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In this paper an iterative method for recovery of the missing samples of signals is investigated in detail, and some novel linear, nonlinear, and adaptive extrapolation techniques are proposed to be used along with it to increase the convergence rate of the recovery system. The proposed methods would remarkably speed up the convergence rate, save processing power, and reduce the delay of the system compared to some well known accelerated versions of the aforementioned iterative algorithm. © 2007 Elsevier B.V. All rights reserved  

This paper is concerned with designing efficient algorithms for recovering sparse signals from noisy underdetermined measurements. More precisely, we consider minimization of a nonsmooth and nonconvex sparsity promoting function subject to an error constraint. To solve this problem, we use an alternating minimization penalty method, which ends up with an iterative proximal-projection approach. Furthermore, inspired by accelerated gradient schemes for solving convex problems, we equip the obtained algorithm with a so-called extrapolation step to boost its performance. Additionally, we prove its convergence to a critical point. Our extensive simulations on synthetic as well as real data verify... 

It has been shown that more accurate signal recovery can be achieved with low-coherence dictionaries in sparse signal processing. In this Letter, the authors extend the low-coherence attribute to receptive fields in convolutional neural networks. A new constrained formulation to train low-coherence convolutional neural network is presented and an efficient algorithm is proposed to train the network. The resulting formulation produces a direct link between the receptive fields of a layer through training procedure that can be used to extract more informative representations from the subsequent layers. Simulation results over three benchmark datasets confirm superiority of the proposed... 

This brief proposes a joint graph signal recovery and topology learning algorithm using a Variational Bayes (VB) framework in the case of non-Gaussian measurement noise. It is assumed that the graph signal is Gaussian Markov Random Field (GMRF) and the graph weights are considered statistical with the Gaussian prior. Moreover, the non-Gaussian noise is modeled using two distributions: Mixture of Gaussian (MoG), and Laplace. All the unknowns of the problem which are graph signal, Laplacian matrix, and the (Hyper)parameters are estimated by a VB framework. All the posteriors are calculated in closed forms and the iterative VB algorithm is devised to solve the problem. The efficiency of the... 

Many real-world systems and applications such as World Wide Web, and social interactions can be modeled as networks of interacting nodes. However, in many cases, one encounters the situation where the pattern of the node-to-node interactions (i.e., edges) or the structure of a network is unknown. We address this issue by studying the Network Reconstruction Problem: Given a network with missing edges, how is it possible to uncover the network structure based on certain observable quantities extracted from partial measurements? We propose a novel framework called CS-NetRec based on a newly emerged paradigm in sparse signal recovery called Compressive Sensing (CS). The results demonstrate that... 

One of the most relevant characteristics of social networks is community structure, in which network nodes are joined together in densely connected groups between which there are only sparser links. Uncovering these sparse links (i.e. intercommunity links) has a significant role in community detection problem which has been of great importance in sociology, biology, and computer science. In this paper, we propose a novel approach, called CS-ComDet, to efficiently detect the inter-community links based on a newly emerged paradigm in sparse signal recovery, called compressive sensing. We test our method on real-world networks of various kinds whose community structures are already known, and... 

Adaptive thresholding methods have proved to yield a high signal-to-noise ratio (SNR) and fast convergence in sparse signal recovery. The robustness of a class of iterative sparse recovery algorithms, such as the iterative method with adaptive thresholding, has been found to outperform the state-of-art methods in respect of reconstruction quality, convergence speed, and sensitivity to noise. In this study, the authors introduce a new method for compressed sensing, using the sensing matrix and measurements. In our method, they iteratively threshold the signal and project the thresholded signal onto the translated null space of the sensing matrix. The threshold level is assigned adaptively.... 

The problem of finding the optimal node density for reconstructing a stochastic signal from its noisy samples in sensor networks is considered. The signal could be nonstationary and nonbandlimited. A weight is assigned to each location that indicates the relative importance of the signal at that location. It is shown that when the number of samples is very large, the optimal density of the samples at each location is proportional to the square root of the weight associated to that location  

Linear sampling of sparse vectors via sensing matrices has been a much investigated problem in the past decade. The nonlinear sampling methods, such as quadratic forms are also studied marginally to include undesired effects in data acquisition devices (e.g., Taylor series expansion up to two terms). In this paper, we introduce customized nonlinear sampling techniques that provide possibility of sparse signal recovery. The main advantage of the nonlinear method over the conventional linear schemes is the reduction in the number of required samples to 2k for recovery of k-sparse signals. We also introduce a low-complexity reconstruction method similar to the annihilating filter in the... 

In this paper, motivated by network inference, we introduce a general framework, called LSR-Weighted, to efficiently recover sparse characteristic of links in weighted networks. The links in many real-world networks are not only binary entities, either present or not, but rather have associated weights that record their strengths relative to one another. Such models are generally described in terms of weighted networks. The LSR-Weighted framework uses a newly emerged paradigm in sparse signal recovery named compressive sensing. We study the problem of recovering sparse link vectors with network topological constraints over weighted networks. We evaluate performance of the proposed framework... 

This paper addresses the problem of identifying central nodes from the information flow standpoint in a social network. Betweenness centrality is the most prominent measure that shows the node importance from the information flow standpoint in the network. High betweenness centrality nodes play crucial roles in the spread of propaganda, ideologies, or gossips in social networks, the bottlenecks in communication networks, and the connector hubs in biological systems. In this paper, we introduce DICeNod, a new approach to efficiently identify central nodes in social networks without direct measurement of each individual node using compressive sensing, which is a well-known paradigm in sparse... 

This letter investigates the problem of sparse signal recovery in the presence of additive impulsive noise. The heavy-tailed impulsive noise is well modeled with stable distributions. Since there is no explicit formula for the probability density function of SαS distribution, alternative approximations are used, such as, generalized Gaussian distribution, which imposes ℓp-norm fidelity on the residual error. In this letter, we exploit a continuous mixed norm (CMN) for robust sparse recovery instead of ℓp-norm. We show that in blind conditions, i.e., in the case where the parameters of the noise distribution are unknown, incorporating CMN can lead to near-optimal recovery. We apply... 

In this paper applications of an iterative method in some signal recovery problems are introduced. It is proved that the distorting effect of linear operators can be removed completely using the iterative scheme. The inverse of monotonic functions can also be made indirectly by the method. A novel approach for separating the messages of different subscribers in a CDMA network will be proposed as well, relying on the recursive approach. It would be shown that Sigma Delta Modulated signals can be decoded via the iterative procedure. We will prove both analytically and with simulations that a broad class of nonlinear operators including speech and image codecs can be approximately inverted with...