is denoising dead image denoising has been a well studied problem in the field of image processing yet researchers continue to focus attention on it to better the current state of the art recently proposed methods take different approaches to the problem and yet their denoising performances are comparable a pertinent question then to ask is whether there is a theoretical limit to denoising performance and more importantly are we there yet as camera manufacturers continue to pack increasing numbers of pixels per unit area an increase in noise sensitivity manifests itself in the form of a noisier image we study the performance bounds for the image denoising problem our work in this paper estimates a lower bound on the mean squared error of the denoised result and compares the performance of current state of the art denoising methods with this bound we show that despite the phenomenal recent progress in the quality of denoising algorithms some room for improvement still remains for a wide class of general images and at certain signal to noise levels therefore image denoising is not dead yet

buchsbaum criterion of segre products of vector bundles on multiprojective space abstract this paper investigates the buchsbaum property of segre product of buchsbaum vector bundles on multiprojective spaces a buchsbaum vector bundle on the projective space is isomorphic to a direct sum of exterior products of differential sheaves with some twist we will give cohomological criteria for the buchsbaum property of the segre products of these bundles

model matching and factorization for nonlinear systems a structural approach the model matching and the left factorization problems for nonlinear systems are investigated using an approach based on the structural algorithm sufficient conditions for the solvability of the f

uniform stability of switched linear systems extensions of lasalle s invariance principle this paper addresses the uniform stability of switched linear systems where uniformity refers to the convergence rate of the multiple solutions that one obtains as the switching signal ranges over a given set we provide a collection of results that can be viewed as extensions of lasalle s invariance principle to certain classes of switched linear systems using these results one can deduce asymptotic stability using multiple lyapunov functions whose lie derivatives are only negative semidefinite depending on the regularity assumptions placed on the switching signals one may be able to conclude just asymptotic stability or uniform exponential stability we show by counter example that the results obtained are tight

buchsbaum rim sheaves and their multiple sections abstract this paper begins by introducing and characterizing buchsbaum rim sheaves on z proj r where r is a graded gorenstein k algebra they are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free r modules then we study multiple sections of a buchsbaum rim sheaf b i e we consider morphisms p b of sheaves on z dropping rank in the expected codimension where h0 z p is a free r module the main purpose of this paper is to study properties of schemes associated to the degeneracy locus s of it turns out that s is often not equidimensional let x denote the top dimensional part of s in this paper we measure the difference between x and s compute their cohomology modules and describe ring theoretic properties of their coordinate rings moreover we produce graded free resolutions of x and s which are in general minimal among the applications we show how one can embed a subscheme into an arithmetically gorenstein subscheme of the same dimension and prove that zero loci of sections of the dual of a null correlation bundle are arithmetically buchsbaum

regular paper model matching for linear systems with delays and 2d systems model matching problem for linear systems with delays is considered via a transfer matrix approach we deal with a general class of neutral delay differential systems which is equivalent to 2d systems from a realizability point of view the solution of the problem is based on the decomposition of the ring of the causal rational functions which is not a principal ideal domain as the intersection of two suitable principal ideal domains

on the stable exact model matching problem abstract the stable exact model matching problem semmp is investigated we state and prove a number of equivalent necessary and sufficient conditions for the existence of proper solutions to the exact model matching problem that are also stable i e have no poles inside a symmetric forbidden subset of the finite complex plane c these results can be viewed as the counterpart of the results in 3 and 9 for the case of the ring of proper and stable rational functions

computing the maximum robust controlled invariant subspace abstract an algorithm is presented to compute the maximum robust controlled invariant subspace contained in a given subspace it is based on a special computational scheme to derive the intersection of a family of subspaces which is particularly convenient when the system coefficients depend polynomially on the uncertain parameter an example is presented to illustrate the algorithm

fir stabilization in discrete one sided model matching problems this note studies stabilization problems arising in discrete estimation or preview tracking problems when unstable exosystems are used to impose steady state behavior constraints the main theme is stabilizability conditions under fir finite impulse response constraints necessary and sufficient stabilizability conditions are derived and all solutions are parametrized unlike the continuous time case where the problem is solvable under the standard detectability condition stabilizability in the discrete time case depends on the length of the impulse response and sometimes also on the smoothing lag length of preview

bounds for the minimum numbers of generators of generalized cohen macaulay ideals throughout this paper r denotes a local ring with maxima1 idea1 m z an ideal of r and s the factor ring r z we call z a generalized cohen macaulay idea1 if s is a generalized cohen macaulay ring by definition 4 3 1 a local ring a with maxima1 ideal is a generalized cohen macaulay ring if the ith local cohomology module h a of a with support b is of finite length for i o dim a 1 a is a cohen macaulay ring iff h a 0 for i o dim a 1 the class of generalized cohen macaulay local rings is rather large for instance if a is a factor ring of a cohen macaulay ring a being a generalized cohen macaulay ring means that a is equidimensional and a is a cohen macaulay ring for all prime ideals y of a 4 2 5 and 381 the aim of this paper is to give bounds for the minimum number u z of generators of a generalized cohen macaulay idea1 z in terms of the following invariants of r and s m u m n v ms r dim r s dim s the multiplicities e r e s and z zyzl s i o s 1 where 1 denotes the length function our interest in such bounds for u z arose from the article 7 of sally there she proved that if r and s are cohen macaulay rings then v z e r e s r s l r s 1 first sally s result may be generalized as

design of exact model matching systems and its applications to output tracking problems this paper is concerned with the exact model matching problem described in the frequency domain a systematic procedure to design a proper and lower order compensator with arbitrary pole position is proposed in particular the order of the compensator can be analytically found furthermore the exact model matching problem in which the model satisfies output tracking is discussed a compensator which includes an internal model of a reference signal generator is obtained as the solution of this exact model matching problem a method which derives a robust compensator is also given

a polynomial characterization of mathcal a mathcal b invariant and reachability subspaces based on the state space model of p fuhrmann a link is laid between the geometric approach to linear system theory as developed by w m wonham and a s morse and the approach based on polynomial matrices in particular polynomial characterizations of a b invariant and reachability subspaces are given these characterizations are used to prove the equivalence of the disturbance decoupling problem and the exact model matching problem and also to connect the polynomial matrix and the geometric approach to the construction of observers finally constructive procedures and conditions are given for computing the supremal a b invariant subspace and reachability space and for checking the solvability of the exact model matching problem

on liaison arithmetical buchsbaum curves and monomial curves in p3 in the context of liaison by 181 and 191 for curves in ip3 the property of being the zero scheme of a section of a rank two bundle on ip3 is connected to that of being ideally the intersection of three surfaces an immediate consequence of this property is that the homogeneous ideal i c of a curve c c p3 is generated by precisely three elements if and only if c is ideally the intersection of three suraces and c is arithmetically cohen macaulay non complete intersection furthermore the characterization of the equivalence classes defined by liaison among curves in p3 yields the well known statement that a curve c is in the liaison class of a complete intersection if and only if c is arithmetically cohen macaulay see e g 2 10 13 or 141 it seems that a cayley see 7 p 1521 in 1847 was the first who posed the problem to describe this liaison class of a complete intersection now in this paper we will begin to investigate the next simple case that is the liaison classes which are characterized by a finite dimensional vector space of dimension l using the theory of buchsbaum rings see section 2 this means we will study liaison among arithmetical buchsbaum curves in p3 first from the point of view of local algebra we get the following more general result

model matching with strong stability in switched linear systems abstract this work deals with model matching by output dynamic feedback in switched linear systems the plant and the model are assumed to be subject to different switching signals a necessary and sufficient condition for achieving model matching with asymptotic stability of both the closed loop compensated system and the compensator for a sufficiently large dwell time is proven such condition is obtained by specializing the structural condition with a suitable redefinition of the robust controlled invariant subspace involved capable of capturing not only the structural aspect of the problem but also the stability aspects the effect of the combined action of nonzero initial states and nonzero inputs is dealt with the solution to a more demanding problem formulation where the dwell time is assumed to be fixed and given is also discussed

necessary and sufficient conditions for asymptotic model matching of switching linear systems this paper investigates the problem of designing a feedback controller to force the response of a given plant to match asymptotically that of a prescribed model in case both the plant and the model are switching linear systems matching has to be achieved with stability of the feedback loop for any initial conditions of the plant the model and the controller in case it is dynamic and for any choice of the switching law solvability of the problem is characterized in terms of necessary and sufficient conditions that in part refer to the geometric structure of the difference system which compares the output of the model and of the plant stability is considered both for slow switching and for arbitrary switching proofs of the solvability conditions provide viable procedures for synthesizing the static or dynamic controllers that achieve the matching respectively when the state of the model is measurable and when it is not weaker sufficient conditions that can be practically checked by simple algorithmic procedures are provided both in the general situation and under slightly restrictive hypotheses

random walk graph laplacian based smoothness prior for soft decoding of jpeg images given the prevalence of joint photographic experts group jpeg compressed images optimizing image reconstruction from the compressed format remains an important problem instead of simply reconstructing a pixel block from the centers of indexed discrete cosine transform dct coefficient quantization bins hard decoding soft decoding reconstructs a block by selecting appropriate coefficient values within the indexed bins with the help of signal priors the challenge thus lies in how to define suitable priors and apply them effectively in this paper we combine three image priors laplacian prior for dct coefficients sparsity prior and graph signal smoothness prior for image patches to construct an efficient jpeg soft decoding algorithm specifically we first use the laplacian prior to compute a minimum mean square error initial solution for each code block next we show that while the sparsity prior can reduce block artifacts limiting the size of the overcomplete dictionary to lower computation would lead to poor recovery of high dct frequencies to alleviate this problem we design a new graph signal smoothness prior desired signal has mainly low graph frequencies based on the left eigenvectors of the random walk graph laplacian matrix lerag compared with the previous graph signal smoothness priors lerag has desirable image filtering properties with low computation overhead we demonstrate how lerag can facilitate recovery of high dct frequencies of a piecewise smooth signal via an interpretation of low graph frequency components as relaxed solutions to normalized cut in spectral clustering finally we construct a soft decoding algorithm using the three signal priors with appropriate prior weights experimental results show that our proposal outperforms the state of the art soft decoding algorithms in both objective and subjective evaluations noticeably

on the h 2 two sided model matching problem with preview the h2 optimization problem with preview and asymptotic behavior constraints is considered in a general two sided model matching setting the solution is obtained in terms of two constrained sylvester equations associated with asymptotic behavior and stabilizing solutions of two algebraic riccati equations the riccati equations do not depend on the preview length yet are affected by asymptotic behavior constraints and are thus different from the standard h2 riccati equations arising in problems with no steady state requirements or in one sided problems

multiresolution graph fourier transform for compression of piecewise smooth images piecewise smooth pws images e g depth maps or animation images contain unique signal characteristics such as sharp object boundaries and slowly varying interior surfaces leveraging on recent advances in graph signal processing in this paper we propose to compress the pws images using suitable graph fourier transforms gfts to minimize the total signal representation cost of each pixel block considering both the sparsity of the signal s transform coefficients and the compactness of transform description unlike fixed transforms such as the discrete cosine transform we can adapt gft to a particular class of pixel blocks in particular we select one among a defined search space of gfts to minimize total representation cost via our proposed algorithms leveraging on graph optimization techniques such as spectral clustering and minimum graph cuts furthermore for practical implementation of gft we introduce two techniques to reduce computation complexity first at the encoder we low pass filter and downsample a high resolution hr pixel block to obtain a low resolution lr one so that a lr gft can be employed at the decoder upsampling and interpolation are performed adaptively along hr boundaries coded using arithmetic edge coding so that sharp object boundaries can be well preserved second instead of computing gft from a graph in real time via eigen decomposition the most popular lr gfts are pre computed and stored in a table for lookup during encoding and decoding using depth maps and computer graphics images as examples of the pws images experimental results show that our proposed multiresolution gft scheme outperforms h 264 intra by 6 8 db on average in peak signal to noise ratio at the same bit rate

disturbance decoupling in hybrid linear systems with state jumps this work investigates the problem of making the output of a hybrid linear system totally insensitive to a disturbance input while attaining global asymptotic stability of the compensated hybrid dynamics in the presence of possibly nonuniformly spaced state jumps meeting the only condition that the minimum time between two consecutive occurrences is no smaller than a given positive real constant both existential and constructive necessary and sufficient conditions for solvability of the problem addressed are proven

wavelet transform domain filters a spatially selective noise filtration technique wavelet transforms are multiresolution decompositions that can be used to analyze signals and images they describe a signal by the power at each scale and position edges can be located very effectively in the wavelet transform domain a spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced a high correlation is used to infer that there is a significant feature at the position that should be passed through the filter the authors have tested the technique on simulated signals phantom images and real mr images it is found that the technique can reduce noise contents in signals and images by more than 80 while maintaining at least 80 of the value of the gradient at most edges the authors did not observe any gibbs ringing or significant resolution loss on the filtered images artifacts that arose from the filtration are very small and local the noise filtration technique is quite robust there are many possible extensions of the technique the authors see its applications in spatially dependent noise filtration edge detection and enhancement image restoration and motion artifact removal they have compared the performance of the technique to that of the weiner filter and found it to be superior

on a theorem of castelnuovo and the equations defining space curves introduction 491 w notat ion and conventions 493 w a regularity theorem 494 w a rationality theorem 498 w the existence of secant lines 501 w open problems 505 references 506

model matching and decoupling for continuous and discrete time linear time varying systems solutions to the exact model matching and block decoupling problems for both continuous and discrete time linear time varying systems are presented the parametrisation of the whole class of proper solutions is given for the decoupling the minimal delay problem is also considered in a time varying setting the approach is algebraic and based on the smith macmillan form at infinity of a transfer matrix of a time varying system which has been recently introduced in systems theory this avoids the difficulties related to the inversion of the transfer matrices with entries in non commutative fields over which the determinants of dieudonne or ore type are much more complicated the solutions presented here involve only standard matrix computations excluding direct matrix inversions and are thus easy to implement in practice examples are treated in detail to illustrate the theoretical results and the way in which the computations are done and a physical example is also shown

special birational transformations of projective spaces abstract extending some results of crauder and katz and ein and shepherd barron on special cremona transformations we study birational transformations of p r onto a prime fano manifold such that the base locus x p r is smooth irreducible and reduced the main results are a complete classification when x has either dimension 1 and 2 or codimension 2 partial results are also obtained when x has dimension 3

the exact model matching problem for linear time varying systems an algebraic approach the exact model matching problem is formulated and solved for linear time varying systems the condition for the existence of a proper solution which is well known in the time invariant case is proven here to still be valid in the time varying case the properness is characterized using the smith macmillan form at infinity recently defined by the authors for the transfer matrices with time varying coefficients

the matching of nonlinear models via dynamic state feedback it is well known that for linear systems the model matching problem is equivalent to a disturbance decoupling problem with disturbance measurement the solution of both problems can be expressed in terms of properties of invariant subspaces of the system and of the model in this paper it is shown that for nonlinear systems under appropriate hypotheses analogous results can be obtained the solvability of a model matching problem can be expressed in terms of properties of suitable invariant distributions it is also shown that as for linear systems those properties are related to the so called structures at infinity of the system and of the model

on equations defining arithmetically cohen macaulay schemes i in this paper we continue the study of the simplest arithmetically cohen macauly cm for short schemes cf 111 and 12 i we describe the hilbert function of an arbitrary cm scheme in p of given degree e lying on a hypersurface of given degree k and such that its general curvilinear section has minimal genus proposition 1 3 we present a geometric construction of all reduced irreducible codimension two cm varieties whose general curvilinear sections have minimal genus with respect to degree theorem 1 7 we also prove the following assertion essentially due to severi there exist smooth nonspecial cm curves of degree n and genus g in p iff r y1 g r d t y 1 2 proposition 1 6 any such curve has minimal genus with respect to degree in the last section we consider d dimensional cm schemes of degree e mvd j jed in p whose general curvilinear sections have minimal genus these are the most accessible cm schemes cf 12 i we prove that the corresponding part of the hilbert scheme is a connected smooth variety naturally birationally equivalent to nd symemvd p provided v d 2 theorem 2 6 this was known for m v d 2 3 1 cf 9 our proof relies on an explicit description of the infinitesimal deformations of a thick subspace of arbitrary codimension see 2 4 we work over an algebraically closed field of characteristic 0 by the genus of a cm curve we mean its arithmetic genus

matrix approach to model matching of asynchronous sequential machines in this note we propose a matrix based approach for asynchronous sequential machines using semi tensor product of matrices we convert an asynchronous machine into a discrete time bilinear system and study its dynamics by investigating its structure matrices we give simple algorithms for cycle detection and reachability analysis and moreover provide a control design method for the model matching of two input state machines

infinite structure and exact model matching problem a geometric approach we first generalize to a b c d quadruples the geometric characterization of the infinite zero structure we then give a new geometric proof for a solvability condition of the exact model matching problem expressed in terms of this concept and previously established in the polynomial context by morse verghese and pernebo this emphasizes the approach independent character of the infinite zero structure

graph laplacian regularization for image denoising analysis in the continuous domain inverse imaging problems are inherently underdetermined and hence it is important to employ appropriate image priors for regularization one recent popular prior the graph laplacian regularizer assumes that the target pixel patch is smooth with respect to an appropriately chosen graph however the mechanisms and implications of imposing the graph laplacian regularizer on the original inverse problem are not well understood to address this problem in this paper we interpret neighborhood graphs of pixel patches as discrete counterparts of riemannian manifolds and perform analysis in the continuous domain providing insights into several fundamental aspects of graph laplacian regularization for image denoising specifically we first show the convergence of the graph laplacian regularizer to a continuous domain functional integrating a norm measured in a locally adaptive metric space focusing on image denoising we derive an optimal metric space assuming non local self similarity of pixel patches leading to an optimal graph laplacian regularizer for denoising in the discrete domain we then interpret graph laplacian regularization as an anisotropic diffusion scheme to explain its behavior during iterations e g its tendency to promote piecewise smooth signals under certain settings to verify our analysis an iterative image denoising algorithm is developed experimental results show that our algorithm performs competitively with state of the art denoising methods such as bm3d for natural images and outperforms them significantly for piecewise smooth images

performance optimization of switched systems a model matching approach in this paper we consider a prototypical model matching problem where the various mappings involved are systems that switch arbitrarily among n stable linear time invariant lti systems the interest is placed on optimizing the worst case performance of this model matching system over all possible switchings with either l infin induced norm or h 2 norm as the performance criterion this optimization is performed over all youla kucera parameters that switch causally in time among n stable lti systems for the particular setup at hand it is shown that the optimal youla kucera parameter need not depend on the switching trajectory in the cases of partially matched switching and unmatched switching and that it can be obtained as an lti solution to an associated standard l 1 or h 2 optimization in the case of matched switching two convergent sequences to the optimal solution from above and below are formulated in terms of linear programs and quadratic programs respectively for the l infin induced and h 2 norm optimizations an approximate solution with any given precision is possible by finite truncation applications of these results to sensitivity minimization linear switched parameter systems and cooperative control are provided

image bit depth enhancement via maximum a posteriori estimation of ac signal when images at low bit depth are rendered at high bit depth displays missing least significant bits needs to be estimated we study the image bit depth enhancement problem estimating an original image from its quantized version from a minimum mean squared error mmse perspective we first argue that a graph signal smoothness prior one defined on a graph embedding the image structure is an appropriate prior for the bit depth enhancement problem we next show that directly solving for the mmse solution is in general too computationally expensive to be practical we then propose an efficient approximation strategy in particular we first estimate the ac component of the desired signal in a maximum a posteriori formulation efficiently computed via convex programming we then compute the dc component with an mmse criterion in a closed form given the computed ac component experiments show that our proposed two step approach has improved performance over the conventional bit depth enhancement schemes in both objective and subjective comparisons

the output regulation problem with stability for linear switching systems a geometric approach abstract this work presents a solution for the output regulation problem with quadratic stability under arbitrary switching in linear switching systems the extension to other stability requirements like asymptotic stability in particular is also considered and it is shown to affect only few specific features of the proposed solution the main reason is that the geometric approach which is at the basis of the developed methodology establishes a neat separation between the structural aspects and the stability aspects of the problem for the same reason continuous time systems and discrete time systems are given a unified treatment as far as the structural issues are concerned while different technicalities characterize the discussion of the stability issues

asymptotic model matching for nonlinear systems this paper investigates the problem of designing a compensating control law for a square invertible nonlinear plant so that the response of the closed loop system asymptotically matches that of a prescribed driven nonlinear model a set of necessary conditions for achieving asymptotic model matching is established one of these involves the stability properties for subdynamics which are common to every model matching closed loop these subdynamics called the fixed dynamics are intrinsically characterized based on these results a new set of sufficient conditions for achieving asymptotic model matching is given the interrelation between the minimum phase and vector relative degree properties of a plant and a matchable model are studied

disturbance decoupling with closed loop modes stability in switched linear systems this work deals with the problem of rendering the output of a switched linear system insensitive to a disturbance input with the requirement that the dynamics of the closed loop system be exponentially stable for all switching signals with a sufficiently large dwell time a necessary and sufficient condition for the problem to have a solution is shown a complete computational procedure to check the solvability condition and to synthesize the compensation scheme is provided a worked out example is presented with the aim of showing the effectiveness of the devised method

fundamentals of statistical signal processing estimation theory minimum variance unbiased estimation cramer rao lower bound linear models general minimum variance unbiased estimation best linear unbiased estimators maximum likelihood estimation least squares method of moments the bayesian philosophy general bayesian estimators linear bayesian estimators kalman filters summary of estimators extension for complex data and parameters

on the robust controlled invariant abstract the robust controlled invariant is defined as a tool to characterize systems subject to parameter changes and to set up a geometric approach to robustness in the large in multi variable control problems as a typical application the robust disturbance decoupling problem an extended version of the well known disturbance decoupling is presented and a necessary and sufficient condition for it to have a solution is derived

the disturbance decoupling problem with stability for switching dynamical systems abstract the disturbance decoupling problem with stability is dealt with by means of the geometric approach for switching systems the existence of feedbacks which decouple the disturbance and at the same time assure stability is difficult to characterize since the action of the feedback couples with that of the switching law under suitable conditions it is shown that the above requirement can be dealt with in separate ways and this allows us to state a checkable necessary condition and on that basis also a sufficient condition for solvability of the problem

a novel numerical method for exact model matching problem with stability in system design the exact model matching problem with stability consists of compensating a given system using a realizable control law of a specified structure in order to ensure the stability of the compensated system and achieve a target closed loop transfer function in this paper we develop a novel numerical method to verify the solvability of the problem for left invertible systems and further construct a desired solution our method has a complexity which is cubic in the state dimension of the system and the desired model and can be implemented in a numerically reliable way

disturbance decoupling with quadratic stability for switched linear systems in this paper disturbance decoupling problems without stability and with quadratic stability for switched linear systems are formulated in the framework of the so called geometric approach firstly necessary and sufficient conditions for the problem without stability to be solvable are given secondly sufficient conditions for the problem with quadratic stability to be solvable are given further for switched linear systems composed of two subsystems necessary and sufficient conditions for the problem with quadratic stability to be solvable are also investigated finally an illustrative example is shown

stability and stabilizability of switched linear systems a survey of recent results during the past several years there have been increasing research activities in the field of stability analysis and switching stabilization for switched systems this paper aims to briefly survey recent results in this field first the stability analysis for switched systems is reviewed we focus on the stability analysis for switched linear systems under arbitrary switching and we highlight necessary and sufficient conditions for asymptotic stability after a brief review of the stability analysis under restricted switching and the multiple lyapunov function theory the switching stabilization problem is studied and a variety of switching stabilization methods found in the literature are outlined then the switching stabilizability problem is investigated that is under what condition it is possible to stabilize a switched system by properly designing switching control laws note that the switching stabilizability problem has been one of the most elusive problems in the switched systems literature a necessary and sufficient condition for asymptotic stabilizability of switched linear systems is described here

design method of exact model matching control for finite volterra series systems this paper is concerned with exact model matching control emm for finite volterra series systems first we show a structure of a causal controller which can achieve the exact model matching to a reference model and clarify the relationship between the proposed method and the emm for linear systems second to analyse the stability of the proposed control system we present an input dependent small gain theorem for the system with an external input then extend it for the system with two external inputs with the help of this theorem we clarify the condition under which the control system is stable for the reference input magnitude within a certain range and is also robust for small disturbances finally the effectiveness of the proposed method is illustated through numerical simulations