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Signal Processing, IEEE Transactions on

Issue 16 • Date Aug.15, 2014

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  • [Front cover]

    Page(s): C1
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  • IEEE Transactions on Signal Processing publication information

    Page(s): C2
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  • Table of Contents

    Page(s): 4035 - 4036
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  • Table of Contents

    Page(s): 4037 - 4038
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  • Towards the Asymptotic Sum Capacity of the MIMO Cellular Two-Way Relay Channel

    Page(s): 4039 - 4051
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4486 KB) |  | HTML iconHTML  

    In this paper, we consider the transceiver and relay design for the multiple-input multiple-output (MIMO) cellular two-way relay channel (cTWRC), where a multi-antenna base station (BS) exchanges information with multiple multiantenna mobile stations via a multi-antenna relay station (RS). We propose a novel two-way relaying scheme to approach the sum capacity of the MIMO cTWRC. A key contribution of this work is a new nonlinear lattice-based precoding technique to precompensate the interstream interference, so as to achieve efficient interference-free lattice decoding at the relay. We derive sufficient conditions for the proposed scheme to asymptotically achieve the sum capacity of the MIMO cTWRC in the high signal-to-noise ratio (SNR) regime. To fully exploit the potential of the proposed scheme, we also investigate the optimal power allocation at the BS and the RS to maximize the weighted sum-rate of the MIMO cTWRC in the general SNR regime. It is shown that the problem can be formulated as a monotonic program, and a polyblock outer approximation algorithm is developed to find the globally optimal solution with guaranteed convergence. We demonstrate by numerical results that the proposed scheme significantly outperforms the existing schemes and closely approaches the sum capacity of the MIMO cTWRC in the high SNR regime. View full abstract»

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  • Distributed Hybrid Power State Estimation Under PMU Sampling Phase Errors

    Page(s): 4052 - 4063
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4216 KB) |  | HTML iconHTML  

    Phasor measurement units (PMUs) have the advantage of providing direct measurements of power states. However, as the number of PMUs in a power system is limited, the traditional supervisory control and data acquisition (SCADA) system cannot be replaced by the PMU-based system overnight. Therefore, hybrid power state estimation taking advantage of both systems is important. As experiments show that sampling phase errors among PMUs are inevitable in practical deployment, this paper proposes a distributed power state estimation algorithm under PMU phase errors. The proposed distributed algorithm only involves local computations and limited information exchange between neighboring areas, thus alleviating the heavy communication burden compared to the centralized approach. Simulation results show that the performance of the proposed algorithm is very close to that of centralized optimal hybrid state estimates without sampling phase error. View full abstract»

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  • Estimation of Amplitude, Phase and Unbalance Parameters in Three-phase Systems: Analytical Solutions, Efficient Implementation and Performance Analysis

    Page(s): 4064 - 4076
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3305 KB) |  | HTML iconHTML  

    This paper focuses on the estimation of the instantaneous amplitude, phase, and unbalance parameters in three-phase power systems. Due to the particular structure of three-phase systems, we demonstrate that the maximum-likelihood estimates (MLEs) of the unknown parameters have simple closed-form expressions and can be easily implemented without matrix algebra libraries. We also derive and analyze the Cramer-Rao Bounds (CRBs) for the considered estimation problem. The performance of the proposed approach is evaluated using synthetic signals compliant with the IEEE Standard C37.118. Simulation results show that the proposed estimators outperform other techniques and reach the CRB under certain conditions. View full abstract»

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  • Tomlinson–Harashima Precoding for Multiuser MIMO Systems With Quantized CSI Feedback and User Scheduling

    Page(s): 4077 - 4090
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3790 KB) |  | HTML iconHTML  

    This paper studies the sum rate performance of a low complexity quantized CSI-based Tomlinson-Harashima (TH) precoding scheme for downlink multiuser MIMO transmission, employing greedy user selection. The asymptotic distribution of the output-signal-to-interference-plus-noise ratio of each selected user and the asymptotic sum rate as the number of users K grows large are derived by using extreme value theory. For fixed finite signal-to-noise ratios and a finite number of transmit antennas nT, we prove that as K grows large, the proposed approach can achieve the optimal sum rate scaling of the MIMO broadcast channel. We also prove that, if we ignore the precoding loss, the average sum rate of this approach converges to the average sum capacity of the MIMO broadcast channel. Our results provide insights into the effect of multiuser interference caused by quantized CSI on the multiuser diversity gain. View full abstract»

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  • Relabeling and Summarizing Posterior Distributions in Signal Decomposition Problems When the Number of Components is Unknown

    Page(s): 4091 - 4104
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2439 KB) |  | HTML iconHTML  

    This paper addresses the problems of relabeling and summarizing posterior distributions that typically arise, in a Bayesian framework, when dealing with signal decomposition problems with an unknown number of components. Such posterior distributions are defined over union of subspaces of differing dimensionality and can be sampled from using modern Monte Carlo techniques, for instance, the increasingly popular RJ-MCMC method. No generic approach is available, however, to summarize the resulting variable-dimensional samples and extract from them component-specific parameters. We propose a novel approach, named Variable-dimensional Approximate Posterior for Relabeling and Summarizing (VAPoRS), to this problem, which consists of approximating the posterior distribution of interest by a “simple”-but still variable-dimensional-parametric distribution. The distance between the two distributions is measured using the Kullback-Leibler divergence, and a Stochastic EM-type algorithm, driven by the RJ-MCMC sampler, is proposed to estimate the parameters. Two signal decomposition problems are considered to show the capability of VAPoRS both for relabeling and for summarizing variable dimensional posterior distributions: the classical problem of detecting and estimating sinusoids in white Gaussian noise on the one hand, and a particle counting problem motivated by the Pierre Auger project in astrophysics on the other hand. View full abstract»

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  • Compressive Shift Retrieval

    Page(s): 4105 - 4113
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2809 KB) |  | HTML iconHTML  

    The classical shift retrieval problem considers two signals in vector form that are related by a shift. This problem is of great importance in many applications and is typically solved by maximizing the cross-correlation between the two signals. Inspired by compressive sensing, in this paper, we seek to estimate the shift directly from compressed signals. We show that under certain conditions, the shift can be recovered using fewer samples and less computation compared to the classical setup. We also illustrate the concept of superresolution for shift retrieval. Of particular interest is shift estimation from Fourier coefficients. We show that under rather mild conditions only one Fourier coefficient suffices to recover the true shift. View full abstract»

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  • Deep Scattering Spectrum

    Page(s): 4114 - 4128
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3815 KB) |  | HTML iconHTML  

    A scattering transform defines a locally translation invariant representation which is stable to time-warping deformation. It extends MFCC representations by computing modulation spectrum coefficients of multiple orders, through cascades of wavelet convolutions and modulus operators. Second-order scattering coefficients characterize transient phenomena such as attacks and amplitude modulation. A frequency transposition invariant representation is obtained by applying a scattering transform along log-frequency. State-the-of-art classification results are obtained for musical genre and phone classification on GTZAN and TIMIT databases, respectively. View full abstract»

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  • Multitask Diffusion Adaptation Over Networks

    Page(s): 4129 - 4144
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4862 KB) |  | HTML iconHTML  

    Adaptive networks are suitable for decentralized inference tasks. Recent works have intensively studied distributed optimization problems in the case where the nodes have to estimate a single optimum parameter vector collaboratively. However, there are many important applications that are multitask-oriented in the sense that there are multiple optimum parameter vectors to be inferred simultaneously, in a collaborative manner, over the area covered by the network. In this paper, we employ diffusion strategies to develop distributed algorithms that address multitask problems by minimizing an appropriate mean-square error criterion with l2-regularization. The stability and performance of the algorithm in the mean and mean-square error sense are analyzed. Simulations are conducted to verify the theoretical findings, and to illustrate how the distributed strategy can be used in several useful applications related to target localization and hyperspectral data unmixing. View full abstract»

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  • Ramanujan Sums in the Context of Signal Processing—Part I: Fundamentals

    Page(s): 4145 - 4157
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3640 KB) |  | HTML iconHTML  

    The famous mathematician S. Ramanujan introduced a summation in 1918, now known as the Ramanujan sum cq(n). For any fixed integer q, this is a sequence in n with periodicity q. Ramanujan showed that many standard arithmetic functions in the theory of numbers, such as Euler's totient function φ(n) and the Möbius function μ(n), can be expressed as linear combinations of cq(n), 1 ≤ q ≤ ∞. In the last ten years, Ramanujan sums have aroused some interest in signal processing. There is evidence that these sums can be used to extract periodic components in discrete-time signals. The purpose of this paper and the companion paper (Part II) is to develop this theory in detail. After a brief review of the properties of Ramanujan sums, the paper introduces a subspace called the Ramanujan subspace Sq and studies its properties in detail. For fixed q, the subspace Sq includes an entire family of signals with properties similar to cq(n). These subspaces have a simple integer basis defined in terms of the Ramanujan sum cq(n) and its circular shifts. The projection of arbitrary signals onto these subspaces can be calculated using only integer operations. Linear combinations of signals belonging to two or more such subspaces follows certain specific periodicity patterns, which makes it easy to identify periods. In the companion paper (Part II), it is shown that arbitrary finite duration signals can be decomposed into a finite sum of orthogonal projections onto Ramanujan subspaces. View full abstract»

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  • Ramanujan Sums in the Context of Signal Processing—Part II: FIR Representations and Applications

    Page(s): 4158 - 4172
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3393 KB) |  | HTML iconHTML  

    The mathematician Ramanujan introduced a summation in 1918, now known as the Ramanujan sum cq(n). In a companion paper (Part I), properties of Ramanujan sums were reviewed, and Ramanujan subspaces Sq introduced, of which the Ramanujan sum is a member. In this paper, the problem of representing finite duration (FIR) signals based on Ramanujan sums and spaces is considered. First, it is shown that the traditional way to solve for the expansion coefficients in the Ramanujan-sum expansion does not work in the FIR case. Two solutions are then developed. The first one is based on a linear combination of the first N Ramanujan-sums (with N being the length of the signal). The second solution is based on Ramanujan subspaces. With q1, q2,..., qK denoting the divisors of N; it is shown that x(n) can be written as a sum of K signals xqi (n) ∈ Sqi. Furthermore, the ith signal xqi (n) has period qi, and any pair of these periodic components is orthogonal. The components xqi (n) can be calculated as orthogonal projections of x(n) onto Ramanujan spaces Sqi. Then, the Ramanujan Periodic Transform (RPT) is defined based on this, and is useful to identify hidden periodicities. It is shown that the projection matrices (which compute xqi (n) from x(n)) are integer matrices except for an overall scale factor. The calculation of projections is therefore rendered easy. To estimate internal periods N <; N of x(n), one only needs to know which projection energies are nonzero. View full abstract»

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  • Efficient Hardware Architecture for Sparse Coding

    Page(s): 4173 - 4186
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3276 KB) |  | HTML iconHTML  

    Sparse coding encodes natural stimuli using a small number of basis functions known as receptive fields. In this work, we design custom hardware architectures for efficient and high-performance implementations of a sparse coding algorithm called the sparse and independent local network (SAILnet). A study of the neuron spiking dynamics uncovers important design considerations involving the neural network size, target firing rate, and neuron update step size. Optimal tuning of these parameters keeps the neuron spikes sparse and random to achieve the best image fidelity. We investigate practical hardware architectures for SAILnet: a bus architecture that provides efficient neuron communications, but results in spike collisions; and a ring architecture that is more scalable, but causes neuron misfires. We show that the spike collision rate is reduced with a sparse spiking neural network, so an arbitration-free bus architecture can be designed to tolerate collisions without the need of arbitration. To reduce neuron misfires, we design a latent ring architecture to damp the neuron responses for an improved image fidelity. The bus and the ring architecture can be combined in a hybrid architecture to achieve both high throughput and scalability. The three architectures are synthesized and place-and-routed in a 65 nm CMOS technology. The proof-of-concept designs demonstrate a high sparse coding throughput up to 952 M pixels per second at an energy consumption of 0.486 nJ per pixel. View full abstract»

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  • Sum-Rate Maximization for Active Channels With Unequal Subchannel Noise Powers

    Page(s): 4187 - 4198
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    In this paper, an active channel, between a source and a destination, refers to a parallel channel where the source transmits power over different subchannels as well as the powers of the subchannels can be adjusted. We herein study the sum-rate maximization for an active channel subject to two constraints, one on the source total transmit power and one on the total channel power. Although this maximization is not convex, we use Karush-Kuhn-Tucker (KKT) conditions to develop a computationally efficient algorithm for optimal source and channel power allocation. To do so, we first show how KKT conditions can be used to determine the number of subchannels that can be active in order for the source power constraint to be feasible. Indeed, we show that not all subchannels but only a subset of them may receive transmit power from the source. Then, for any feasible number of active subchannels, we obtain the optimal source power allocation. In fact, we prove that for any feasible number of active subchannels, there is only one or two solutions for the optimal source power allocation. As such, the optimal solution can be obtained by comparing a finite number of points in the feasible set and by introducing the point, which yields the best sum-rate performance, as the optimal solution. Our analysis and simulation results show that active channels can offer a significantly higher sum-rate compared to their passive counterparts, which rely on water-filling scheme for source power allocation across subchannels. View full abstract»

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  • Bayesian Estimation of Clean Speech Spectral Coefficients Given a Priori Knowledge of the Phase

    Page(s): 4199 - 4208
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    While most short-time discrete Fourier transform-based single-channel speech enhancement algorithms only modify the noisy spectral amplitude, in recent years the interest in phase processing has increased in the field. The goal of this paper is twofold. First, we derive Bayesian probability density functions and estimators for the clean speech phase when different amounts of prior knowledge about the speech and noise amplitudes is given. Second, we derive a joint Bayesian estimator of the clean speech amplitudes and phases, when uncertain a priori knowledge on the phase is available. Instrumental measures predict that by incorporating uncertain prior information of the phase, the quality and intelligibility of processed speech can be improved both over traditional phase insensitive approaches, and approaches that treat prior information on the phase as deterministic. View full abstract»

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  • Sparse Recovery of Streaming Signals Using \ell _1 -Homotopy

    Page(s): 4209 - 4223
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    Most of the existing sparse-recovery methods assume a static system: the signal is a finite-length vector for which a fixed set of measurements and sparse representation are available and an l1 problem is solved for the reconstruction. However, the same representation and reconstruction framework is not readily applicable in a streaming system: the signal changes over time, and it is measured and reconstructed sequentially over small intervals. This is particularly desired when dividing signals into disjoint blocks and processing each block separately is infeasible or inefficient. In this paper, we discuss two streaming systems and a new homotopy algorithm for quickly solving the associated l1 problems: 1) recovery of smooth, time-varying signals for which, instead of using block transforms, we use lapped orthogonal transforms for sparse representation and 2) recovery of sparse, time-varying signals that follows a linear dynamic model. For both systems, we iteratively process measurements over a sliding interval and solve a weighted l1-norm minimization problem for estimating sparse coefficients. Since we estimate overlapping portions of the signal while adding and removing measurements, instead of solving a new l1 program as the system changes, we use available signal estimates as starting point in a homotopy formulation and update the solution in a few simple steps. We demonstrate with numerical experiments that our proposed streaming recovery framework provides better reconstruction compared to the methods that represent and reconstruct signals as independent, disjoint blocks, and that our proposed homotopy algorithm updates the solution faster than the current state-of-the-art solvers. View full abstract»

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  • Optimal Index Policies for Anomaly Localization in Resource-Constrained Cyber Systems

    Page(s): 4224 - 4236
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (3470 KB) |  | HTML iconHTML  

    The problem of anomaly localization in a resource-constrained cyber system is considered. Each anomalous component of the system incurs a cost per unit time until its anomaly is identified and fixed. Different anomalous components may incur different costs depending on their criticality to the system. Due to resource constraints, only one component can be probed at each given time. The observations from a probed component are realizations drawn from two different distributions depending on whether the component is normal or anomalous. The objective is a probing strategy that minimizes the total expected cost, incurred by all the components during the detection process, under reliability constraints. We consider both independent and exclusive models. In the former, each component can be abnormal with a certain probability independent of other components. In the latter, one and only one component is abnormal. We develop optimal index policies under both models. The proposed index policies apply to a more general case where a subset (more than one) of the components can be probed simultaneously. The problem under study also finds applications in spectrum scanning in cognitive radio networks and event detection in sensor networks. View full abstract»

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  • Likelihood Estimators for Dependent Samples and Their Application to Order Detection

    Page(s): 4237 - 4244
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (1873 KB) |  | HTML iconHTML  

    Estimation of the dimension of the signal subspace, or order detection, is one of the key issues in many signal processing problems. Information theoretic criteria are widely used to estimate the order under the independently and identically distributed (i.i.d.) sampling assumption. However, in many applications, the i.i.d. sampling assumption does not hold. Previous approaches address the dependent sample issue by downsampling the data set so that existing order detection methods can be used. By discarding data, the sample size is decreased causing degradation in the accuracy of the order estimation. In this paper, we introduce two likelihood estimators for dependent samples based on two signal models. The likelihood for each signal model is developed based on the entire data set and used in an information theoretic framework to achieve reliable order estimation performance for dependent samples. Experimental results show the desirable performance of the new method. View full abstract»

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  • Blind Source Separation by Entropy Rate Minimization

    Page(s): 4245 - 4255
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2801 KB) |  | HTML iconHTML  

    By assuming latent sources are statistically independent, independent component analysis separates underlying sources from a given linear mixture. Since in many applications, latent sources are both non-Gaussian and have sample dependence, it is desirable to exploit both properties jointly. In this paper, we use mutual information rate to construct a general framework for analysis and derivation of algorithms that take both properties into account. We discuss two types of source models for entropy rate estimation-a Markovian and an invertible filter model-and give the general independent component analysis cost function, update rule, and performance analysis based on these. We also introduce four algorithms based on these two models, and show that their performance can approach the Cramér-Rao lower bound. In addition, we demonstrate that the algorithms with flexible models exhibit very desirable performance for “natural” data. View full abstract»

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  • A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

    Page(s): 4256 - 4269
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (5415 KB) |  | HTML iconHTML  

    Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured “noises”. As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data. View full abstract»

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  • An MGF-Based Unified Framework to Determine the Joint Statistics of Partial Sums of Ordered i.n.d. Random Variables

    Page(s): 4270 - 4283
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    The joint statistics of partial sums of ordered random variables (RVs) are often needed for the accurate performance characterization of a wide variety of wireless communication systems. A unified analytical framework to determine the joint statistics of partial sums of ordered independent and identically distributed (i.i.d.) random variables was recently presented. However, the identical distribution assumption may not be valid in several real-world applications. With this motivation in mind, we consider in this paper the more general case in which the random variables are independent but not necessarily identically distributed (i.n.d.). More specifically, we extend the previous analysis and introduce a new more general unified analytical framework to determine the joint statistics of partial sums of ordered i.n.d. RVs. Our mathematical formalism is illustrated with an application on the exact performance analysis of the capture probability of generalized selection combining (GSC)-based RAKE receivers operating over frequency-selective fading channels with a non-uniform power delay profile. View full abstract»

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  • An Online Algorithm for Separating Sparse and Low-Dimensional Signal Sequences From Their Sum

    Page(s): 4284 - 4297
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (4242 KB) |  | HTML iconHTML  

    This paper designs and extensively evaluates an online algorithm, called practical recursive projected compressive sensing (Prac-ReProCS), for recovering a time sequence of sparse vectors St and a time sequence of dense vectors Lt from their sum, Mt: = St + Lt, when the Lt's lie in a slowly changing low-dimensional subspace of the full space. A key application where this problem occurs is in real-time video layering where the goal is to separate a video sequence into a slowly changing background sequence and a sparse foreground sequence that consists of one or more moving regions/objects on-the-fly. Prac-ReProCS is a practical modification of its theoretical counterpart which was analyzed in our recent work. Extension to the undersampled case is also developed. Extensive experimental comparisons demonstrating the advantage of the approach for both simulated and real videos, over existing batch and recursive methods, are shown. View full abstract»

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  • Kernel Additive Models for Source Separation

    Page(s): 4298 - 4310
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (2590 KB) |  | HTML iconHTML  

    Source separation consists of separating a signal into additive components. It is a topic of considerable interest with many applications that has gathered much attention recently. Here, we introduce a new framework for source separation called Kernel Additive Modelling, which is based on local regression and permits efficient separation of multidimensional and/or nonnegative and/or non-regularly sampled signals. The main idea of the method is to assume that a source at some location can be estimated using its values at other locations nearby, where nearness is defined through a source-specific proximity kernel. Such a kernel provides an efficient way to account for features like periodicity, continuity, smoothness, stability over time or frequency, and self-similarity. In many cases, such local dynamics are indeed much more natural to assess than any global model such as a tensor factorization. This framework permits one to use different proximity kernels for different sources and to separate them using the iterative kernel backfitting algorithm we describe. As we show, kernel additive modelling generalizes many recent and efficient techniques for source separation and opens the path to creating and combining source models in a principled way. Experimental results on the separation of synthetic and audio signals demonstrate the effectiveness of the approach. View full abstract»

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Aims & Scope

IEEE Transactions on Signal Processing covers novel theory, algorithms, performance analyses and applications of techniques for the processing, understanding, learning, retrieval, mining, and extraction of information from signals

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Meet Our Editors

Editor-in-Chief
Zhi-Quan (Tom) Luo
University of Minnesota