Combined Sparse Regularization for Nonlinear Adaptive Filters

Nonlinear adaptive filters often show some sparse behavior due to the fact that not all the coefficients are equally useful for the modeling of any nonlinearity. Recently, a class of proportionate algorithms has been proposed for nonlinear filters to leverage sparsity of their coefficients. However, the choice of the norm penalty of the cost function may be not always appropriate depending on the problem. In this paper, we introduce an adaptive combined scheme based on a block-based approach involving two nonlinear filters with different regularization that allows to achieve always superior performance than individual rules. The proposed method is assessed in nonlinear system identification problems, showing its effectiveness in taking advantage of the online combined regularization.

[1]  R. Tibshirani.  Regression Shrinkage and Selection via the Lasso , 1996 .

[2]  Danilo Comminiello,et al.  Group sparse regularization for deep neural networks , 2016, Neurocomputing.

[3]  Jie Chen,et al.  Transient Performance Analysis of Zero-Attracting LMS , 2016, IEEE Signal Processing Letters.

[4]  Alfred O. Hero,et al.  Sparse LMS for system identification , 2009, 2009 IEEE International Conference on Acoustics, Speech and Signal Processing.

[5]  Danilo Comminiello,et al.  Functional Link Adaptive Filters for Nonlinear Acoustic Echo Cancellation , 2013, IEEE Transactions on Audio, Speech, and Language Processing.

[6]  ChakrabortyMrityunjoy,et al.  Improving the performance of the PNLMS algorithm using l1 norm regularization , 2016 .

[7]  G. L. Sicuranza,et al.  A Generalized FLANN Filter for Nonlinear Active Noise Control , 2011, IEEE Transactions on Audio, Speech, and Language Processing.

[8]  Danilo Comminiello,et al.  Full proportionate functional link adaptive filters for nonlinear acoustic echo cancellation , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[9]  H. Vincent Poor,et al.  Sparse Channel Estimation and Equalization for OFDM-Based Underwater Cooperative Systems With Amplify-and-Forward Relaying , 2016, IEEE Transactions on Signal Processing.

[10]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[11]  Danilo Comminiello,et al.  Sparse functional link adaptive filter using an ℓ1-norm regularization , 2018, 2018 IEEE International Symposium on Circuits and Systems (ISCAS).

[12]  Nithin V. George,et al.  Design of Adaptive Exponential Functional Link Network-Based Nonlinear Filters , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[13]  José Antonio Apolinário,et al.  ${{\bf L}_1}$-Constrained Normalized LMS Algorithms for Adaptive Beamforming , 2015, IEEE Transactions on Signal Processing.

[14]  Mrityunjoy Chakraborty,et al.  Improving the Performance of the PNLMS Algorithm Using $l_1$ Norm Regularization , 2016, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[15]  Jacob Benesty,et al.  Acoustic MIMO Signal Processing (Signals and Communication Technology) , 2006 .

[16]  Danilo Comminiello,et al.  Introducing complex functional link polynomial filters , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[17]  Georgios B. Giannakis,et al.  Nonparametric Basis Pursuit via Sparse Kernel-Based Learning: A Unifying View with Advances in Blind Methods , 2013, IEEE Signal Processing Magazine.

[18]  Tareq Y. Al-Naffouri,et al.  Efficient Coordinated Recovery of Sparse Channels in Massive MIMO , 2014, IEEE Transactions on Signal Processing.

[19]  Georgios B. Giannakis,et al.  Sparse Volterra and Polynomial Regression Models: Recoverability and Estimation , 2011, IEEE Transactions on Signal Processing.

[20]  Yuanming Shi,et al.  Robust Group Sparse Beamforming for Multicast Green Cloud-RAN With Imperfect CSI , 2015, IEEE Transactions on Signal Processing.

[21]  Dong Ni,et al.  Relational-Regularized Discriminative Sparse Learning for Alzheimer’s Disease Diagnosis , 2017, IEEE Transactions on Cybernetics.

[22]  Danilo Comminiello,et al.  Nonlinear Acoustic Echo Cancellation Based on Sparse Functional Link Representations , 2014, IEEE/ACM Transactions on Audio, Speech, and Language Processing.

[23]  Ali H. Sayed,et al.  Combinations of Adaptive Filters: Performance and convergence properties , 2021, IEEE Signal Processing Magazine.

[24]  Danilo Comminiello,et al.  A block-based combined scheme exploiting sparsity in nonlinear acoustic echo cancellation , 2016, 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP).

[25]  Danilo Comminiello,et al.  Combined nonlinear filtering architectures involving sparse functional link adaptive filters , 2017, Signal Process..

[26]  Sridhar Krishnan,et al.  Two-pass ℓp-regularized least-squares algorithm for compressive sensing , 2017, 2017 IEEE International Symposium on Circuits and Systems (ISCAS).

[27]  Weifeng Liu,et al.  An Information Theoretic Approach of Designing Sparse Kernel Adaptive Filters , 2009, IEEE Transactions on Neural Networks.

[28]  Danilo Comminiello,et al.  Combined adaptive beamforming schemes for nonstationary interfering noise reduction , 2013, Signal Process..