In this paper, we propose a unified algebraic design of the generalized Moreau enhancement matrix (GME matrix) for the Linearly involved Generalized-Moreau-Enhanced (LiGME) model. The LiGME model has been established as a framework to construct linearly involved nonconvex regularizers for sparsity (or low-rank) aware estimation, where the design of GME matrix is a key to guarantee the overall convexity of the model. The proposed design is applicable to general linear operators involved in the regularizer of the LiGME model, and does not require any eigendecomposition or iterative computation. We also present an application of the LiGME model with the proposed GME matrix to a group sparsity aware least squares estimation problem. Numerical experiments demonstrate the effectiveness of the proposed GME matrix in the LiGME model.

Underwater acoustic channels (UWA) are usually sparse, which can be exploited for adaptive equalization to improve the system performance. For the shallow UWA channels, based on the proportional minimum symbol error rate (PMSER) criterion, the adaptive equalization framework requires the sparsity selection. Since the sparsity of the L0 norm is stronger than that of the L1, we choose it to achieve better convergence. However, because the L0 norm leads to NP-hard problems, it is difficult to find an efficient solution. In order to solve this problem, we choose the Gaussian function to approximate the L0 norm. Simulation results show that the proposed scheme obtains better performance than the L1 based counterpart.

We propose an algorithm for the constrained design of FIR filters with sparse coefficients. In general filter design approaches, as the length of the filter increases, the number of multipliers used to construct the filter increases. This is a serious problem, especially in two-dimensional FIR filter designs. The FIR filter coefficients designed by the least-squares method with peak error constraint are optimal in the sense of least-squares within a given order, but not necessarily optimal in terms of constructing a filter that meets the design specification under the constraints on the number of coefficients. That is, a higher-order filter with several zero coefficients can construct a filter that meets the specification with a smaller number of multipliers. We propose a two-step approach to design constrained sparse FIR filters. Our method minimizes the number of non-zero coefficients while the frequency response of the filter that meets the design specification. It achieves better performance in terms of peak error than conventional constrained least-squares designs with the same or higher number of multipliers in both one-dimensional and two-dimensional filter designs.

Nowadays recommender systems (RS) keep drawing attention from academia, and collaborative filtering (CF) is the most successful technique for building RS. To overcome the inherent limitation, which is referred to as data sparsity in CF, various solutions are proposed to incorporate additional social information into recommendation processes, such as trust networks. However, existing methods suffer from multi-source data integration (i.e., fusion of social information and ratings), which is the basis for similarity calculation of user preferences. To this end, we propose a social collaborative filtering method based on novel trust metrics. Firstly, we use Graph Convolutional Networks (GCNs) to learn the associations between social information and user ratings while considering the underlying social network structures. Secondly, we measure the direct-trust values between neighbors by representing multi-source data as user ratings on popular items, and then calculate the indirect-trust values based on trust propagations. Thirdly, we employ all trust values to create a social regularization in user-item rating matrix factorization in order to avoid overfittings. The experiments on real datasets show that our approach outperforms the other state-of-the-art methods on usage of multi-source data to alleviate data sparsity.

A light field, which is equivalent to a dense set of multi-view images, has various applications such as depth estimation and 3D display. One of the essential problems in light field applications is light field interpolation, i.e., view interpolation. The interpolation accuracy is enhanced by exploiting an inherent property of a light field. One example is that an epipolar plane image (EPI), which is a 2D subset of the 4D light field, consists of many lines, and these lines have almost the same slope in a local region. This structure induces a sparse representation in the frequency domain, where most of the energy resides on a line passing through the origin. On the basis of this observation, we propose a group sparsity prior suitable for light fields to exploit their line structure fully for interpolation. Specifically, we designed the directional groups in the discrete Fourier transform (DFT) domain so that the groups can represent the concentration of the energy, and we thereby formulated an LF interpolation problem as an overlapping group lasso. We also introduce several techniques to improve the interpolation accuracy such as applying a window function, determining group weights, expanding processing blocks, and merging blocks. Our experimental results show that the proposed method can achieve better or comparable quality as compared to state-of-the-art LF interpolation methods such as convolutional neural network (CNN)-based methods.

Distributed compressive video sensing (DCVS) has received considerable attention due to its potential in source-limited communication, e.g., wireless video sensor networks (WVSNs). Multi-hypothesis (MH) prediction, which treats the target block as a linear combination of hypotheses, is a state-of-the-art technique in DCVS. The common approach is under the supposition that blocks that are dissimilar from the target block are given lower weights than blocks that are more similar. This assumption can yield acceptable reconstruction quality, but it is not suitable for scenarios with more details. In this paper, based on the joint sparsity model (JSM), the authors present a Tikhonov-regularized MH prediction scheme in which the most similar block provides the similar common portion and the others blocks provide respective unique portions, differing from the common supposition. Specifically, a new scheme for generating hypotheses and a Euclidean distance-based metric for the regularized term are proposed. Compared with several state-of-the-art algorithms, the authors show the effectiveness of the proposed scheme when there are a limited number of hypotheses.

An underdetermined direction of arrival estimation method based on signal sparsity is proposed when independent and coherent signals coexist. Firstly, the estimate of the mixing matrix of the impinging signals is obtained by clustering the single source points which are detected by the ratio of time-frequency transforms of the received signals. Then, each column vector of the mixing matrix is processed by exploiting the forward and backward vectors in turn to obtain the directions of arrival of all signals. The number of independent signals and coherent signal groups that can be estimated by the proposed method can be greater than the number of sensors. The validity of the method is demonstrated by simulations.

In this paper, we consider a group testing (GT) problem. We derive a lower bound on the probability of error for successful decoding of defected binary signals. To this end, we exploit Fano's inequality theorem in the information theory. We show that the probability of error is bounded as an entropy function, a density of a pooling matrix and a sparsity of a binary signal. We evaluate that for decoding of highly sparse signals, the pooling matrix is required to be dense. Conversely, if dense signals are needed to decode, the sparse pooling matrix should be designed to achieve the small probability of error.

Generalized approximate message passing (GAMP) is introduced into distributed compressed sensing (DCS) to reconstruct jointly sparse signals under the mixed support-set model. A GAMP algorithm with known support-set is presented and the matching pursuit generalized approximate message passing (MPGAMP) algorithm is modified. Then, a new joint recovery algorithm, referred to as the joint MPGAMP algorithm, is proposed. It sets up the jointly shared support-set of the signal ensemble with the support exploration ability of matching pursuit and recovers the signals' amplitudes on the support-set with the good reconstruction performance of GAMP. Numerical investigation shows that the joint MPGAMP algorithm provides performance improvements in DCS reconstruction compared to joint orthogonal matching pursuit, joint look ahead orthogonal matching pursuit and regular MPGAMP.

Massive multiple-input multiple-output (MIMO) systems are a key promising technology for future broadband cellular networks. The propagation paths within massive MIMO radio channels are often sparse, both in the sub-6GHz frequency band and at millimeter wave frequencies. Herein, we propose a two-layer beamforming scheme for downlink transmission over massive multiuser MIMO sparse beam-space channels. The first layer employs a bipartite graph to dynamically group users in the beam-space domain; the aim is to minimize inter-user interference while significantly reducing the effective channel dimensionality. The second layer performs baseband linear MIMO precoding to maximize spatial multiplexing gain and system throughput. Simulation results demonstrate the proposed two-layer beamforming scheme outperforms other, more conventional algorithms.

Compressed sensing theory provides a new approach to acquire data as a sampling technique and makes sure that a sparse signal can be reconstructed from few measurements. The construction of compressed sensing matrices is a main problem in compressed sensing theory (CS). In this paper, the deterministic constructions of compressed sensing matrices based on affine singular linear space over finite fields are presented and a comparison is made with the compressed sensing matrices constructed by DeVore based on polynomials over finite fields. By choosing appropriate parameters, our sparse compressed sensing matrices are superior to the DeVore's matrices. Then we use a new formulation of support recovery to recover the support sets of signals with sparsity no more than k on account of binary compressed sensing matrices satisfying disjunct and inclusive properties.

Existing trajectory prediction methods suffer from the “data sparsity” and neglect “time awareness”, which leads to low accuracy. Aiming to the problem, we propose a fast time-aware sparse trajectories prediction with tensor factorization method (TSTP-TF). Firstly, we do trajectory synthesis based on trajectory entropy and put synthesized trajectories into the original trajectory space. It resolves the sparse problem of trajectory data and makes the new trajectory space more reliable. Then, we introduce multidimensional tensor modeling into Markov model to add the time dimension. Tensor factorization is adopted to infer the missing regions transition probabilities to further solve the problem of data sparsity. Due to the scale of the tensor, we design a divide and conquer tensor factorization model to reduce memory consumption and speed up decomposition. Experiments with real dataset show that TSTP-TF improves prediction accuracy generally by as much as 9% and 2% compared to the Baseline algorithm and ESTP-MF algorithm, respectively.

A dynamic neural network has ternary connection parameters and can generate various binary periodic orbits. In order to analyze the dynamics, we present two feature quantities which characterize stability and transient phenomenon of a periodic orbit. Calculating the feature quantities, we investigate influence of connection sparsity on stability of a target periodic orbit corresponding to a circuit control signal. As the sparsity increases, at first, stability of a target periodic orbit tends to be stronger. In the next, the stability tends to be weakened and various transient phenomena exist. In the most sparse case, the network has many periodic orbits without transient phenomenon.

In this paper, an optimal method is proposed to design sparse-coefficient notch filters with principal basic vectors in the column space of a matrix constituted with frequency samples. The proposed scheme can perform in two stages. At the first stage, the principal vectors can be determined in the least-squares sense. At the second stage, with some components of the principal vectors, the notch filter design is formulated as a linear optimization problem according to the desired specifications. Optimal results can form sparse coefficients of the notch filter by solving the linear optimization problem. The simulation results show that the proposed scheme can achieve better performance in designing a sparse-coefficient notch filter of small order compared with other methods such as the equiripple method, the orthogonal matching pursuit based scheme and the L1-norm based method.

Existing moving object's trajectory prediction algorithms suffer from the data sparsity problem, which affects the accuracy of the trajectory prediction. Aiming to the problem, we present an Entropy-based Sparse Trajectories Prediction method enhanced by Matrix Factorization (ESTP-MF). Firstly, we do trajectory synthesis based on trajectory entropy and put synthesized trajectories into the trajectory space. It can resolve the sparse problem of trajectory data and make the new trajectory space more reliable. Secondly, under the new trajectory space, we introduce matrix factorization into Markov models to improve the sparse trajectory prediction. It uses matrix factorization to infer transition probabilities of the missing regions in terms of corresponding existing elements in the transition probability matrix. It aims to further solve the problem of data sparsity. Experiments with a real trajectory dataset show that ESTP-MF generally improves prediction accuracy by as much as 6% and 4% compared to the SubSyn algorithm and STP-EE algorithm respectively.

In this paper, we propose an algorithm that enhances the number of pixels for high-speed imaging. High-speed cameras have a principle problem that the number of pixels reduces when the number of frames per second (fps) increases. To enhance the number of pixels, we suppose an optical structure that block-randomly selects some percent of pixels in an image. Then, we need to reconstruct the entire image. For this, a state-of-the-art method takes three-dimensional reconstruction strategy, which requires a heavy computational cost in terms of time. To reduce the cost, the proposed method reconstructs the entire image frame-by-frame using a new cost function exploiting two types of sparsity. One is within each frame and the other is induced from the similarity between adjacent frames. The latter further means not only in the image domain, but also in a sparsifying transformed domain. Since the cost function we define is convex, we can find the optimal solution using a convex optimization technique with small computational cost. We conducted simulations using grayscale image sequences. The results show that the proposed method produces a sequence, mostly the same quality as the state-of-the-art method, with dramatically less computational time.

Much attention has recently been paid to sparsity-aware space-time adaptive processing (STAP) algorithms. The idea of sparsity-aware technology is commonly based on the convex l1-norm penalty. However, some works investigate the lq (0 < q < 1) penalty which induces more sparsity owing to its lack of convexity. We herein consider the design of an lq penalized STAP processor with a generalized sidelobe canceler (GSC) architecture. The lq cyclic descent (CD) algorithm is utilized with the least squares (LS) design criterion. It is validated through simulations that the lq penalized STAP processor outperforms the existing l1-based counterparts in both convergence speed and steady-state performance.

Synthetic aperture radar (SAR) imagery is significantly deteriorated by the random phase noises which are generated by the frequency jitter of the transmit signal and atmospheric turbulence. In this paper, we recast the SAR imaging problem via the phase-corrupted data as for a special case of quadratic compressed sensing (QCS). Although the quadratic measurement model has potential to mitigate the effects of the phase noises, it also leads to a nonconvex and quartic optimization problem. In order to overcome these challenges and increase reconstruction robustness to the phase noises, we proposed a QCS-based SAR imaging algorithm by greedy local search to exploit the spatial sparsity of scatterers. Our proposed imaging algorithm can not only avoid the process of precise random phase noise estimation but also acquire a sparse representation of the SAR target with high accuracy from the phase-corrupted data. Experiments are conducted by the synthetic scene and the moving and stationary target recognition Sandia laboratories implementation of cylinders (MSTAR SLICY) target. Simulation results are provided to demonstrate the effectiveness and robustness of our proposed SAR imaging algorithm.

Most of the existing algorithms cannot effectively solve the data sparse problem of trajectory prediction. This paper proposes a novel sparse trajectory prediction method based on L-Z entropy estimation. Firstly, the moving region of trajectories is divided into a two-dimensional plane grid graph, and then the original trajectories are mapped to the grid graph so that each trajectory can be represented as a grid sequence. Secondly, an L-Z entropy estimator is used to calculate the entropy value of each grid sequence, and then the trajectory which has a comparatively low entropy value is segmented into several sub-trajectories. The new trajectory space is synthesised by these sub-trajectories based on trajectory entropy. The trajectory synthesis can not only resolve the sparse problem of trajectory data, but also make the new trajectory space more credible. In addition, the trajectory scale is limited in a certain range. Finally, under the new trajectory space, Markov model and Bayesian Inference is applied to trajectory prediction with data sparsity. The experiments based on the taxi trajectory dataset of Microsoft Research Asia show the proposed method can make an effective prediction for the sparse trajectory. Compared with the existing methods, our method needs a smaller trajectory space and provides much wider predicting range, faster predicting speed and better predicting accuracy.

We propose a cooperative spectrum sensing scheme based on sub-Nyquist sampling in cognitive radios. Our main purpose is to understand the uncertainty caused by sub-Nyquist sampling and to present a sensing scheme that operates at low sampling rates. In order to alleviate the aliasing effect of sub-Nyquist sampling, we utilize cooperation among secondary users and the sparsity order of channel occupancy. The simulation results show that the proposed scheme can achieve reasonable sensing performance even at low sampling rates.