Published papers

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(1) 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.

We present image edge detection using the total variation functional and morphological methods. First, we derive the total variation functional from first principles and vector gradient method. The total variation functional is then minimized using the Euler-Lagrange optimization method. The steady state equation which results from the minimization of the total variation functional is then used as an anisotrpic filter on images. While the total variation method has proven to be a better edge detector than the Marr-Hildreth method, it also segments the image into regions delineated by strong edges. To achieve results similar to the Marr-Hildreth method, we apply morphological considerations. We develop new operations based on erosion, dilation, opening and closing to achieve morphological edge detection of total variation filtered images.

We present a unified analytic tool named variable-metric adaptive projected subgradient method (V-APSM) that encompasses the important family of adaptive variable-metric projection algorithms. The family includes the transform-domain adaptive filter, the Newton-method-based adaptive filters such as quasi-Newton, the proportionate adaptive filter, and the Krylov-proportionate adaptive filter. We provide a rigorous analysis of V-APSM regarding several invaluable properties including monotone approximation, which indicates stable tracking capability, and convergence to an asymptotically optimal point. Small metric-fluctuations are the key assumption for the analysis. Numerical examples show (i) the robustness of V-APSM against violation of the assumption and (ii) the remarkable advantages over its constant-metric counterpart for colored and nonstationary inputs under noisy situations. Copyright (C) 2009 M. Yukawa and I. Yamada. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 Adaptively 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 convergence speed as fast as the proportionate affine projection algorithm.

This paper presents an efficient acoustic echo cancellation (AEC) scheme based on reduced-rank interpolated adaptive filtering with parallel decimation, motivated by diversity techniques developed in wireless communications. The proposed scheme jointly optimizes an interpolation filter, a decimator unit and a reduced-rank filter in such a way that the output error is minimized, leading to very substantial improvements of the mean squared error performance. With a practical choice of parameters in AEC, the total computational complexity of the proposed scheme is approximately half of the one of the NLMS algorithm. The numerical examples demonstrate that the proposed algorithm offers very significant reduction in mean squared error performance.

The contribution of this paper is twofold. We first clarify geometrically an inherent difference in convergence speed between two adaptive algorithms, projected-NLMS (PNLMS) and constrained-NLMS (CNLMS), both of which are widely used for linearly constrained adaptive filtering problems. A simple geometric interpretation suggests that CNLMS converges faster than PNLMS especially in the challenging situations of the adaptive beamforming where there exist spatially-correlated interferences (i.e., interferences that have small angular separation with the desired signal). To enhance the advantage of CNLMS in convergence speed while keeping linear computational complexity, we then propose an efficient adaptive beamformer that utilizes multiple data at each iteration by extending the constrained parallel projection algorithm to complex cases. The simulation results demonstrate that the proposed beamformer exhibits even faster convergence than the constrained affine projection algorithm (CAPA) as well as CNLMS.

This paper indicates that an appropriate design of metric leads to significant improvements in the, adaptive projected subgradient method (APSM), which unifies a wide range of projection-based algorithms [including normalized least mean square (NLMS) and affine projection algorithm (APA)]. The key is to incorporate a priori (or a posteriori) information on characteristics of an estimandum, a system to be estimated, into the metric design. We propose a family of efficient adaptive filtering algorithms based on a parallel use of quadratic-metric projection, which assigns every point to the nearest point in a closed convex set in a quadratic-metric sense. We present two versions: 1) constant-metric and 2) variable-metric, i.e., the metric function employed is 1) constant and 2) variable among iterations. As a constant-metric version, adaptive parallel quadratic-metric projection (APQP) and adaptive parallel min-max quadratic-metric projection (APMQP) algorithms are naturally derived by APSM, being endowed with desirable properties such as convergence to a point optimal in asymptotic sense. As a variable-metric version, adaptive parallel variable-metric projection (APVP) algorithm is derived by a generalized APSM, enjoying an extended monotone property at each iteration: By employing a simple quadratic-metric, the computational complexity of the proposed algorithms is kept linear with respect to the filter length. Numerical examples demonstrate the remarkable advantages of the proposed algorithms in an application to acoustic echo cancellation.

In this paper, we propose a novel adaptive filtering algorithm named adaptive parallel variable-metric projection (APVP) algorithm, which includes the proportionate normalized least mean square (PNLMS) algorithm as its special example. The proposed algorithm is based on parallel projection (onto multiple closed convex sets) with time-varying metrics. A convergence analysis of the proposed algorithm is presented with the aid of the adaptive projected subgradient method. Numerical examples demonstrate that the proposed algorithm realizes echo cancellation superior to the conventional algorithms.

The adaptive projected subgradient method offers a unified mathematical perspective for the adaptive (setmember-ship / set-theoretic) filtering schemes. In this paper, we introduce an overview of its recent theoretical advances and successful applications to robust signal processing problems including the stereo acoustic echo canceling, the MAI suppression in DS/CIDMA receivers, and the robust adaptive beamforming with array antenna systems.

This paper proposes a robust reduced-rank scheme for adaptive beamforming based on joint iterative optimization (JIO) of adaptive filters. The novel scheme is designed according to the constant modulus (CM) criterion subject to different constraints. The proposed scheme consists of a bank of full-rank adaptive filters that forms the transformation matrix, and an adaptive reduced-rank filter that operates at the output of the bank of filters to estimate the desired signal. We describe the proposed scheme for both the direct-form processor (DFP) and the generalized sidelobe canceller (GSC) structures. For each structure, we derive stochastic gradient (SG) and recursive least squares (RLS) algorithms for its adaptive implementation. The Gram-Schmidt (GS) technique is applied to the adaptive algorithms for reformulating the transformation matrix and improving the performance. An automatic rank selection technique is developed and employed to determine the most adequate rank for the derived algorithms. A detailed complexity study and a convexity analysis are carried out. Simulation results show that the proposed algorithms outperform the existing full-rank and reduced-rank methods in convergence and tracking performance.

In this paper, we present an efficient downlink power control scheme, for wireless networks, based on two key ideas: (i) global-local fixed-point-approximation technique (GLOFPAT) and (ii) bottleneck removal criterion (BRC). The proposed scheme copes with all scenarios including infeasible case where no power allocation can provide all multiple accessing users with target quality of service (QoS). For feasible case, the GLOFPAT efficiently computes a desired power allocation which corresponds to the allocation achieved by conventional algorithms. For infeasible case, the GLOFPAT offers valuable information to detect bottleneck users, to be removed based on the BRC, which deteriorate overall QoS. The GLOFPAT is a mathematically-sound distributed algorithm approximating desired power allocation as a unique fixed-point of an isotone mapping. The unique fixed-point of the global mapping is iteratively computed by fixed-point-approximations of multiple distributed local mappings, which can be computed in parallel by base stations respectively. For proper detection of bottleneck users, complete analysis of the GLOFPAT is presented with aid of the Tarski's fixed-point theorem. Extensive simulations demonstrate that the proposed scheme converges faster than the conventional algorithm and successfully increases the number of happy users receiving target QoS.

This paper proposes a novel heuristic approach to the infeasible power control problem [i.e., no power allocation can provide users with specified quality of service (QoS)] in wireless communication systems. In such infeasible cases, it has been in great demand to increase the number of accepted users (i.e., users provided with the specified QoS) by certain distributed algorithms, which require no communication among base stations (BSs).The number of accepted users is often suppressed by a small number of users in severe environments, hence removing such users obviously helps many other users be accepted. The proposed algorithm, which is fully distributed, detects and removes such users based on simple criteria including: (a) the QoS is below the necessary level, and (b) the BS is already transmitting with the maximum possible power to the user. Simulation results demonstrate that the proposed algorithm significantly increases the number of accepted users with low computational complexity.

We propose a novel kernel adaptive filtering algorithm that selectively updates a few coefficients at each iteration by projecting the current filter onto the zero instantaneous-error hyperplane along a certain time-dependent affine subspace. Coherence is exploited for selecting the coefficients to be updated as well as for measuring the novelty of new data. The proposed algorithm is a natural extension of the normalized kernel least mean squares algorithm operating iterative hyperplane projections in a reproducing kernel Hilbert space. The proposed algorithm enjoys low computational complexity. Numerical examples indicate high potential of the proposed algorithm.

This paper presents an automatic kernel weighting technique for multikernel adaptive filtering. The full potential of the multikernel adaptive filtering approach can only be achieved when the kernels are weighted appropriately. The proposed technique balances the dominance of the kernels by making the mean eigenvalues of their associated autocorrelation matrices be equal to each other. The overall complexity of the proposed approach is low because the mean eigenvalues can be computed efficiently. The numerical results verify that the proposed technique balances the coefficient updates and yields reasonable performance.

We propose a distributed optimization framework to generate accurate sparse estimates while allowing an algorithmic solution with guaranteed convergence to a global minimizer. To this end, the proposed problem formulation involves the minimax concave penalty together with an additional penalty called consensus promoting penalty (CPP) that induces convexity to the resulting optimization problem. This problem is solved with an exact first-order proximal gradient algorithm, which employs a pair of proximity operators and is referred to as the distributed proximal and debiasing-gradient (DPD) method. Numerical examples show that CPP not only convexifies the whole cost function, but it also accelerates the convergence speed with respect to the system mismatch.

We propose a promising framework for distributed sparse optimization based on weakly convex regularizers. More specifically, we pose two distributed optimization problems to recover sparse signals in networks. The first problem formulation relies on statistical properties of the signals, and it uses an approximate Moreau enhanced penalty. In contrast, the second formulation does not rely on any statistical assumptions, and it uses an additional consensus promoting penalty (CPP) that convexifies the cost function over the whole network. To solve both problems, we propose a distributed proximal debiasing-gradient (DPD) method, which uses the exact first-order proximal gradient algorithm. The DPD method features a pair of proximity operators that play complementary roles: one sparsifies the estimate, and the other reduces the bias caused by the sparsification. Owing to the overall convexity of the whole cost functions, the proposed method guarantees convergence to a global minimizer, as demonstrated by numerical examples. In addition, the use of CPP improves the convergence speed significantly.

This paper presents a novel training-based adaptive linear receiver to suppress the multiple access interference, which has been one of the central issues in DS/CDMA wireless communication systems. The proposed receiver is derived by extending the Krylov-proportionate normalized least-mean-square (KPNLMS) algorithm to complex-valued signals. The key idea KPNLMS is (a) sparse representation of the minimum mean square error (MMSE) receiver based on a certain Krylov subspace, (b) use of the 'sparsity' for fast convergence, and (c) simplification to keep linear complexity per iteration. To clarify the convergence properties of the proposed receiver, its derivation front the variable-metric version of the adaptive projected subgradient method (V-APSM) is presented. The simulation results demonstrate the efficacy of the proposed receiver.

We propose a novel adaptive beamforming algorithm based on the multi-domain adaptive filtering approach (Yukawa et al., 2009). The proposed algorithm exploits, as a soft constraint in a transform domain, the information that the array responses to the interference direction should be sufficiently low. Additional operations introduced are linear transformations and a metric projection onto a closed ball that bounds the energy of the transformed weight vector. The efficacy of the proposed algorithm is shown by simulations.

This paper presents a new approach to efficient acoustic echo cancellation (AEC) based on reduced-rank adaptive filtering equipped with selective-decimation and adaptive interpolation. We propose a novel structure of an AEC scheme that jointly optimizes an interpolation filter, a decimation unit, and a reduced-rank filter. With a practical choice of parameters in AEC, the total computational complexity of the proposed reduced-rank scheme with the normalized least mean square (NLMS) algorithm is approximately half of that of the full-rank NLMS algorithm. We discuss the convergence properties of the proposed scheme and present a convergence condition. First, we examine the performance of the proposed scheme in a single-talk situation with an error-minimization criterion adopted in the decimation selection. Second, we investigate the potential of the proposed scheme in a double-talk situation by employing an ideal decimation selection. In addition to mean squared error (MSE) and power spectrum analysis of the echo estimation error, subjective assessments based on absolute category rating are performed, and the results demonstrate that the proposed structure provides significant improvements compared to the full-rank NLMS algorithm.

A novel dictionary dividing scheme for online non-linear estimation algorithms with multiscale Gaussians is pro-posed to perform a projection in an appropriate reproducing kernel Hilbert space. The proposed dictionary dividing strategy mitigates the in equivalence of the norm of multiscale Gaussians, which leads to degradations of adaptation speed for certain Gaussians. Based on a Hilbertian projection with the dictionary dividing strategy, a fast nonlinear estimation algorithm, which adapts scales and centers of Gaussians as well as its heights, is presented. The numerical example shows that using the Hilber-tian projection with the proposed dictionary dividing scheme ameliorates the adaptation speed of Gaussian heights.