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Millimeter-wave (mmWave) massive antenna array has shown great potential in gaining high-accuracy localization for user equipments (UEs). Yet, mmWave signals suffer from non-line-of-sight (NLOS) propagation and fast time-scale fading in practice, which will affect UE localization performance. It is non-trivial to reveal the impact of multipath propagation and fast time-scale fading on mmWave-based localization, and gain guidelines for harnessing NLOS propagation. In this paper, we aim to provide a unified framework for performance analysis of mmWave-based UE localization and channel estimation. Firstly, closed-form Cramer-Rao lower bounds for UE localization and channel estimation, respectively, are derived to shed lights on their performance limits. Secondly, the effect of system elements (e.g., channel correlation and fast time-scale fading) on UE localization performance is quantitatively analyzed. In addition, information contribution from NLOS channel is quantified to reveal the impact of multipath propagation on UE localization. Finally, we show that the NLOS propagation-caused localization error can be alleviated by using a NLOS model folding-based localization scheme1, which strikes a balance between computational complexity and localization performance. [ABSTRACT FROM AUTHOR]

This paper is concerned with detecting an integer parameter vector inside a box from a linear model that is corrupted with a noise vector following the Gaussian distribution. One of the commonly used detectors is the maximum likelihood detector, which is obtained by solving a box-constrained integer least squares problem, that is NP-hard. Two other popular detectors are the box-constrained rounding and Babai detectors due to their high efficiency of implementation. In this paper, we first present formulas for the success probabilities (the probabilities of correct detection) of these three detectors for two different situations: the integer parameter vector is deterministic and is uniformly distributed over the constraint box. Then, we give two simple examples to respectively show that the success probability of the box-constrained rounding detector can be larger than that of the box-constrained Babai detector and the latter can be larger than the success probability of the maximum likelihood detector when the parameter vector is deterministic, and prove that the success probability of the box-constrained rounding detector is always not larger than that of the box-constrained Babai detector when the parameter vector is uniformly distributed over the constraint box. Some relations between the results for the box constrained and ordinary cases are presented, and two bounds on the success probability of the maximum likelihood detector, which can easily be computed, are developed. Finally, simulation results are provided to illustrate our main theoretical findings. [ABSTRACT FROM AUTHOR]

In numerous applications from communications and signal processing, we often need to acquire a K-sparse binary signal from sparse noisy linear measurements. In this work, we first develop an algorithm called binary matching pursuit (BMP) to recover the K-sparse binary signal. According to whether the residual vector is explicitly formed or not at each iteration, we develop two implementations of BMP which are respectively called explicit BMP and implicit BMP. We then analyze their complexities and show that, compared to the batch-orthogonal matching pursuit (OMP), which is the fastest implementation of OMP, the improvements of the explicit and implicit BMP algorithms are respectively n/(2K) and K times when some quantities are pre-computed. Finally, we provide sharp sufficient conditions of stable recovery of the support of the sparse signal using mutual coherence and restricted isometry property of the sensing matrix. Simulation tests indicate that the implicit BMP algorithm is around or more than n/(2K) times faster than batch-OMP with around or more than 20% lower rates of missed detection and false alarm. [ABSTRACT FROM AUTHOR]

Lattice reduction is a popular preprocessing strategy in multiple-input multiple-output (MIMO) detection. In a quest for developing a low-complexity reduction algorithm for large-scale problems, this paper investigates a new framework called sequential reduction (SR), which aims to reduce the lengths of all basis vectors. The performance upper bounds of the strongest reduction in SR are given when the lattice dimension is no larger than 4. The proposed new framework enables the implementation of a hash-based low-complexity lattice reduction algorithm, which becomes especially tempting when applied to large-scale MIMO detection. Simulation results show that, compared to other reduction algorithms, the hash-based SR algorithm exhibits the lowest complexity while maintaining comparable error performance. [ABSTRACT FROM AUTHOR]

In this paper, we use the block orthogonal matching pursuit (BOMP) algorithm to recover block sparse signals x from measurements y = A x + v , where v is an ℓ 2 -bounded noise vector (i.e., ‖ v ‖ 2 ≤ ϵ for some constant ϵ). We investigate some sufficient conditions based on the block restricted isometry property (block-RIP) for exact (when v = 0) and stable (when v ≠ 0) recovery of block sparse signals x . First, on the one hand, we show that if A satisfies the block-RIP with δ K + 1 < 1 / K + 1 , then every block K -sparse signal x can be exactly or stably recovered by BOMP in K iterations. On the other hand, we show that, for any K ≥ 1 and 1 / K + 1 ≤ δ < 1 , there exists a matrix A satisfying the block-RIP with δ K + 1 = δ and a block K -sparse signal x such that BOMP may fail to recover x in K iterations. Then, we study some sufficient conditions for recovering block α -strongly-decaying K -sparse signals. We show that if A satisfies the block-RIP with δ K + 1 < 2 / 2 , then every α -strongly-decaying block K -sparse signal can be exactly or stably recovered by BOMP in K iterations under some conditions on α. Our newly found sufficient condition on the block-RIP of A is less restrictive than that for ℓ 1 minimization for this special class of sparse signals. Furthermore, for any K ≥ 1 , α > 1 and 2 / 2 ≤ δ < 1 , the recovery of x may fail in K iterations for a sensing matrix A which satisfies the block-RIP with δ K + 1 = δ. Finally, we study some sufficient conditions for partial recovery of block sparse signals. Specifically, if A satisfies the block-RIP with δ K + 1 < 2 / 2 , then BOMP is guaranteed to recover some blocks of x if these blocks satisfy a sufficient condition. We further show that this condition is also sharp. [ABSTRACT FROM AUTHOR]

Sparse recovery aims to accurately recover the support of sparse vector from a very limited number of noisy linear measurements. By utilizing the covariance and mean of the sparse coefficients, we propose a new algorithm: generalized covariance-assisted matching pursuit (GCAMP). It preserves the elegance and practicality of generalized orthogonal matching pursuit (gOMP) and provides better performance than the CAMP algorithm. In the framework of restricted isometry property (RIP), we present some sufficient conditions on RIP and the minimum magnitude of the nonzero elements of the sparse coefficients, which can guarantee that GCAMP identifies at least one index in the support of any K -sparse signal in each iteration in the noisy case. Numerical experiments are also presented to verify the effectiveness of GCAMP. [ABSTRACT FROM AUTHOR]

The key aim of compressed sensing is to stably recover a $K$ -sparse signals ${\boldsymbol{x}}$ from a linear model ${\boldsymbol{y}}=\boldsymbol{A}{\boldsymbol{x}}+\boldsymbol{v}$ , where $\boldsymbol{v}$ is a noise vector. Minimization of $\Vert {\boldsymbol{x}}\Vert _1-\Vert {\boldsymbol{x}}\Vert _2$ is a recently proposed effective recovery method. In this paper, we show that if the mutual coherence $\mu$ of $\boldsymbol{A}$ satisfies $\mu < \frac{1}{3K}$ , then this method can stably recover any $K$ -sparse signal ${\boldsymbol{x}}$ based on ${\boldsymbol{y}}$ and $\boldsymbol{A}$. As far as we know, this is the first sufficient condition based on mutual coherence for such method. [ABSTRACT FROM AUTHOR]

The Korkine–Zolotareff (KZ) reduction is one of the often used reduction strategies for lattice decoding. In this paper, we first investigate some important properties of KZ reduced matrices. Specifically, we present a linear upper bound on the Hermit constant which is around 7/8 times of the existing sharpest linear upper bound, and an upper bound on the KZ constant which is polynomially smaller than the existing sharpest one. We also propose upper bounds on the lengths of the columns of KZ reduced matrices, and an upper bound on the orthogonality defect of KZ reduced matrices which are even polynomially and exponentially smaller than those of boosted KZ reduced matrices, respectively. Then, we derive upper bounds on the magnitudes of the entries of any solution of a shortest vector problem (SVP) when its basis matrix is LLL reduced. These upper bounds are useful for analyzing the complexity and understanding numerical stability of the basis expansion in a KZ reduction algorithm. Finally, we propose a new KZ reduction algorithm by modifying the commonly used Schnorr–Euchner search strategy for solving SVPs and the basis expansion method proposed by Zhang et al. Simulation results show that the new KZ reduction algorithm is much faster and more numerically reliable than the KZ reduction algorithm proposed by Zhang et al., especially when the basis matrix is ill conditioned. [ABSTRACT FROM AUTHOR]

In many applications, including integer-forcing linear multiple-input and multiple-output (MIMO) receiver design, one needs to solve a successive minima problem (SMP) on an $n$ -dimensional lattice to get an optimal integer coefficient matrix $\boldsymbol {A}^\star \in {Z}^{n\times n}$. In this paper, we first propose an efficient optimal SMP algorithm with an ${\mathcal {O}}(n^{2})$ memory complexity. The main idea behind the new algorithm is it first initializes with a suitable suboptimal solution, which is then updated via a novel algorithm with only ${\mathcal {O}}(n^{2})$ flops in each updating, until $\boldsymbol {A}^{\star }$ is obtained. Different from existing algorithms which find $\boldsymbol {A}^\star $ column by column through using a sphere decoding search strategy $n$ times, the new algorithm uses a search strategy once only. We then rigorously prove the optimality of the proposed algorithm. Furthermore, we theoretically analyze its complexity. In particular, we not only show that the new algorithm is $\Omega (n)$ times faster than the most efficient existing algorithm with polynomial memory complexity, but also assert that it is even more efficient than the most efficient existing algorithm with exponential memory complexity. Finally, numerical simulations are presented to illustrate the optimality and efficiency of our novel SMP algorithm. [ABSTRACT FROM AUTHOR]

Edge computing is expected to enable the cloud computing services in proximity and leverage the computational capacities at the edge of a network. Driven by massive data-hungry and energy-hungry applications, future wireless networks will need to provide various cloud-based multimedia services in a "greener" manner. However, limited computing capacity, wireless resources, and power supply prevent edge computing from evolving and maturing in terms of high sustainability and energy efficiency. In this article, we attempt to further improve the energy-efficient communication in mobile edge computing by proposing a device-to-device (D2D) offloading architecture. The D2D technique, in line with mobile edge computing, is responsible for offloading wireless traffic as well as computational tasks. Cooperative relay-aided transmission is also used in this architecture to pursue further improvements in a multi-cell scenario. Finally, offloading and balancing technologies are introduced to increase the total energy efficiency, decrease the inter/ intra-cell interference, deal with traffic/computational congestion, and provide better services to end users. [ABSTRACT FROM AUTHOR]

In recent years, smart logistics has captured wide attention and witnessed quick improvements. Swarm robotics, steadily evolving toward high artificial intelligence and capabilities, ensures warehouse delivery management and implementation of more intelligence for many challenging tasks. Self-organized as a community, the smart swarm robotics system thus can be viewed as a prototype of the future smart management and service system, and consequently reveals several critical properties of our next generation smart communities. How to design an efficient communication and management platform of swarm robotics is one of the fundamental problems in the smart logistics industry. This article refers to several imminent challenges of swarm robotics in logistics and reviews some groundbreaking applications for next generation logistics. [ABSTRACT FROM AUTHOR]

In this paper, we study the orthogonal least squares (OLS) algorithm for sparse recovery. On one hand, we show that if the sampling matrix \mathbf A satisfies the restricted isometry property of order K + 1 with isometry constant \delta _{K+ 1} < \frac{1}{\sqrt{K+1}} then OLS exactly recovers the support of any K-sparse vector \mathbf x from its samples \mathbf y = \mathbf A \mathbf x in K iterations. On the other hand, we show that OLS may not be able to recover the support of a K-sparse vector \mathbf x in K iterations for some $K$ if \delta _{K+ 1} \geq \frac{1}{\sqrt{K+\frac{1}{4}}} . [ABSTRACT FROM AUTHOR]

Exact support recovery of K-group sparse matrices X from the multiple measurement vectors (MMV) model Y = A X arises from many applications and has been extensively studied. In this paper, we investigate the restricted isometry property (RIP) based condition that guarantees exact support recovery of K-group sparse matrices X from the MMV model with greedy block coordinate descent (GBCD) algorithm in K iterations. We show that if A satisfies the RIP with $\delta _{K+1}<1/\sqrt {K+1}$ , then GBCD recovers the support of any K-group sparse matrix X in K iterations. This RIP condition is sharp since GBCD may fail to recover the support of a K-group sparse matrix in K iterations if $\delta _{K+1}\geq 1/\sqrt {K+1}$ . As far as we know, this is the first sharp condition for GBCD. [ABSTRACT FROM AUTHOR]

Support recovery of sparse signals from noisy measurements with orthogonal matching pursuit (OMP) has been extensively studied. In this paper, we show that for any K -sparse signal {\boldsymbol{x}} , if a sensing matrix \boldsymbol{A} satisfies the restricted isometry property (RIP) with restricted isometry constant \delta K+1 < 1/\sqrt{K+1}, then under some constraints on the minimum magnitude of nonzero elements of {\boldsymbol{x}} , OMP exactly recovers the support of \boldsymbolx from its measurements \boldsymboly=\boldsymbolA\boldsymbolx+\boldsymbolv in K iterations, where \boldsymbol{v} is a noise vector that is \ell _2 or \ell \infty bounded. This sufficient condition is sharp in terms of \delta K+1 since for any given positive integer K and any 1/\sqrt{K+1}\leq \delta <1, there always exists a matrix \boldsymbol{A} satisfying the RIP with \delta K+1=\delta for which OMP fails to recover a K-sparse signal \boldsymbolx in $K$ iterations. Also, our constraints on the minimum magnitude of nonzero elements of \boldsymbolx are weaker than existing ones. Moreover, we propose worst case necessary conditions for the exact support recovery of \boldsymbolx, characterized by the minimum magnitude of the nonzero elements of \boldsymbolx. [ABSTRACT FROM PUBLISHER]

In many applications including communications, one may encounter a linear model where the parameter vector \hat x is an integer vector in a box. To estimate \hat x , a typical method is to solve a box-constrained integer least squares problem. However, due to its high complexity, the box-constrained Babai integer point x^ \scriptscriptstyle \text BB is commonly used as a suboptimal solution. In this paper, we first derive formulas for the success probability P^ \scriptscriptstyle \text BB of x^ \scriptscriptstyle \text BB and the success probability P^ \scriptscriptstyle \text OB of the ordinary Babai integer point x^ \scriptscriptstyle \text OB when \hat x is uniformly distributed over the constraint box. Some properties of P^ \scriptscriptstyle \text BB and P^ \scriptscriptstyle \text OB and the relationship between them are studied. Then, we investigate the effects of some column permutation strategies on P^ \scriptscriptstyle \text BB . In addition to V-BLAST and SQRD, we also consider the permutation strategy involved in the LLL lattice reduction, to be referred to as LLL-P. On the one hand, we show that when the noise is relatively small, LLL-P always increases P^ \scriptscriptstyle \text BB and argue why both V-BLAST and SQRD often increase P^ \scriptscriptstyle \text BB ; and on the other hand, we show that when the noise is relatively large, LLL-P always decreases P^ \scriptscriptstyle \text BB and argue why both V-BLAST and SQRD often decrease P^ \scriptscriptstyle \text BB . We also derive a column permutation invariant bound on P^ \scriptscriptstyle \text BB , which is an upper bound and a lower bound under these two opposite conditions, respectively. Numerical results demonstrate our findings. Finally, we consider a conjecture concerning x^ \scriptscriptstyle \text OB proposed by Ma et al. We first construct an example to show that the conjecture does not hold in general, and then show that it does hold under some conditions. [ABSTRACT FROM PUBLISHER]

In this paper, we show that, under the assumption that ‖ e ‖ 2 ≤ ϵ , every k -sparse signal x ∈ R n can be stably ( ϵ ≠ 0 ) or exactly recovered ( ϵ = 0 ) from y = A x + e via l p -minimization with p ∈ ( 0 , p ¯ ] , where p ¯ = { 50 31 ( 1 − δ 2 k ) , δ 2 k ∈ [ 2 2 , 0.7183 ) 0.4541 , δ 2 k ∈ [ 0.7183 , 0.7729 ) 2 ( 1 − δ 2 k ) , δ 2 k ∈ [ 0.7729 , 1 ) , even if the restricted isometry constant of A satisfies δ 2 k ∈ [ 2 2 , 1 ) . Furthermore, under the assumption that n ≤ 4 k , we show that the range of p can be further improved to p ∈ ( 0 , 3 + 2 2 2 ( 1 − δ 2 k ) ] . This not only extends some discussions of only the noiseless recovery (Lai et al. (2011) [16] and Wu et al. (2013) [17] ) to the noise recovery, but also greatly improves the best existing results where p ∈ ( 0 , min ⁡ { 1 , 1.0873 ( 1 − δ 2 k ) } ) (Wu et al. (2013) [17] ). [ABSTRACT FROM AUTHOR]

An introduction is presented in which the editor discusses articles in the issue on topics including restricted isometry property (RIP), oblique projection, and banknotes.

A common method to estimate an unknown integer parameter vector in a linear model is to solve an integer least squares (ILS) problem. A typical approach to solving an ILS problem is sphere decoding. To make a sphere decoder faster, the well-known LLL reduction is often used as preprocessing. The Babai point produced by the Babai nearest plane algorithm is a suboptimal solution of the ILS problem. First, we prove that the success probability of the Babai point as a lower bound on the success probability of the ILS estimator is sharper than the lower bound given by Hassibi and Boyd refid="ref1"/. Then, we show rigorously that applying the LLL reduction algorithm will increase the success probability of the Babai point and give some theoretical and numerical test results. We give examples to show that unlike LLL's column permutation strategy, two often used column permutation strategies SQRD and V-BLAST may decrease the success probability of the Babai point. Finally, we show rigorously that applying the LLL reduction algorithm will also reduce the computational complexity of sphere decoders, which is measured approximately by the number of nodes in the search tree in the literature. [ABSTRACT FROM AUTHOR]

Text processing tasks commonly grapple with the challenge of high dimensionality. One of the most effective solutions to this challenge is to preprocess text data through feature selection methods. Feature selection can select the most advantageous features for subsequent operations (e.g., classification) from the native feature space of the text. This process effectively trims the feature space's dimensionality, enhancing subsequent operations' efficiency and accuracy. This paper proposes a straightforward and efficient filter feature selection method based on document-term matrix unitization (DTMU) for text processing. Diverging from previous filter feature selection methods that concentrate on scoring criteria definition, our method achieves more optimal feature selection by unitizing each column of the document-term matrix. This approach mitigates feature-to-feature influence and reinforces the role of the weighting proportion within the features. Subsequently, our scoring criterion subtracts the sum of weights for negative samples from positive samples and takes the absolute value. We conduct numerical experiments to compare DTMU with four advanced filter feature selection methods: max–min ratio metric, proportional rough feature selector, least loss, and relative discrimination criterion, along with two classical filter feature selection methods: Chi-square and information gain. The experiments are performed on four ten-thousand-dimensional feature space datasets: b o o k , d v d , m u s i c , m o v i e and two thousand-dimensional feature space datasets: i m d b , a m a z o n _ c e l l s , sourced from Amazon product reviews and movie reviews. Experimental findings demonstrate that DTMU selects more advantageous features for subsequent operations and achieves a higher dimensionality reduction rate than those of the other six methods used for comparison. Moreover, DTMU exhibits robust generalization capabilities across various classifiers and dimensional datasets. Notably, the average CPU time for a single run of DTMU is measured at 1.455 s. • This paper offers DTMU, a filter feature selection method enhancing feature quality via unitization for improved properties. • DTMU is notably user-friendly, involving only two straightforward steps. • This paper substantiates, through numerical experiments, that DTMU stands as an advanced and effective method. [ABSTRACT FROM AUTHOR]

First, a counter example is constructed to show that for any given positive integer K ≥ 2 and for any (1/√K + 1) ≤ t < 1, there always exists a K‐sparse x and a matrix A with the restricted isometry constant δK+1 = t such that the orthogonal matching pursuit (OMP) algorithm fails in K iterations. Secondly, it is shown that even when δK + 1 = (1/(√K + 1)), the OMP algorithm can also perfectly recover every K‐sparse vector x from y = Ax in K iterations. This improves the best existing results which were independently given by Mo and Shen and Wang and Shim. [ABSTRACT FROM AUTHOR]

In this paper, we present a fully discrete and structure-preserving scheme for the nonlinear fractional Schrödinger equations. The key is to introduce a scalar auxiliary variable and rewrite the equations as a new family of systems. The new systems are approximated by using the implicit midpoint rule, the repeated trapezoidal rule and the fractional centered difference method. It is shown the fully discrete scheme is mass- and energy-conserved. This is sharp contrast to the former result, i.e., the fully discrete scheme is only mass-conserved for the original equations. [ABSTRACT FROM AUTHOR]

In wireless communication networks, one of the most significant problems in Compute-and-Forward (CPF) strategy based on Integer-Forcing (IF) technique is to search the optimal integer coefficient vector for a relay to decode the received messages. While this is a variant of shortest vector problem (SVP), which is prohibitively complex in its general form. In this paper, we mainly focus on the optimal integer solution with non-zero entries in multi-source one-relay model. For comparison we extend the number (or dimension) of communication nodes from 2 to any larger integer n based on an existing 2-dimensional search algorithm with non-zero entries. Then we add this non-zero-entries constraint to an existing search algorithm and make some improvements to search the optimal integer vector by solving an optimization problem over only one variable instead of searching all vector components, which has a much lower time complexity. We prove that our new search algorithm is more efficient with polynomial complexity compared with the extended n-dimensional algorithm, meanwhile the same optimal integer solution is guaranteed. [ABSTRACT FROM AUTHOR]

A correction is presented to the article "Editorial: Multimedia in Technology Enhanced Learning" which was published in previous issue if the periodical.

The recently introduced spatially coupled turbo‐like codes are attractive in trading‐off performances between the error‐floor region and the water‐fall region. This letter is concerned with the construction of spatially coupled serially concatenated codes. Particularly, a new construction of spatially coupled serially concatenated codes is presented, in which a portion of the encoding output of the previous inner encoder is taken as the input of the current inner encoder. The authors show that by proper selection of the component codes and the re‐encoding ratio, performance gain about 0.25 dB is obtained with the proposed construction. [ABSTRACT FROM AUTHOR]

Filtering technology has been widely applied in signal processing and object tracking for decades, and most recently it has become a useful instrument for time series analysis. In this article, we introduce several popular technologies developed for analysis of the dynamic state space model, including Kalman and particle filtering, Markov chain Monte Carlo algorithms, as well as the sequential Bayesian learning method. Their applications in fields of interest are also discussed. Filtering technologies have great superiority in solving the problems arising from management and communications, making them deserving of further exploration. [ABSTRACT FROM AUTHOR]

The Internet of Things has motivated a paradigm shift in the development of various applications such as mobile health. The wireless body area network (WBAN) comprises many low-power devices in, on, or around the human body, which offers a desirable solution to monitoring physiological signals for mobile health applications. In the implant WBAN, an implanted medical device transmits its measured biological parameters to a target hub with the help of at least one on-body device(s) to satisfy its strict requirements on size, quality of service (QoS, e.g., reliability), and power consumption. In this article, we first review the recent advances in conventional cooperative WBANs. Afterward, to address the drawbacks of the conventional cooperative WBAN, a QoS-aware buffer-aided relaying framework is proposed for the implant WBAN. In the proposed framework, hierarchical modulations are considered to fulfill the different QoS requirements of different sensor data from an implanted medical device. We further conceive some new transmission strategies for the buffer-aided signal-relay and multi-relay implant WBANs. Simulation results show that the proposed cooperative WBAN provides better performance than its conventional cooperative counterparts. Finally, some open research challenges regarding the buffer-aided multi-relay implant WBAN are pointed out to inspire more research activities. [ABSTRACT FROM AUTHOR]

In this short study, we investigate the long time stability of the compact finite difference method for the reaction–diffusion equations with delay. It is shown that the spatial discretization leads to a reduction of the asymptotic stability region of the corresponding PDE if the compact finite difference method is applied to discretize the diffusion operator. A way to improve the stability region of the method is also presented. Finally, some numerical experiments are proposed to confirm our findings. [ABSTRACT FROM AUTHOR]

In numerous applications, such as DNA microarrays, face recognition, and spectral unmixing, we need to acquire a non-negative K -sparse signal x from an underdetermined linear model y = A x + v , where A is a sensing matrix and v is a noise vector. In this paper, we first propose a ReLU-based hard-thresholding algorithm (RHT) to recover x by taking advantage of its non-negative sparsity. Two sufficient conditions for stable recovery with RHT are then developed, which are respectively based on the restricted isometry property (RIP) and mutual coherence of the sensing matrix A. As far as we know, these two sufficient conditions are the best for hard-thresholding-type algorithms. Numerical experiments show that RHT has better overall recovery performance in the recovery non-negative sparse signals than the non-negative least squares (NNLS) algorithm, some hard-thresholding-type algorithms including the iterative hard-thresholding (IHT) algorithm, hard-thresholding pursuit (HTP), Newton-step-based iterative hard-thresholding algorithm (NSIHT), and Newton-step-based hard-thresholding pursuit (NSHTP), several non-negative sparse recovery approaches including non-negative orthogonal matching pursuit (NNOMP), fast NNOMP (FNNOMP), non-negative orthogonal least squares (NNOLS), and non-negative regularization (NNREG) method. In terms of efficiency, RHT has a similar performance to IHT, and is much more efficient than other tested algorithms. • Efficient hard-thresholding-type algorithm for non-negative sparse recovery. • Sufficient conditions for stable recovery with RHT based on RIP and mutual coherence. • RHT achieves good recovery performance in both stimulated and real-world experiments. • RHT shows similar efficiency with IHT, and outperforms the remaining algorithms. [ABSTRACT FROM AUTHOR]

Functions with low differential uniformity have important applications in cryptography, coding theory, and sequence design. The differential spectrum of a cryptographic function is of great interest for estimating its resistance to some variants of differential cryptanalysis. Finding power permutations (i.e., monomial bijective mappings) over finite fields with low differential uniformity and determining their differential spectra have received a lot of attention over the past two decades. The objective of this paper is to study the differential properties of the well-known Kasami power permutations $x^{p^{2k}-p^{k}+1}$ over $ {\mathrm {GF}}(p^{n})$ , where $p$ is an odd prime and $k$ is an integer with $\gcd (n,k)=1$. It turns out that this family of monomials is differentially $(p+1)$ -uniform. Our result in the case of $p=3$ gives an affirmative solution to a recent conjecture by Xu, Cao, and Xu. Most notably, the differential spectrum of this family of power permutations is completely determined. [ABSTRACT FROM AUTHOR]

Text classification is a challenging problem due to the high dimensionality of the text, which can limit classification performance. The orthogonal matching pursuit (OMP) algorithm is one of the most popular sparse recovery algorithms. An OMP based text classification algorithm, called the Logistic-OMP algorithm, was recently proposed by Skianis et al.. Simulation tests indicate that Logistic-OMP has excellent performance in text dimensionality reduction. This paper optimizes the Logistic-OMP algorithm, and proposes a new text classification algorithm called the Logistic Regression Matching Pursuit (LRMP) algorithm. The LRMP algorithm defines a new loss function and residual update function. It requires only one iteration to solve the negative log likelihood minimization problem, and its classification performance is guaranteed by the strong Wolfe condition, which makes it optimizes the classification accuracy while significantly speeding up the training speed. Simulation tests on topic classification and sentiment analysis from 20Newsgroups, Amazon product reviews, and movie reviews datasets show that the LRMP algorithm has a shorter computation time of a single iteration than the Logistic-OMP algorithm, with a total training time of 8.08%–21.16% shorter than that of the Logistic-OMP algorithm, and the memory usage is 3.20%–6.21% lower than that of the Logistic-OMP algorithm. Furthermore, the average Accuracy and F1-Score of the LRMP algorithm are improved by 1.61%–26.55% and 1.83%–25.46%, respectively, compared with the benchmark classifier. Compared with the advanced classifiers (including Logistic-OMP), the average Accuracy and F1-Score of the LRMP algorithm are improved by 0.46%–8.97% and 0.57%–9.40%, respectively. [ABSTRACT FROM AUTHOR]

Fluorescence microscopy images captured in low light and short exposure time conditions are always contaminated by photons and readout noises, which reduce the fluorescence microscopy images quality. In most cases, this kind of noise can be modeled as Poisson–Gaussian noise. Correspondingly, its denoising task has always been a hot but challenging topic in recent years. In this paper, by integrating model-driven and learning-driven methodologies, we propose an end-to-end supervised neural network for fluorescence microscopy images denoising, named MCSC-net, which embeds the multi-layer learned iterative soft threshold algorithm (ML-LISTA) into deep convolutional neural network (DCNN). Our approach not only uses the strong learning ability of DCNN to adaptively update all parameters in the ML-LISTA, but also introduces dilated convolution into network training without additional parameters to improve denoising performance. In addition, compared with several related methods on a real data set of fluorescence microscopy images, MCSC-net achieves the best denoising effects both in qualitative and quantitative aspects, which shows its strong appeal in practical denoising applications. • The network is an extension of pursuit algorithm (ML-LISTA). • The network can be deepened without introducing additional parameters. • The introduction of dilated convolution improves the denoising effect. • Our method achieves attractive results in all the comparison methods. [ABSTRACT FROM AUTHOR]

The complementary error function is a fundamental function in statistics and plays a central role in numerous applications. Its upper bound is essential for simplifying many performance analysis in communications. This Letter develops a new upper bound, which is sharper than existing upper bounds, on the complementary error function. Simulation tests are also performed to illustrate the sharpness of the new upper bound. [ABSTRACT FROM AUTHOR]

The complementary error function is a fundamental function in statistics and plays a central role in numerous applications. Its upper bound is essential for simplifying many performance analysis in communications. This Letter develops a new upper bound, which is sharper than existing upper bounds, on the complementary error function. Simulation tests are also performed to illustrate the sharpness of the new upper bound. [ABSTRACT FROM AUTHOR]

This paper is concerned with stability analysis of additive Runge-Kutta methods for delay-integro-differential equations. We show that if the additive Runge-Kutta methods are algebraically stable, the perturbations of the numerical solutions are controlled by the initial perturbations from the system and the methods. [ABSTRACT FROM AUTHOR]

Zero correlation zone (ZCZ) sequences are a class of spreading sequences having ideal auto-correlation and cross correlation in a zone around the origin. They have been extensively studied in recent years due to their important applications in quasi-synchronous code division multiple access systems. In this paper, a construction of ZCZ sequence sets is proposed based on perfect nonlinear functions. It generates multiple ZCZ sequence sets with the properties: 1) each sequence is perfect in the sense that its out-of-phase auto-correlation is always zero; 2) each ZCZ sequence set is optimal with respect to the Tang–Fan–Matsufuji bound in which all the sequences are pairwise cyclically distinct; and 3) the maximum inter-set cross correlation of multiple sequence sets achieves the well-known Sarwate bound. [ABSTRACT FROM AUTHOR]