Conference Paper

# An improved proportionate NLMS algorithm based on the l0 norm

Telecommun. Dept., Univ. Politeh. of Bucharest, Bucharest, Romania

DOI: 10.1109/ICASSP.2010.5495903 Conference: Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on Source: IEEE Xplore

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**ABSTRACT:**In this paper, we propose a novel adaptive filtering algorithm based on an iterative use of (i) the proximity operator and (ii) the parallel variable-metric projection. Our time-varying cost function is a weighted sum of squared distances (in a variable-metric sense) plus a possibly nonsmooth penalty term, and the proposed algorithm is derived along the idea of proximal forward-backward splitting in convex analysis. For application to sparse-system identification problems, we employ the (weighted) ℓ<sub>1</sub> norm as the penalty term, leading to a time-varying soft-thresholding operator. As the simple example of the proposed algorithm, we present the variable-metric affine projection algorithm composed with the time-varying soft-thresholding operator. Numerical examples demonstrate that the proposed algorithms notably outperform their counterparts without soft-thresholding both in convergence speed and steady-state mismatch, while the extra computational complexity due to the additional soft-thresholding is negligibly low.Acoustics Speech and Signal Processing (ICASSP), 2010 IEEE International Conference on; 04/2010 · 4.63 Impact Factor -
##### Conference Paper: Acceleration of adaptive proximal forward-backward splitting method and its application to sparse system identification

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**ABSTRACT:**In this paper, we propose an acceleration technique of the adaptive filtering scheme called adaptive proximal forward-backward splitting method. For accelerating the convergence rate, the proposed method includes a step to shift the current estimate in the direction of the difference between the current and previous estimates based on the Fast Iterative Shrinkage/Thresholding Algorithm (FISTA). The computational complexity for this additional step is fairly low compared to the overall complexity of the algorithm. As an example of the proposed method, we derive an acceleration of the composition of the Adoptively Weighted Soft-Thresholding (AWST) operator and the exponentially weighted adaptive parallel projection. AWST shrinks the estimated filter coefficients to zero for exploiting the sparsity of the system to be estimated and the exponentially weighted adaptive parallel projection algorithm realizes high accuracy by utilizing all available information at each iteration. This accelerated method improves the steady-state mismatch drastically with its con vergence speed as fast as the proportionate affine projection algorithm.Acoustics, Speech and Signal Processing (ICASSP), 2011 IEEE International Conference on; 06/2011 · 4.63 Impact Factor

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