Some Results for Exact Support Recovery of Block Joint Sparse Matrix via Block Multiple Measurement Vectors Algorithm

Block multiple measurement vectors (BMMV) is a reconstruction algorithm that can be used to recover the support of block K-joint sparse matrix X from Y = ΨX + V. In this paper, we propose a sufficient condition for accurate support recovery of the block K-joint sparse matrix via the BMMV algorithm in the noisy case. Furthermore, we show the optimality of the condition we proposed in the absence of noise when the problem reduces to single measurement vector case.

Analysis on unit maximum capacity of orthogonal multiple watermarking for multimedia signals in B5G wireless communications

Beyond-5G(B5G)aims to meet the growing demands of mobile traffic and expand the communication space.Considering that intelligent applications to B5G wireless communications will involve security issues regarding user data and operational data,this paper analyzes the maximum capacity of the multi-watermarking method for multimedia signal hiding as a means of alleviating the information security problem of B5G.The multiwatermarking process employs spread transform dither modulation.During the watermarking procedure,Gram-Schmidt orthogonalization is used to obtain the multiple spreading vectors.Consequently,multiple watermarks can be simultaneously embedded into the same position of a multimedia signal.Moreover,the multiple watermarks can be extracted without affecting one another during the extraction process.We analyze the effect of the size of the spreading vector on the unit maximum capacity,and consequently derive the theoretical relationship between the size of the spreading vector and the unit maximum capacity.A number of experiments are conducted to determine the optimal parameter values for maximum robustness on the premise of high capacity and good imperceptibility.

Two properties of sequence of vector measures on effect algebras

Let （L, ,0, 1） be an effect algebra and let X be a Banach space. A function ： L→ X is called a vector measure if μ（a b） =μ（a） ＋ μ（b） whenever a⊥b in L. The function μ is said to be 8-bounded if limn→∞μ（an） = 0 in X for any orthogonal sequence （an）n∈N in L. In this paper, we introduce two properties of sequence of s-bounded vector measures and give some results on these properties.

P-Indeterminate Vector Similarity Measures of Orthopair Neutrosophic Number Sets and Their Decision-MakingMethod with Indeterminate Degrees

In the complexity and indeterminacy of decision making(DM)environments,orthopair neutrosophic number set(ONNS)presented by Ye et al.can be described by the truth and falsity indeterminacy degrees.Then,ONNS demonstrates its advantages in the indeterminate information expression,aggregations,and DM problems with some indeterminate ranges.However,the existing research lacks some similarity measures between ONNSs.They are indispensable mathematical tools and play a crucial role in DM,pattern recognition,and clustering analysis.Thus,it is necessary to propose some similaritymeasures betweenONNSs to supplement the gap.To solve the issue,this study firstly proposes the p-indeterminate cosine measure,p-indeterminate Dice measure,p-indeterminate Jaccard measure of ONNSs(i.e.,the three parameterized indeterminate vector similarity measures of ONNSs)in vector space.Then,a DMmethod based on the parameterized indeterminate vector similarity measures of ONNSs is developed to solve indeterminate multiple attribute DM problems by choosing different indeterminate degrees of the parameter p,such as the small indeterminate degree(p=0)or the moderate indeterminate degree(p=0.5)or the big indeterminate degree(p=1).Lastly,an actual DM example on choosing a suitable logistics supplier is provided to demonstrate the flexibility and practicability of the developed DM approach in indeterminate DM problems.By comparison with existing relative DM methods,the superiority of this study is that the established DMapproach indicates its flexibility and suitability depending on decision makers’indeterminate degrees(decision risks)in ONNS setting.

The Multifractal Formalism for Measures, Review and Extension to Mixed Cases

The mulfifractal formalism for single measure is reviewed. Next, a mixed generalized multifractal formalism is introduced which extends the multifractal formalism of a single measure based on generalizations of the Hausdorff and packing measures to a vector of simultaneously many measures. Borel-Cantelli and Large deviations Theorems are extended to higher orders and thus applied for the validity of the new variant of the multifractal formalism for some special cases of multi-doubling type measures.

A MAXIMUM PRINCIPLE FOR DISTRIBUTED PARAMETER SYSTEMS WITH MIXED PHASE-CONTROL CONSTRAINTS ANDENDPOINT CONSTRAINTS

This paper considered the optimal control problem for distributed parameter systems with mixed phase-control constraints and end-point constraints. Pontryagin's maximum principle for optimal control are derived via Duboviskij-Milujin theorem.

Rank-defective millimeter-wave channel estimation based on subspace-compressive sensing

Millimeter-wave communication （mmWC） is considered as one of the pioneer candidates for 5G indoor and outdoor systems in E-band. To subdue the channel propagation characteristics in this band, high dimensional antenna arrays need to be deployed at both the base station （BS） and mobile sets （MS）. Unlike the conventional MIMO systems, Millimeter-wave （mmW） systems lay away to employ the power predatory equipment such as ADC or RF chain in each branch of MIMO system because of hardware constraints. Such systems leverage to the hybrid precoding （combining） architecture for downlink deployment. Because there is a large array at the transceiver, it is impossible to estimate the channel by conventional methods. This paper develops a new algorithm to estimate the mmW channel by exploiting the sparse nature of the channel. The main contribution is the representation of a sparse channel model and the exploitation of a modified approach based on Multiple Measurement Vector （MMV） greedy sparse framework and subspace method of Multiple Signal Classification （MUSIC） which work together to recover the indices of non-zero elements of an unknown channel matrix when the rank of the channel matrix is defected. In practical rank-defective channels, MUSIC fails, and we need to propose new extended MUSIC approaches based on subspace enhancement to compensate the limitation of MUSIC. Simulation results indicate that our proposed extended MUSIC algorithms will have proper performances and moderate computational speeds, and that they are even able to work in channels with an unknown sparsity level.

Automatic Determination of Water Hardness by Vector Colorimetry with Acid Chrome Blue K

Based on the Mg^(2+)complexation with acid chrome blue K(ACBK)at pH 10.2,an automatic system was designed to determine total hardness of water.The system consists of a vector colorimeter,a multi-channel sampling pump and both reagents A and B.Two kinds of reagent solutions were prepared and used in this system,i.e.,ammoniacal buffer and ACBK—disodium magnesium EDTA solutions.The experimental results of the standard solutions containing 2 and 3 mg/L of total hardness showed that the relative standard deviations(RSDs)were 1.9%and 2.2%,respectively,and the limit of detection(LOD)was only 0.035 mg/L.The detection of four natural water samples showed that the recoveries were between 85.0%and 108.6%,consistent with those obtained by ICP-AES method.

Interpolation of Vector Measures

Let （Ω, ∑） be a measurable space and mo ： E→ Xo and m1 ： E → X1 be positive vector measures with values in the Banach KSthe function spaces Xo and X1. If 0 〈 a 〈 1, we define a X01-ax1a new vector measure [m0, m]a with values in the Calderdn lattice interpolation space and we analyze the space of integrable functions with respect to measure [m0, m1]a in order to prove suitable extensions of the classical Stein Weiss formulas that hold for the complex interpolation of LP-spaces. Since each p-convex order continuous Kothe function space with weak order unit can be represented as a space of p-integrable functions with respect to a vector measure, we provide in this way a technique to obtain representations of the corresponding complex interpolation spaces. As applications, we provide a Riesz-Thorin theorem for spaces of p-integrable functions with respect to vector measures and a formula for representing the interpolation of the injective tensor product of such spaces.

ORTHOGONAL VECTOR MEASURES

This paper introduces the concept of orthogonal vector measures, and gives the Yosida-Hewittdecomposition theorem for this kind of vector measures. The major results are(a) Any orthogonal vector measure can gain it countable additivity by enlarging its domain;(b) Every orthogonal vector measure can be represented as the sum of two orthogonal vectormeasures, one of which is countably additive, and the other is purely finitely additive. Furthermore,these vector measures are completely perpendicular to each other.

Iterative subspace matching pursuit for joint sparse recovery

Joint sparse recovery(JSR)in compressed sensing(CS)is to simultaneously recover multiple jointly sparse vectors from their incomplete measurements that are conducted based on a common sensing matrix.In this study,the focus is placed on the rank defective case where the number of measurements is limited or the signals are significantly correlated with each other.First,an iterative atom refinement process is adopted to estimate part of the atoms of the support set.Subsequently,the above atoms along with the measurements are used to estimate the remaining atoms.The estimation criteria for atoms are based on the principle of minimum subspace distance.Extensive numerical experiments were performed in noiseless and noisy scenarios,and results reveal that iterative subspace matching pursuit(ISMP)outperforms other existing algorithms for JSR.

A Class of Nonlinear Markov Iterated Function System Attractors

In this article the theory of NMIFS （Nonlinear Markov Iterated Function System） and the construction method of an NMIFS are presented. The balanced vector measure and the recursive calculation of the ＂moment＂ of a class of NMIFS attractors are discussed, and the structure characteristics are analyzed. The result shows that we can calculate the moments ^M^（i） （i = 1, 2,...） for MIFS, but for NMIFS, we cannot calculate ^M^（i） directly because the calculation of ^M^（i）depends on the value of ^M^（j） （j ≥ i）. So only the approximated value of ^M^（i）could be obtained.

A Novel Stable Clustering Design Method for Hierarchical Satellite Network

This article proposes a novel stable clustering design method for hierarchical satellite network in order to increase its stability,reduce the overhead of storage and exert effective control of the delay performances based on a 5-dimensional vector model. According to the function of stability measureinent and owing to the limitation of minimal average routing table length, the hierarchical satellite network is grouped into separate stable connected clusters to improve destruction resistance and reconstruction ability in the future integrated network. In each cluster, redundant communication links with little contribution to network stability and slight influences on delay variation are deleted to satisfy the requirements for stability and connectivity by means of optimal link resources, and, also, the idea of logical weight is introduced to select the optimal satellites used to communicate with neighboring cluster satellites. Finally, the feasibility and effectiveness of the proposed method are verified by comparing it with the simulated performances of other two typical hierarchical satellite networks, double layer satellite constellation（DLSC） and satellite over satellite（SOS）.

ACCURATE AND EFFICIENT IMAGE RECONSTRUCTION FROM MULTIPLE MEASUREMENTS OF FOURIER SAMPLES

Several problems in imaging acquire multiple measurement vectors(MMVs)of Fourier samples for the same underlying scene.Image recovery techniques from MMVs aim to exploit the joint sparsity across the measurements in the sparse domain.This is typically accomplished by extending the use of`1 regularization of the sparse domain in the single measurement vector(SMV)case to using`2,1 regularization so that the“jointness”can be accounted for.Although effective,the approach is inherently coupled and therefore computationally inefficient.The method also does not consider current approaches in the SMV case that use spatially varying weighted`1 regularization term.The recently introduced variance based joint sparsity(VBJS)recovery method uses the variance across the measurements in the sparse domain to produce a weighted MMV method that is more accurate and more efficient than the standard`2,1 approach.The efficiency is due to the decoupling of the measurement vectors,with the increased accuracy resulting from the spatially varying weight.Motivated by these results,this paper introduces a new technique to even further reduce computational cost by eliminating the requirement to first approximate the underlying image in order to construct the weights.Eliminating this preprocessing step moreover reduces the amount of information lost from the data,so that our method is more accurate.Numerical examples provided in the paper verify these benefits.