382 | ||
20dB | Optimized | 3.4868 | 0.9737 | |
Fixed value | 3.4427 | 0.9696 | ||
Fixed value | 3.4722 | 0.9726 | ||
Unprocessed | 3.2468 | 0.9697 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0119 | 0.7661 | |
Fixed value | 1.9895 | 0.7519 | ||
Fixed value | 2.0042 | 0.7619 | ||
Unprocessed | 1.6665 | 0.7377 | ||
5 dB | Optimized | 2.3972 | 0.8615 | |
Fixed value | 2.3716 | 0.8492 | ||
Fixed value | 2.3913 | 0.8580 | ||
Unprocessed | 1.9615 | 0.8387 | ||
10 dB | Optimized | 2.8102 | 0.9275 | |
Fixed value | 2.7735 | 0.9183 | ||
Fixed value | 2.7976 | 0.9246 | ||
Unprocessed | 2.2989 | 0.9146 | ||
15dB | Optimized | 3.1973 | 0.9652 | |
Fixed value | 3.1472 | 0.9594 | ||
Fixed value | 3.1844 | 0.9636 | ||
Unprocessed | 2.6442 | 0.9613 | ||
20dB | Optimized | 3.5007 | 0.9858 | |
Fixed value | 3.4286 | 0.9797 | ||
Fixed value | 3.4796 | 0.9826 | ||
Unprocessed | 2.9839 | 0.9845 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0119 | 0.7661 | |
Fixed value | 1.9895 | 0.7519 | ||
Fixed value | 2.0042 | 0.7619 | ||
Unprocessed | 1.6665 | 0.7377 | ||
5 dB | Optimized | 2.3972 | 0.8615 | |
Fixed value | 2.3716 | 0.8492 | ||
Fixed value | 2.3913 | 0.8580 | ||
Unprocessed | 1.9615 | 0.8387 | ||
10 dB | Optimized | 2.8102 | 0.9275 | |
Fixed value | 2.7735 | 0.9183 | ||
Fixed value | 2.7976 | 0.9246 | ||
Unprocessed | 2.2989 | 0.9146 | ||
15dB | Optimized | 3.1973 | 0.9652 | |
Fixed value | 3.1472 | 0.9594 | ||
Fixed value | 3.1844 | 0.9636 | ||
Unprocessed | 2.6442 | 0.9613 | ||
20dB | Optimized | 3.5007 | 0.9858 | |
Fixed value | 3.4286 | 0.9797 | ||
Fixed value | 3.4796 | 0.9826 | ||
Unprocessed | 2.9839 | 0.9845 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0699 | 0.7234 | |
Fixed value | 2.0525 | 0.7129 | ||
Fixed value | 2.0634 | 0.7212 | ||
Unprocessed | 1.8938 | 0.7145 | ||
5 dB | Optimized | 2.4185 | 0.8282 | |
Fixed value | 2.4084 | 0.8195 | ||
Fixed value | 2.4150 | 0.8258 | ||
Unprocessed | 2.2203 | 0.8130 | ||
10 dB | Optimized | 2.7672 | 0.9064 | |
Fixed value | 2.7529 | 0.8996 | ||
Fixed value | 2.7586 | 0.9045 | ||
Unprocessed | 2.5434 | 0.8899 | ||
15dB | Optimized | 3.1187 | 0.9540 | |
Fixed value | 3.0736 | 0.9507 | ||
Fixed value | 3.0790 | 0.9530 | ||
Unprocessed | 2.8556 | 0.9423 | ||
20dB | Optimized | 3.3898 | 0.9785 | |
Fixed value | 3.3703 | 0.9760 | ||
Fixed value | 3.3822 | 0.9775 | ||
Unprocessed | 3.1674 | 0.9734 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0699 | 0.7234 | |
Fixed value | 2.0525 | 0.7129 | ||
Fixed value | 2.0634 | 0.7212 | ||
Unprocessed | 1.8938 | 0.7145 | ||
5 dB | Optimized | 2.4185 | 0.8282 | |
Fixed value | 2.4084 | 0.8195 | ||
Fixed value | 2.4150 | 0.8258 | ||
Unprocessed | 2.2203 | 0.8130 | ||
10 dB | Optimized | 2.7672 | 0.9064 | |
Fixed value | 2.7529 | 0.8996 | ||
Fixed value | 2.7586 | 0.9045 | ||
Unprocessed | 2.5434 | 0.8899 | ||
15dB | Optimized | 3.1187 | 0.9540 | |
Fixed value | 3.0736 | 0.9507 | ||
Fixed value | 3.0790 | 0.9530 | ||
Unprocessed | 2.8556 | 0.9423 | ||
20dB | Optimized | 3.3898 | 0.9785 | |
Fixed value | 3.3703 | 0.9760 | ||
Fixed value | 3.3822 | 0.9775 | ||
Unprocessed | 3.1674 | 0.9734 |
SNR | Method s | PESQ | STOI | |
0 dB | Optimized | 2.2328 | 0.7629 | |
Fixed value | 2.2256 | 0.7602 | ||
Fixed value | 2.2078 | 0.7622 | ||
Unprocessed | 1.9271 | 0.7524 | ||
5 dB | Optimized | 2.5651 | 0.8441 | |
Fixed value | 2.5589 | 0.8414 | ||
Fixed value | 2.5569 | 0.8436 | ||
Unprocessed | 2.2955 | 0.8281 | ||
10 dB | Optimized | 2.8773 | 0.9084 | |
Fixed value | 2.8699 | 0.9056 | ||
Fixed value | 2.8742 | 0.9081 | ||
Unprocessed | 2.6132 | 0.8902 | ||
15dB | Optimized | 3.1775 | 0.9530 | |
Fixed value | 3.1710 | 0.9509 | ||
Fixed value | 3.1732 | 0.9529 | ||
Unprocessed | 2.9256 | 0.9382 | ||
20dB | Optimized | 3.4819 | 0.9768 | |
Fixed value | 3.4375 | 0.9750 | ||
Fixed value | 3.4469 | 0.9766 | ||
Unprocessed | 3.2468 | 0.9697 |
SNR | Method s | PESQ | STOI | |
0 dB | Optimized | 2.2328 | 0.7629 | |
Fixed value | 2.2256 | 0.7602 | ||
Fixed value | 2.2078 | 0.7622 | ||
Unprocessed | 1.9271 | 0.7524 | ||
5 dB | Optimized | 2.5651 | 0.8441 | |
Fixed value | 2.5589 | 0.8414 | ||
Fixed value | 2.5569 | 0.8436 | ||
Unprocessed | 2.2955 | 0.8281 | ||
10 dB | Optimized | 2.8773 | 0.9084 | |
Fixed value | 2.8699 | 0.9056 | ||
Fixed value | 2.8742 | 0.9081 | ||
Unprocessed | 2.6132 | 0.8902 | ||
15dB | Optimized | 3.1775 | 0.9530 | |
Fixed value | 3.1710 | 0.9509 | ||
Fixed value | 3.1732 | 0.9529 | ||
Unprocessed | 2.9256 | 0.9382 | ||
20dB | Optimized | 3.4819 | 0.9768 | |
Fixed value | 3.4375 | 0.9750 | ||
Fixed value | 3.4469 | 0.9766 | ||
Unprocessed | 3.2468 | 0.9697 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0454 | 0.7829 | |
Fixed value | 2.0395 | 0.7721 | ||
Fixed value | 2.0403 | 0.7775 | ||
Unprocessed | 1.6665 | 0.7377 | ||
5 dB | Optimized | 2.4148 | 0.8735 | |
Fixed value | 2.4129 | 0.8638 | ||
Fixed value | 2.4101 | 0.8695 | ||
Unprocessed | 1.9615 | 0.8387 | ||
10 dB | Optimized | 2.8009 | 0.9338 | |
Fixed value | 2.7937 | 0.9261 | ||
Fixed value | 2.7948 | 0.9308 | ||
Unprocessed | 2.2989 | 0.9146 | ||
15dB | Optimized | 3.1967 | 0.9673 | |
Fixed value | 3.1421 | 0.9623 | ||
Fixed value | 3.1514 | 0.9652 | ||
Unprocessed | 2.6442 | 0.9613 | ||
20dB | Optimized | 3.4393 | 0.9864 | |
Fixed value | 3.3930 | 0.9807 | ||
Fixed value | 3.4175 | 0.9823 | ||
Unprocessed | 2.9839 | 0.9845 |
SNR | Methods | PESQ | STOI | |
0 dB | Optimized | 2.0454 | 0.7829 | |
Fixed value | 2.0395 | 0.7721 | ||
Fixed value | 2.0403 | 0.7775 | ||
Unprocessed | 1.6665 | 0.7377 | ||
5 dB | Optimized | 2.4148 | 0.8735 | |
Fixed value | 2.4129 | 0.8638 | ||
Fixed value | 2.4101 | 0.8695 | ||
Unprocessed | 1.9615 | 0.8387 | ||
10 dB | Optimized | 2.8009 | 0.9338 | |
Fixed value | 2.7937 | 0.9261 | ||
Fixed value | 2.7948 | 0.9308 | ||
Unprocessed | 2.2989 | 0.9146 | ||
15dB | Optimized | 3.1967 | 0.9673 | |
Fixed value | 3.1421 | 0.9623 | ||
Fixed value | 3.1514 | 0.9652 | ||
Unprocessed | 2.6442 | 0.9613 | ||
20dB | Optimized | 3.4393 | 0.9864 | |
Fixed value | 3.3930 | 0.9807 | ||
Fixed value | 3.4175 | 0.9823 | ||
Unprocessed | 2.9839 | 0.9845 |
[1] |
Jin-Zan Liu, Xin-Wei Liu. A dual Bregman proximal gradient method for relatively-strongly convex optimization. Numerical Algebra, Control and Optimization, 2021 doi: 10.3934/naco.2021028 |
[2] |
Tengteng Yu, Xin-Wei Liu, Yu-Hong Dai, Jie Sun. Variable metric proximal stochastic variance reduced gradient methods for nonconvex nonsmooth optimization. Journal of Industrial and Management Optimization, 2022, 18 (4) : 2611-2631. doi: 10.3934/jimo.2021084 |
[3] |
Igor Griva, Roman A. Polyak. Proximal point nonlinear rescaling method for convex optimization. Numerical Algebra, Control and Optimization, 2011, 1 (2) : 283-299. doi: 10.3934/naco.2011.1.283 |
[4] |
Yan Gu, Nobuo Yamashita. A proximal ADMM with the Broyden family for convex optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2715-2732. doi: 10.3934/jimo.2020091 |
[5] |
Oliver Jenkinson. Optimization and majorization of invariant measures. Electronic Research Announcements, 2007, 13: 1-12. |
[6] |
Jianjun Zhang, Yunyi Hu, James G. Nagy. A scaled gradient method for digital tomographic image reconstruction. Inverse Problems and Imaging, 2018, 12 (1) : 239-259. doi: 10.3934/ipi.2018010 |
[7] |
Sanming Liu, Zhijie Wang, Chongyang Liu. On convergence analysis of dual proximal-gradient methods with approximate gradient for a class of nonsmooth convex minimization problems. Journal of Industrial and Management Optimization, 2016, 12 (1) : 389-402. doi: 10.3934/jimo.2016.12.389 |
[8] |
Foxiang Liu, Lingling Xu, Yuehong Sun, Deren Han. A proximal alternating direction method for multi-block coupled convex optimization. Journal of Industrial and Management Optimization, 2019, 15 (2) : 723-737. doi: 10.3934/jimo.2018067 |
[9] |
Fan Jiang, Zhongming Wu, Xingju Cai. Generalized ADMM with optimal indefinite proximal term for linearly constrained convex optimization. Journal of Industrial and Management Optimization, 2020, 16 (2) : 835-856. doi: 10.3934/jimo.2018181 |
[10] |
Xia Zhao, Jianping Dou. Bi-objective integrated supply chain design with transportation choices: A multi-objective particle swarm optimization. Journal of Industrial and Management Optimization, 2019, 15 (3) : 1263-1288. doi: 10.3934/jimo.2018095 |
[11] |
Yuan-mei Xia, Xin-min Yang, Ke-quan Zhao. A combined scalarization method for multi-objective optimization problems. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2669-2683. doi: 10.3934/jimo.2020088 |
[12] |
Zhongqiang Wu, Zongkui Xie. A multi-objective lion swarm optimization based on multi-agent. Journal of Industrial and Management Optimization, 2022 doi: 10.3934/jimo.2022001 |
[13] |
Predrag S. Stanimirović, Branislav Ivanov, Haifeng Ma, Dijana Mosić. A survey of gradient methods for solving nonlinear optimization. Electronic Research Archive, 2020, 28 (4) : 1573-1624. doi: 10.3934/era.2020115 |
[14] |
Yanmei Sun, Yakui Huang. An alternate gradient method for optimization problems with orthogonality constraints. Numerical Algebra, Control and Optimization, 2021, 11 (4) : 665-676. doi: 10.3934/naco.2021003 |
[15] |
Cristian Barbarosie, Anca-Maria Toader, Sérgio Lopes. A gradient-type algorithm for constrained optimization with application to microstructure optimization. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1729-1755. doi: 10.3934/dcdsb.2019249 |
[16] |
Shungen Luo, Xiuping Guo. Multi-objective optimization of multi-microgrid power dispatch under uncertainties using interval optimization. Journal of Industrial and Management Optimization, 2021 doi: 10.3934/jimo.2021208 |
[17] |
Yuan Shen, Wenxing Zhang, Bingsheng He. Relaxed augmented Lagrangian-based proximal point algorithms for convex optimization with linear constraints. Journal of Industrial and Management Optimization, 2014, 10 (3) : 743-759. doi: 10.3934/jimo.2014.10.743 |
[18] |
Yan Gu, Nobuo Yamashita. Alternating direction method of multipliers with variable metric indefinite proximal terms for convex optimization. Numerical Algebra, Control and Optimization, 2020, 10 (4) : 487-510. doi: 10.3934/naco.2020047 |
[19] |
Jie Shen, Jian Lv, Fang-Fang Guo, Ya-Li Gao, Rui Zhao. A new proximal chebychev center cutting plane algorithm for nonsmooth optimization and its convergence. Journal of Industrial and Management Optimization, 2018, 14 (3) : 1143-1155. doi: 10.3934/jimo.2018003 |
[20] |
Zhiyuan Wen, Meirong Zhang. On the optimization problems of the principal eigenvalues of measure differential equations with indefinite measures. Discrete and Continuous Dynamical Systems - B, 2020, 25 (8) : 3257-3274. doi: 10.3934/dcdsb.2020061 |
2020 Impact Factor: 1.801
Tools
Metrics
Other articles
by authors
[Back to Top]