zero crossings of a wavelet transform the completeness stability and application to pattern recognition of a multiscale representation based on zero crossings is discussed an alternative projection algorithm is described that reconstructs a signal from a zero crossing representation which is stabilized by keeping the value of the wavelet transform integral between each pair of consecutive zero crossings the reconstruction algorithm has a fast convergence and each iteration requires o n log sup 2 n computation for a signal of n samples the zero crossings of a wavelet transform define a representation which is particularly well adapted for solving pattern recognition problems as an example the implementation and results of a coarse to fine stereo matching algorithm are described

constrained consensus in continuous time multiagent systems under weighted graph this paper studies constrained consensus for continuous time multiagent systems where agents are subject to different state constraints a projection based consensus protocol is presented where a projection operator is used on top of the traditional consensus protocol in order to keep the state staying inside the constraint set this operator can ensure the smoothness of the state trajectory under projection and it will only be used when the state is close to the boundary of the constraint set and about to move outside under this protocol each individual agent only needs to know its own state and constraint set as well as the relative states to its neighboring agents with the assumption that all constraint sets are convex and have nonempty intersection it is proven that global consensus can be achieved without violating any state constraints during the transience

asynchronous distributed algorithms for solving linear algebraic equations two asynchronous distributed algorithms are presented for solving a linear equation of the form ax b with at least one solution the equation is simultaneously and asynchronously solved by m agents assuming that each agent knows only a subset of the rows of the partitioned matrix a b the estimates of the equation s solution generated by its neighbors and nothing more neighbor relationships are characterized by a time dependent directed graph whose vertices correspond to agents and whose arcs depict neighbor relationships each agent recursively updates its estimate of a solution at its own event times by utilizing estimates generated by its neighbors which are transmitted with delays the event time sequences of different agents are not assumed to be synchronized it is shown that for any matrix vector pair a b for which the equation has a solution and any repeatedly jointly strongly connected sequence of neighbor graphs defined on the merged sequence of all agents event times the algorithms cause all agents estimates to converge exponentially fast to the same solution to ax b the first algorithm requires a specific initialization step at each agent and the second algorithm works for arbitrary initializations explicit expressions for convergence rates are provided and a relation between local initializations and limiting consensus solutions is established which is used to solve the least 2 norm solution

exponential convergence of a distributed algorithm for solving linear algebraic equations abstract in a recent paper a distributed algorithm was proposed for solving linear algebraic equations of the form a x b assuming that the equation has at least one solution the equation is presumed to be solved by m agents assuming that each agent knows a subset of the rows of the matrix a b the current estimates of the equation s solution generated by each of its neighbors and nothing more neighbor relationships are represented by a time dependent directed graph n t whose vertices correspond to agents and whose arcs characterize neighbor relationships sufficient conditions on n t were derived under which the algorithm can cause all agents estimates to converge exponentially fast to the same solution to a x b these conditions were also shown to be necessary for exponential convergence provided the data about a b available to the agents is non redundant the aim of this paper is to relax this non redundant assumption this is accomplished by establishing exponential convergence under conditions which are the weakest possible for the problem at hand the conditions are based on a new notion of graph connectivity an improved bound on the convergence rate is also derived

signal representation in the combined phase spatial space reconstruction and criteria for uniqueness motivated by the major roles of the spectral phase in signal structure and by previous results on the importance of localized representation in images we develop conditions for unique representation of a signal by a combination of its spectral fourier phase and spatial samples methods for signal reconstruction from various combinations of spatial and phase information are introduced it is concluded that most of the previous results in the area of phase only representation and reconstruction are special cases of the general approach presented here

state consensus for multi agent systems with switching topologies and time varying delays in this paper we investigate state consensus problems for discrete time multi agent systems with changing communications topologies and bounded time varying communication delays the analysis in this paper is based on the properties of non negative matrices we first extend the model of networks of dynamic agents to the case with multiple time delays and prove that if the communication topology time delays and weighting factors are time invariant then the necessary and sufficient condition that the multi agent system solves a consensus problem is that the communication topology represented by a directed graph has spanning trees then we allow for dynamically changing communication topologies and bounded time varying communication delays and present some sufficient conditions for state consensus of system finally as a special case of our model the problem of asynchronous information exchange is also discussed

optimal reconstruction of images from localized phase the importance of localized phase in signal representation is investigated the convergence rate of the pocs algorithm projection onto convex sets used for image reconstruction from spectral phase is defined and analyzed and the characteristics of images optimally reconstructed from phase only information are presented it is concluded that images of geometric form are most efficiently reconstructed from their spectral phase whereas images of symmetric form have the poorest convergence characteristics the transition between the two extremes is shown to be continuous the results provide a new approach and analysis of the previously reported advantages of the localized phase representation over the global approach and suggest possible compression schemes

the reconstruction of a multidimensional sequence from the phase or magnitude of its fourier transform this paper addresses two fundamental issues involved in the reconstruction of a multidimensional sequence from either the phase or magnitude of its fourier transform the first issue relates to the uniqueness of a multidimensional sequence in terms of its phase or magnitude although phase or magnitude information alone is not sufficient in general to uniquely specify a sequence a large class of sequences are shown to be recoverable from their phase or magnitude the second issue which is addressed in this paper concerns the actual reconstruction of a multidimensional sequence from its phase or magnitude for those sequences which are uniquely specified by their phase several practical algorithms are described which may be used to reconstruct a sequence from its phase several examples of phase only reconstruction are also presented unfortunately however even for those sequences which are uniquely defined by their magnitude it appears that a practical algorithm is yet to be developed for reconstructing a sequence from only its magnitude nevertheless an iterative procedure which has been proposed is briefly discussed and evaluated

distributed consensus for multiagent systems with communication delays and limited data rate this paper considers the average consensus problem for multiagent networks with communication delays and limited data rate on one hand communication delays often exist in information acquisition and transmission on the other hand only limited state information of agents can be transmitted to their neighbors at each time step due to bandwidth constraints the average consensus problem becomes much more complicated when both delays and data rate constraints are to be considered in this paper a distributed consensus protocol is proposed based on dynamic encoding and decoding it is shown that for a connected network as long as the time delays are bounded the average consensus can be achieved with a finite communication data rate in particular it is shown that merely a one bit information exchange between each pair of adjacent agents at each time step suffices to guarantee the average consensus

consensus conditions of continuous time multi agent systems with time delays and measurement noises this work is concerned with stochastic consensus conditions of multi agent systems with both time delays and measurement noises for the case of additive noises we develop some necessary conditions and sufficient conditions for stochastic weak consensus by estimating the differential resolvent function for delay equations by the martingale convergence theorem we obtain necessary conditions and sufficient conditions for stochastic strong consensus for the case of multiplicative noises we consider two kinds of time delays appeared in the measurement term and the noise term respectively we first show that stochastic weak consensus with the exponential convergence rate implies stochastic strong consensus then by constructing degenerate lyapunov functional we find the sufficient consensus conditions and show that stochastic consensus can be achieved by carefully choosing the control gain according to the noise intensities and the time delay in the measurement term

an extension of lasalle s invariance principle and its application to multi agent consensus in the paper an extension of lasalle s invariance principle to a class of switched linear systems is studied one of the motivations is the consensus problem in multi agent systems unlike most existing results in which each switching mode in the system needs to be asymptotically stable this paper allows that the switching modes are only lyapunov stable under certain ergodicity assumptions an extension of lasalle s invariance principle for global asymptotic stability is obtained then it is used to solve the consensus reaching problem of certain multi agent systems in which each agent is modeled by a double integrator and the associated interaction graph is switching and is assumed to be only jointly connected

novel criteria of uniqueness for signal reconstruction from phase an approach for ascertaining whether a signal is uniquely determined by its fourier transform phase is proposed it is shown that uniqueness corresponds to the nonsingularity of a matrix which can be formed from the finite length real sequence the criterion of uniqueness for reconstructing a one dimensional finite length sequence from its phase is discussed the criterion of uniqueness for reconstructing a multidimensional finite length sequence is presented

connectivity and set tracking of multi agent systems guided by multiple moving leaders in this paper we investigate distributed multi agent tracking of a convex set specified by multiple moving leaders with unmeasurable velocities various jointly connected interaction topologies of the follower agents with uncertainties are considered in the study of set tracking based on the connectivity of the time varying multi agent system necessary and sufficient conditions are obtained for set input to state stability and set integral input to state stability for a nonlinear neighbor based coordination rule with switching directed topologies conditions for asymptotic set tracking are also proposed with respect to the polytope spanned by the leaders

iterative techniques for minimum phase signal reconstruction from phase or magnitude in this paper we develop iterative algorithms for reconstructing a minimum phase sequence from the phase or magnitude of its fourier transform these iterative solutions involve repeatedly imposing a causality constraint in the time domain and incorporating the known phase or magnitude function in the frequency domain this approach is the basis of a new means of computing the hilbert transform of the log magnitude or phase of the fourier transform of a minimum phase sequence which does not require phase unwrapping finally we discuss the potential use of this iterative computation in determining samples of the unwrapped phase of a mixed phase sequence

constrained consensus and optimization in multi agent networks we present distributed algorithms that can be used by multiple agents to align their estimates with a particular value over a network with time varying connectivity our framework is general in that this value can represent a consensus value among multiple agents or an optimal solution of an optimization problem where the global objective function is a combination of local agent objective functions our main focus is on constrained problems where the estimates of each agent are restricted to lie in different convex sets to highlight the effects of constraints we first consider a constrained consensus problem and present a distributed projected consensus algorithm in which agents combine their local averaging operation with projection on their individual constraint sets this algorithm can be viewed as a version of an alternating projection method with weights that are varying over time and across agents we establish convergence and convergence rate results for the projected consensus algorithm we next study a constrained optimization problem for optimizing the sum of local objective functions of the agents subject to the intersection of their local constraint sets we present a distributed projected subgradient algorithm which involves each agent performing a local averaging operation taking a subgradient step to minimize its own objective function and projecting on its constraint set we show that with an appropriately selected stepsize rule the agent estimates generated by this algorithm converge to the same optimal solution for the cases when the weights are constant and equal and when the weights are time varying but all agents have the same constraint set

constrained consensus in unbalanced networks with communication delays in this note a constrained consensus problem is studied for multi agent systems in unbalanced networks in the presence of communication delays here each agent needs to lie in a closed convex constraint set while reaching a consensus the communication graphs are directed dynamically changing and not necessarily balanced and only the union of the graphs is assumed to be strongly connected among each time interval of a certain bounded length the analysis is performed based on an undelayed equivalent system that is composed of a linear main body and an error auxiliary to tackle the loss of symmetry caused by unbalanced graphs and communication delays a novel approach is proposed the idea is to estimate the distance from each agent to the intersection set of all agents constraint sets based on the properties of the projection on convex sets so as to show consensus convergence by contradiction it is shown that the error auxiliary vanishes as time evolves and the linear main body converges to a vector with an exponential rate as a separate system it is also shown that the communication delays do not affect the consensus stability and constrained consensus is reached even if the communication delays are arbitrarily bounded finally a numerical example is included to illustrate the obtained theoretical results

interpretation and identification of minimum phase reflection coefficients if the acoustic reflection coefficient is minimum phase then the causality condition can be used to reconstruct its phase from its magnitude such reconstructions are useful when environmental conditions obscure the phase which is vital to understanding the dynamics of the reflecting object however the reconstructions are usually impossible because one cannot be sure that the reflection coefficient is minimum phase the present work addresses this difficulty by formulating a time domain description of the minimum phase condition and by identifying classes of submerged objects that always create minimum phase reflection coefficients numerical examples are used to confirm the analytical findings and to illustrate their applicability to objects that reflect sound with a wide range of magnitudes

constrained consensus of asynchronous discrete time multi agent systems with time varying topology the union graph is assumed to be strongly connected over each finite interval an approach is proposed to transform the original network to a synchronous one we show that the linear part converges and the projection error vanishes over time in this paper the constrained consensus problem is studied for asynchronous discrete time multi agent system where each agent needs to lie in a closed convex constraint set while reaching consensus the communication graphs are assumed to be directed unbalanced dynamically changing in addition their union graph is assumed to be strongly connected among certain intervals of finite length to deal with the asynchronous communications among agents the original asynchronous system is equivalently transformed to the synchronous one by adding new agents by employing the properties of the projection on the convex sets the distance from the states of the agents in the newly constructed system to the intersection set of all agents constraint sets is estimated based on this estimation the original system is proven to reach consensus by showing that the linear parts of the newly constructed systems converge and the nonlinear parts vanish over time finally two numerical examples are provided to show the effectiveness of the theoretical results

distributed nonlinear control of mobile autonomous multi agents abstract this paper studies the distributed nonlinear control of mobile autonomous agents with variable and directed topology a new distributed nonlinear design scheme is presented for multi agent systems modeled by double integrators with the new design the outputs of the controlled agents asymptotically converge to each other as long as a mild connectivity condition is satisfied moreover the velocity derivative of the output of each agent can be restricted to be within any specified neighborhood of the origin which is of practical interest for systems under such physical constraint the new design is still valid if one of the agents is a leader and the control objective is to achieve leader following as an illustration of the generality and effectiveness of the presented methodology the formation control of a group of unicycle mobile robots with nonholonomic constraints is revisited instead of assuming the point robot model the unicycle model is transformed into two double integrators by dynamic feedback linearization and the proposed distributed nonlinear design method is used to overcome the singularity problem caused by the nonholonomic constraint by properly restricting the velocities simulation results are included to illustrate the theoretical results

acoustical inverse problems regularization direct definition of filter factors using signal to noise ratio abstract acoustic imaging aims at localization and characterization of sound sources using microphone arrays in this paper a new regularization method for acoustic imaging by inverse approach is proposed the method first relies on the singular value decomposition of the plant matrix and on the projection of the measured data on the corresponding singular vectors in place of regularization using classical methods such as truncated singular value decomposition and tikhonov regularization the proposed method involves the direct definition of the filter factors on the basis of a thresholding operation defined from the estimated measurement noise the thresholding operation is achieved using modified filter functions the originality of the approach is to propose the definition of a filter factor which provides more damping to the singular components dominated by noise than that given by the tikhonov filter this has the advantage of potentially simplifying the selection of the best regularization amount in inverse problems theoretical results show that this method is comparatively more accurate than tikhonov regularization and truncated singular value decomposition

on the approximation of l_ 2 inner products from sampled data most signal processing applications are based on discrete time signals although the origin of many sources of information is analog in this paper we consider the task of signal representation by a set of functions focusing on the representation coefficients of the original continuous time signal the question considered herein is to what extent the sampling process keeps algebraic relations such as inner product intact by interpreting the sampling process as a bounded operator a vector like interpretation for this approximation problem has been derived giving rise to an optimal discrete approximation scheme different from the riemann type sum often used the objective of this optimal scheme is in the min max sense and no bandlimitedness constraints are imposed tight upper bounds on this optimal and the riemann type sum approximation schemes are then derived we further consider the case of a finite number of samples and formulate a closed form solution for such a case the results of this work provide a tool for finding the optimal scheme for approximating an l2 inner product and to determine the maximum potential representation error induced by the sampling process the maximum representation error can also be determined for the riemann type sum approximation scheme examples of practical applications are given and discussed

consensus seeking in multiagent systems under dynamically changing interaction topologies this note considers the problem of information consensus among multiple agents in the presence of limited and unreliable information exchange with dynamically changing interaction topologies both discrete and continuous update schemes are proposed for information consensus this note shows that information consensus under dynamically changing interaction topologies can be achieved asymptotically if the union of the directed interaction graphs have a spanning tree frequently enough as the system evolves

distributed velocity constrained consensus of discrete time multi agent systems with nonconvex constraints switching topologies and delays in this technical note a distributed velocity constrained consensus problem is studied for discrete time multi agent systems where each agent s velocity is constrained to lie in a nonconvex set a distributed constrained control algorithm is proposed to enable all agents to converge to a common point using only local information the gains of the algorithm for all agents need not to be the same or predesigned and can be adjusted by each agent itself based on its own and neighbors information it is shown that the algorithm is robust to arbitrarily bounded communication delays and arbitrarily switching communication graphs provided that the union of the graphs has directed spanning trees among each certain time interval the analysis approach is based on multiple novel model transformations proper control parameter selections boundedness analysis of state dependent stochastic matrices1 exploitation of the convexity of stochastic matrices and the joint connectivity of the communication graphs numerical examples are included to illustrate the theoretical results

distributed h constrained consensus problem abstract this paper is concerned with the distributed h constrained consensus problem for multi agent systems the objective is to use local information to make all agents reach a consensus in a given convex set while satisfying a desired h performance index in the presence of external disturbances a nonlinear distributed algorithm is adopted to solve this constrained consensus problem to measure the effects of the disturbance on the consensus of all agents and the convergence of all agents to the convex set a nonlinear function is constructed as the h output function by analyzing the convexity of the convex set a sufficient condition is given to solve the constrained consensus problem with the desired h performance finally a numerical simulation example is provided to show the effectiveness of our theoretical results

image restoration by the method of convex projections part 1ߞtheory a projection operator onto a closed convex set in hilbert space is one of the few examples of a nonlinear map that can be defined in simple abstract terms moreover it minimizes distance and is nonexpansive and therefore shares two of the more important properties of ordinary linear orthogonal projections onto closed linear manifolds in this paper we exploit the properties of these operators to develop several iterative algorithms for image restoration from partial data which permit any number of nonlinear constraints of a certain type to be subsumed automatically their common conceptual basis is as follows every known property of an original image f is envisaged as restricting it to lie in a well defined closed convex set thus m such properties place f in the intersection e0 ei of the corresponding closed convex sets e1 e2 em given only the projection operators pi onto the individual ei s i 1 m we restore f by recursive means clearly in this approach the realization of the pi s in a hilbert space setting is one of the major synthesis problems section i describes the geometrical significance of the three main theorems in considerable detail and most of the underlying ideas are illustrated with the aid of simple diagrams section ii presents rules for the numerical implementation of 11 specific projection operators which are found to occur frequently in many signal processing applications and the appendix contains proofs of all the major results

containment control of multi agent systems in a noisy communication environment the containment problem of first order and second order integral multi agent systems with communication noises is investigated in this paper motivated by the previous work a time varying gain a t is introduced to attenuate the noise effect it is proved that the proposed protocol can solve the mean square containment problem if the following conditions hold 1 the communication topology graph has a spanning forest whose roots are leaders of the multi agent system 2 0 a t dt 3 lim t a t 0 moreover if a t is uniformly continuous these conditions are necessary for ensuring the mean square containment in addition the proposed protocol is also extended to allow the case where each agent has its own gain a i t it is proved that the mean square containment problem can still be solved if all agent dependent gains are infinitesimals of the same order as time goes to infinity finally two simulation examples are provided to demonstrate the effectiveness of the proposed protocols

the generalized gabor scheme of image representation in biological and machine vision a scheme suitable for visual information representation in a combined frequency position space is investigated through image decomposition into a finite set of two dimensional gabor elementary functions gef the scheme is generalized to account for the position dependent gabor sampling rate oversampling logarithmic frequency scaling and phase quantization characteristic of the visual system comparison of reconstructed signal highlights the advantages of the generalized gabor scheme in coding typical bandlimited images it is shown that there exists a tradeoff between the number of frequency components used per position and the number of such clusters sampling rate utilized along the spatial coordinate

distributed consensus of second order multiagent systems with nonconvex velocity and control input constraints this paper is devoted to a distributed consensus problem for second order multiagent systems with nonconvex velocity and control input constraints a distributed control algorithm is introduced using local information it is shown that consensus can be achieved as long as the union of the communication graphs has directed spanning trees among each time interval of certain bounded length in the presence of arbitrarily bounded communication delays finally a numerical example is included to illustrate the theoretical results

lyapunov based approach to multiagent systems with switching jointly connected interconnection this note addresses a coordination problem of a multiagent system with jointly connected interconnection topologies neighbor based rules are adopted to realize local control strategies for these continuous time autonomous agents described by double integrators although the interagent connection structures vary over time and related graphs may not be connected a sufficient condition to make all the agents converge to a common value is given for the problem by a proposed lyapunov based approach and related space decomposition technique

applications of the causality condition to one dimensional acoustic reflection problems the causality condition is examined as a means of determining frequency domain information about a submerged object from a partial knowledge of its acoustic reflection characteristics a one dimensional problem is considered in which an acoustic wave reflects from an object that is described by the impedance it presents to the fluid two new applications of the causality condition to the frequency domain analysis of this problem are investigated and illustrated by numerical examples in each application the causality condition is used to find the object s complex impedance from a knowledge of the reflected wave s magnitude the first application is to experimental studies where one desires a knowledge of an object s complex impedance but practical limitations only allow a measurement of the reflected wave amplitude analysis shows that the causality condition may be used to determine the phase of the reflected wave and hence the object s impedance if the reflection coefficient is minimum phase when this is true examples suggest that the phase of the reflection coefficient may be accurately determined from the causality condition even in the presence of noise and band limited data the second application is to design situations where one wishes to create an object that reflects sound with a specified frequency dependent magnitude the causality condition may aid the designer by providing a knowledge of all causal object impedances that produce the same reflection coefficient magnitude a numerical example is presented in which a variety of causal object impedances produce the same reflection coefficient magnitude over an infinite frequency range

stochastic strongly convex optimization via distributed epoch stochastic gradient algorithm this article considers the problem of stochastic strongly convex optimization over a network of multiple interacting nodes the optimization is under a global inequality constraint and the restriction that nodes have only access to the stochastic gradients of their objective functions we propose an efficient distributed non primal dual algorithm by incorporating the inequality constraint into the objective via a smoothing technique we show that the proposed algorithm achieves an optimal o 1 t t is the total number of iterations convergence rate in the mean square distance from the optimal solution in particular we establish a high probability bound for the proposed algorithm by showing that with a probability at least 1 the proposed algorithm converges at a rate of o ln ln t t finally we provide numerical experiments to demonstrate the efficacy of the proposed algorithm

stability of multiagent systems with time dependent communication links we study a simple but compelling model of network of agents interacting via time dependent communication links the model finds application in a variety of fields including synchronization swarming and distributed decision making in the model each agent updates his current state based upon the current information received from neighboring agents necessary and or sufficient conditions for the convergence of the individual agents states to a common value are presented thereby extending recent results reported in the literature the stability analysis is based upon a blend of graph theoretic and system theoretic tools with the notion of convexity playing a central role the analysis is integrated within a formal framework of set valued lyapunov theory which may be of independent interest among others it is observed that more communication does not necessarily lead to faster convergence and may eventually even lead to a loss of convergence even for the simple models discussed in the present paper