singular value analysis of the jacobian matrix in microwave image reconstruction for non linear inverse scattering problems utilizing gauss newton methods the jacobian matrix encodes rich information concerning the system performance and algorithm efficiency in this paper we perform an analytical evaluation of a single iteration jacobian matrix based on a previously derived nodal adjoint representation concepts for studying linear ill posed problems such as the degree of ill posedness are used to assess the impact of important system parameters on the expected image quality analytical singular value decomposition svd of the jacobian matrix for a circular imaging domain is derived along with the numerical svd for optimizing imaging system configurations the results show significant reductions in the degree of ill posedness when signal frequency antenna array density and property parameter sampling are increased specifically the decay rate in the singular spectrum of the jacobian decreases monotonically with signal frequency being approximately 1 3 of its 0 1 ghz value at 3 ghz is improved with antenna array density up to about 35 equally spaced circumferentially positioned elements and drops significantly with increased property parameter sampling to more than twice the amount of measurement data these results should serve as useful guidelines in the development of design specifications for an optimized hardware installation

an effective mom solution with nested complex source beam method for electromagnetic scattering problems a nested complex source beam ncsb method based on octree structure is proposed to accelerate the method of moments mom solution for three dimensional 3 d electromagnetic scattering analysis at the finest level the far field contribution of each basis function is expressed with that of complex source beams csbs distributed on the equivalent sphere surface for every group furthermore the far field radiated by csbs of the source group at child level can be represented by that radiated by csbs of the source group at parent level similarly the received field of csbs for each observation group at the parent level can be expressed with that of csbs belong to their child level group an equivalent relationship of csbs between every two adjacent levels is built to obtain the nested equivalent process for ncsb method and only the csbs at the finest level have the direct association with the basis functions in their group the ncsb method is shown to be o nlogn computational complexity for both matrix vector product mvp time and memory storage by numerical examples with appropriate parameters and numerical results demonstrate the better efficiency of the proposed method than the current multilevel csb method

knowledge based antenna pattern interpolation we examine the problem of interpolating antenna radiation patterns from a small number of measurements and propose an algorithm to perform the interpolation when naive methods fail often due to multipath corruption of the pattern this algorithm exploits constraints on the antenna s underlying design to avoid ambiguities but is sufficiently general to address many different antenna types a theoretical basis for the robustness of this algorithm is developed and its performance is verified in simulation using a number of popular antenna designs and with a controlled laboratory experiment

on the spatial bandwidth of scattered fields it is shown that the scattered fields are almost space bandlimited functions the effective bandwidth w is introduced and evaluated for a very general scattering system as well as the error made using functions bandlimited to w w for representing the scattered field the effective bandwidth is very simply related to the maximum dimension of the scattering system the error drops to negligible values for modest increases of w compared to w in the case of large scatterers important consequences of the above general results are finally stressed

strong asymptotics for gegenbauer sobolev orthogonal polynomials we study the asymptotic behaviour of the manic orthogonal polynomials with respect to the gegenbauer sobolev inner product f s s f g au 9 where f g s f x g x l x d x with ci i and 1 0 the asymptotics of the zeros and norms of these polynomials are also established

alternating adaptive projections in antenna synthesis the projection operator is a basic building block in the application of the alternating projections method to antenna synthesis in general it is a non linear operator that is repeatedly applied in the course of a single synthesis process thus having a considerable impact on the convergence properties of the resulting algorithm a novel approach to the computation of these projections is presented which exploits a simple definition of the relevant spaces particularly that of radiated fields characterization of field mask specification as scale invariant under this definition adds a further degree of freedom namely reference level which impacts on the sensitive to scaling projector in order to compute the optimum reference level an iterative procedure is proposed which is simple to implement easily integrable in standard alternating projection routines and adds negligible computational burden numerical tests confirm an improved performance with respect to the fixed scaling projection operator in terms of convergence rate and robustness against the initial guess supporting our approach as a valid aid in overcoming the drawbacks of the alternating projections based antenna synthesis

on the interpolation of electromagnetic near field without prior knowledge of the radiating source a method is proposed to interpolate the electromagnetic near field when no information on the radiating source is available in the absence of a priori knowledge general properties of the electromagnetic field are exploited to estimate the field namely the minimum complexity of the field and the continuity of the first derivatives these properties are enforced by minimizing the nuclear norm and using the thin plate spline interpolation results respectively the proposed procedure is validated experimentally by interpolating the planar electrical near field radiated by three antennas the quality of the interpolation and its robustness to noise are investigated despite its simplicity the interpolation method is able to properly estimate the near field from a random coarse sampling of 2 lambda the quality of the near field interpolation is also confirmed by deriving the far field these promising results pave the way for the development of fast antenna measurement procedures

asymptotics of sobolev orthogonal polynomials for symmetrically coherent pairs of measures with compact support we study the strong asymptotics for the sequence of manic polynomials q c orthogonal with respect to the inner product u 3 9 s s f xmx h x 1 s f x s x 44x a 0 with x outside of the support of the measure 2 we assume that 1 and 2 are symmetric and compactly supported measures on lr satisfying a coherence condition as a consequence the asymptotic behaviour of q q s and of the zeros of qn is obtained

asymptotics of sobolev orthogonal polynomials for hermite 1 1 coherent pairs abstract in this paper we will discuss asymptotic properties of monic polynomials s n x n 0 orthogonal with respect to the sobolev inner product p q s r p x q x d 0 r p x q x d 1 with 0 d 0 e x 2 d x d 1 x 2 a x 2 b e x 2 d x a b r and a b it is well known that 0 1 is a pair of symmetric 1 1 coherent measures this means that there exist sequences a n n n b n n n a n b n for every n n such that the algebraic relation h n x b n 2 h n 2 x q n x a n 2 q n 2 x n 2 is satisfied where q n x n 0 is the sequence of monic orthogonal polynomials associated with 1 and h n x n 0 is the sequence of monic hermite polynomials we will study the relative asymptotics for sobolev scaled polynomials and we will obtain mehler heine type formulas among others

the simple with forbidden tasks in first or last position a problem more complex that it seems abstract the classical f2 cmax problem is solved optimally by the famous johnson s algorithm in o n log n where n is the number of jobs for solving the f no idle cmax with a branch and bound algorithm it is necessary to solve problem closed to the f2 cmax the only difference is an additive constraint a set of jobs that cannot be placed in the first or the last position this problem is linear and can be solved by testing systematically all allowed jobs in first position the other one being scheduled according to johnson s rule but this exhaustive procedure in o n2 is not satisfying while it seems natural to think that a single rule like johnson s one can be applied all intuitive rules can be refuted by counterexamples surprisingly this f2 cmax with this additive constraint appears to be more complicated than the initial problem even if it stay linear once again the f2 cmax appears to be a peculiarity in a complex environment

the truncation error in the application of sampling series to electromagnetic problems truncation error interpolation methods used in the evaluation and representation of scattered fields are discussed three main points are considered the choice of the sampling point lattice the choice of the type of sampling expansion and the determination of the number of terms of the sampling series that must be retained to insure a negligible truncation error the aim is to provide a clear reference frame for the applications which allow the optimal choice for the reconstruction algorithm the cases of bounded and square integrable band limited functions are separately dealt with in order to exploit the properties of each method a general analysis of the multidimensional truncation error is carried out no particular assumption on the sampling expansion is made except for that concerning the use of a rectangular sampling lattice simple and effective expressions relating the multidimensional error to the corresponding one dimensional bounds are derived the one dimensional error is then analyzed in detail with reference to the most relevant case of central interpolation by very simple methods error bounds for all the sampling expansions explicitly considered in the literature are derived in a systematic way expressions providing the values of the sampling rate and number of retained samples which minimize the overall computer time and memory requirement are derived some numerical examples are presented and briefly discussed

the fast multipole method we study integral methods applied to the resolution of the maxwell equations where the linear system is solved using an iterative method which requires only matrix vector products the fast multipole method fmm is one of the most efficient methods used to perform matrix vector products and accelerate the resolution of the linear system a problem involving n degrees of freedom may be solved in cniternlogn floating operations where c is a constant depending on the implementation of the method in this article several techniques allowing one to reduce the constant c are analyzed this reduction implies a lower total cpu time and a larger range of application of the fmm in particular new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms several numerical tests are also described these confirm the efficiency and the theoretical complexity of the fmm

dealing with multifrequency scattering data through the imsa a set of representative results are presented that are obtained with two multiresolution strategies developed for dealing with multifrequency inverse scattering experiments starting from the iterative multiscaling approach previously studied for monochromatic illuminations the first approach is concerned with the integration of the iterative multiscaling algorithm into a frequency hopping reconstruction scheme while the second one allows a multiresolution simultaneous processing of multifrequency data the numerical and the experimental analysis are aimed at assessing both the reconstruction effectiveness and the required computational costs of the two and three dimensional implementations of the proposed inversion schemes in comparison with the monochromatic multistep process and to the single step optimization strategy as well

chromatic scheduling in a cyclic open shop abstract we consider the computational complexity of some problems of scheduling in a cyclic open shop which is a variation of a standard open shop system in particular we show that the problem of scheduling is np hard for a 3 processor system and polynomial for a 2 processor one moreover we prove that the problem of determining if a given shop can be scheduled in 3 time units is polynomially solvable we also consider another variation of a cyclic open shop a compact open shop for this system we prove that the problem of minimizing c max for 2 processor system and the problem of determining if there exists a legal schedule are np hard moreover we give polynomial time algorithms for determining if c max 3 in a general case and for determining if c max 4 in the case of zero unit time tasks

an improved simple method for imaging the shape of complex targets the linear sampling method lsm is a simple and effective approach to image the shape of an unknown target through the solution of a linear equation whose known term is the field radiated by an elementary i e monopolar source located in a set of test points in this paper we extend the lsm formulation by generalizing the right hand side of the equation to higher order multipoles in particular we discuss which is the expected method s outcome after such a change and propose a post processing scheme to combine the results obtained for different multipoles as shown with simulated and experimental data the proper combination of higher order multipoles allows to achieve better images of complex shaped targets as compared to the standard lsm and to overcome some of its limitations

np hardness of compact scheduling in simplified open and flow shops abstract in practical task scheduling it is sometimes required that the components of a system perform consecutively such a scheduling is called scheduling without waiting periods or no wait and or no idle in this article we study the complexity of some simplified scheduling problems of this kind in open shop and flow shop settings in particular we show that many trivial questions about the existence of schedule become np hard even if there are only two machines or if the scheduling graph of a system is a path or a cycle

entire domain basis functions for scattering from large curved surfaces formulated by transformation optics a complete set of entire domain basis functions are introduced for the analysis of scattering from bodies with curved surfaces they are defined via the application of a generalization of the shannon sampling theorem these basis functions are defined for curved patches with arbitrary contours via a three step procedure first the curved patch is mapped via transformation optics onto a flat parametric domain surrounded by a virtual anisotropic inhomogeneous space next linear phase functions are defined on the parametric flat domain the sufficient and non redundant number of functions is found by using a spectral domain completeness relationship of the delta function finally the back transformation from flat anisotropic to curved isotropic space yields the basis functions for the curved patch the number of basis functions so obtained matches the degrees of freedom of the field known in the literature numerical results show the effectiveness of the representation for both fields and currents

an effective near field far field transformation technique from truncated and inaccurate amplitude only data a general approach to the near field far field transformation from amplitude only near field data is presented the estimation of the far field is stated as an intersection finding problem and is solved by the minimization of a suitable functional the difficulties related to the possible trapping of the algorithm by a false solution common to any nonlinear inverse problem are mitigated by setting the problem in the space of the squared field amplitudes as already done in a number of existing papers and by incorporating all the a priori knowledge concerning the system under test in the formulation of the problem accordingly the a priori information concerning the far field the near field outside the measurement region and the accuracy of the measurement setup and its dynamic range are properly taken into account in the objective functional the intrinsic ill conditioning of the problem is managed by adopting a general flexible and nonredundant sampling representation of the field which takes into account the geometrical characteristics of the source as a consequence the number of unknowns is minimized and a technique is obtained which easily matches the available knowledge concerning the behavior of the field the effectiveness of the approach is shown by reporting the main results of an extensive numerical analysis as well as an experimental validation performed by using a very low cost near field facility available at the electronic engineering department university of napoli italy

asymptotics of sobolev orthogonal polynomials for hermite coherent pairs abstract let qn be the polynomials orthogonal with respect to the sobolev inner product f g s fg d 0 f g d 1 being 0 1 a coherent pair where one of the measures is the hermite measure the outer relative asymptotics for qn with respect to hermite polynomials are found on the other hand we consider the sobolev scaled polynomials and we obtain the plancherel rotach asymptotics for those as well as a consequence about their zeros

on the degrees of freedom of scattered fields starting from the observation that fields differing less than a prescribed error cannot be resolved as distinct entities the degrees of freedom of the scattered field are introduced and then computed the degrees of freedom are shown to be practically equal to the nyquist number appropriate to the effective spatial bandwidth of the scattered field and to the extension of the observation domain accordingly a finite number of elements of information can be used to determine the scattered field to a prescribed approximation error it is also shown that the field representation can be made in terms of field values and simple sampling functions provided that a marginal increase in the approximation error is tolerated the results not only completely justify the use of sampling interpolation for representing scattering fields but also demonstrate that such representation is practically an optimal one an algorithm for the reconstruction of scattered fields given the maximum allowed error is then produced

what is beyond coherent pairs of orthogonal polynomials abstract usually coherent pairs of orthogonal polynomials have been considered in the wider context of sobolev orthogonality in this paper we focus our attention on the problem of coherence between two orthogonal polynomial sequences in terms of the corresponding linear functionals we deduce some conditions about the linear functionals in order that the corresponding orthogonal polynomial sequences constitute a coherent pair

zero distribution of orthogonal polynomials in a certain discrete sobolev space abstract we study the zero distribution of the polynomials snn which are orthogonal with respect to the discrete sobolev inner product f g 0 x g x d x nf r 0 g r 0 where is a distribution function n 0 r 1 snn has n real simple zeros at most one of them is outside 0 the location of these zeros is given in relation to the position of the zeros of some classical polynomials i e polynomials with respect to an inner product with n 0

fast evaluation of the radiation patterns of true time delay arrays with beam steering a multilevel algorithm for the computation of the transient radiation patterns of true time delay ttd conformal arrays over a range of observation and beam steering directions is presented the multilevel algorithm is based on hierarchical decomposition of the array into smaller sub arrays of elements at the finest level of decomposition the angular temporal radiation patterns of single element sub arrays are obtained over a sparse angular grid of directions and short temporal duration by either measurement or calculation subsequent steps of the algorithm comprise multilevel aggregation of delayed sub array contributions this process continues until the transient radiation pattern of the whole array is obtained at each level the radiation pattern is interpolated to a finer angular grid of observations and steering directions followed by temporal delay compensation the multilevel array decomposition algorithm attains a computational complexity substantially lower than that of the direct evaluation furthermore the algorithm is particularly efficient for large arrays with large numbers of elements

a new method for avoiding the truncation error in near field antennas measurements a new method to avoid the truncation error in antenna near field measurements is presented the approach relies on the concept of information content of the field according to this point of view the truncation problem is solved by picking up the information that is lost due to the finite size of scanning area in points of the space reachable by the measurement system the method can be applied to any scanning geometry including the planar and cylindrical ones whenever the set up allows to vary the distance between the antenna under test and the probe during the scanning procedure application of the method to cylindrical near field scanning is numerically investigated assessing the effectiveness of the proposed technique

singular value decomposition of the radiation operator application to model order and far field reduction the time harmonic electromagnetic scattering or radiation problem is considered the singular value decomposition svd is applied to the radiation operator that maps the set of electric and magnetic currents defined on the surface of an inhomogeneous object onto the set of the far fields scattered or radiated from this object the svd yields orthonormal bases for both sets because the radiation operator is compact and regularizing it is demonstrated that the far field calculated from the series expansions of the currents on these bases converges exponentially fast to the exact one if a sufficient number of terms is considered in these series this number is closely related to the degrees of freedom that characterize the far field the latter can be computed from a reduced number of unknowns in the discretized integral equation that links electric and magnetic surface currents by writing it in the new currents bases also it allows the reduction of the far field in a given angular sector the numerical complexity of this technique is addressed and 2d numerical examples are presented that illustrate its potentialities

fast solutions of the 2d inverse scattering problem based on a tsvd approximation of the internal field for the forward model an alternative formulation of the microwave tomography problem is proposed in order to reduce the computation time of the inversion procedure the well known multiplicative regularized contrast source inversion method is used as reference algorithm our formulation is based on a truncated singular value decomposition of the matrix involved in the most computationally intensive operations of the inversion algorithm after theoretical and practical investigation of the behavior of the singular values it is shown that the corresponding approximation does not yield any significant degradation of the quality of the solutions even for large complex permittivity contrasts while the computation times are reduced by a factor ranging between 1 1 and 6 with respect to the original method

generalized coherent pairs abstract a pair of quasi definite moment functionals u0 u1 is a generalized coherent pair if monic orthogonal polynomials pn x n 0 and rn x n 0 relative to u0 and u1 respectively satisfy a relation r n x 1 n 1 p n 1 x n n p n x n 1 n 1 p n 1 x n 2 where n and n are arbitrary constants which may be zero if u0 u1 is a generalized coherent pair then u0 and u1 must be semiclassical we find conditions under which either u0 or u1 is classical in such a case we also determine the types of the companion moment functionals also some illustrating examples and two ways of generating generalized coherent pairs are given we also discuss the corresponding sobolev orthogonal polynomials

truncation error reduction in 2d cylindrical spherical near field scanning we introduce a near field to far field transformation for two dimensional cylindrical spherical scanning that significantly reduces angular truncation errors after examining the limitations of the traditional multipole based expansion of truncated scan data we consider an alternative expansion based on slepian functions and show how far field values can be extracted from the resulting expansion coefficients we compare the performance and computational cost of the new transformation with those of the traditional one

some asymptotics for sobolev orthogonal polynomials involving gegenbauer weights we consider the sobolev inner product email protected 1 1f x g x 1 x 2 a 1 email protected f x g x email protected x a 12 where email protected is a measure involving a gegenbauer weight and with mass points outside the interval 1 1 we study the asymptotic behaviour of the polynomials which are orthogonal with respect to this inner product we obtain the asymptotics of the largest zeros of these polynomials via a mehler heine type formula these results are illustrated with some numerical experiments

a travelling salesman approach to solve the f no idle cmax problem this paper investigates the f no idle cmax problem where machines work continuously without idle time intervals the idle characteristic is a very strong constraint and it affects seriously the value of cmax criterion we treat here only the permutation flow shop configuration for machine no idle problems with the objective to minimise the makespan based on the idea that this problem can be modelled as a travelling salesman problem an adaptation of the well known nearest insertion rule is proposed to solve it a computational study shows the result quality

asymptotic properties of sobolev orthogonal polynomials abstract in this report we will survey some of the main ideas and tools which appeared recently in the study of the analytic properties of polynomials orthogonal with respect to inner products involving derivatives although some results on weak asymptotics are mentioned the strong outer asymptotics constitutes the core of the paper both the discrete and the continuous cases are considered and several open problems and conjectures are posed

on landau s eigenvalue theorem and information cut sets a variation of landau s eigenvalue theorem describing the phase transition of the eigenvalues of a time frequency limiting self adjoint operator is presented the total number of degrees of freedom of square integrable multidimensional bandlimited functions is defined in terms of kolmogorov s n width and computed in some limiting regimes where the original theorem cannot be directly applied results are used to characterize up to order the total amount of information that can be transported in time and space by multiple scattered electromagnetic waves rigorously addressing a question originally posed in the early works of toraldo di francia and gabor applications in the context of wireless communication and electromagnetic sensing are discussed

new aspects of electromagnetic information theory for wireless and antenna systems this paper investigates information theoretic characterization via shannon s information capacity and number of degrees of freedom of wave radiation antenna and wireless propagation systems specifically the paper derives from the fundamental physical point of view of maxwell s equations describing electromagnetic fields the shannon information capacity of space time wireless channels formed by electromagnetic sources and receivers in a known background medium the theory is developed first for the case of sources working at a fixed frequency time harmonic case and is expanded later to the more general case of temporally bandlimited systems time domain fields in the bandlimited case we consider separately the two cases of time limited and essentially bandlimited systems and of purely bandlimited systems the developments take into account the physical radiated power constraint in addition to a constraint in the source l 2 norm which acts to avoid antenna superdirectivity based on such radiated power and current l 2 norm constraints we derive the shannon information capacity of canonical wireless and antenna systems in free space for a given additive gaussian noise level as well as an associated number of degrees of freedom resulting from such capacity calculations the derived results also illustrate from a new information theoretic point of view the transition from near to far fields

fast and accurate near field far field transformation by sampling interpolation of plane polar measurements an optimal sampling interpolation algorithm which allows the accurate recovery of plane rectangular near field samples from the knowledge of the plane polar ones is developed this enables the standard near field far field nf ff transformation which takes full advantage of the fast fourier transform fft algorithm to be applied to plane polar scanning the maximum allowable sample spacing is also rigorously derived and it is shown that it can be significantly greater than lambda 2 as the measurement place moves away from the source this allows a remarkable reduction of both measurement time and memory storage requirements the sampling approach is compared with that based on the bivariate lagrange interpolation bli method the sampling reconstruction agrees with the exact results significantly better than the bli in spite of the significantly lower number of required measurements

a nested multi scaling inexact newton iterative approach for microwave imaging a microwave imaging technique based on the integration of the inexact newton method within a multi scaling strategy is proposed in the framework of the contrast field formulation of the electromagnetic inverse scattering the inversion problem is solved by means of a nested procedure that considers three different logical levels a an outer multi focusing loop aimed at implementing a synthetic zoom for focusing the scatterer support within the investigation domain b a local linearization of the original full nonlinear inverse scattering function and c a truncated landweber inner loop devoted to regularize the arising ill posed linear problem thanks to the features of the integrated approach a reliable inversion technique able to suitably face the non linearity and the ill posedness ill conditioning issues of the imaging problem is designed a numerical validation dealing with different objects measurement setups and noise conditions is carried out to assess the features and the potentialities as well as the limitations of the proposed strategy comparisons with bare approaches and other multi resolution formulations are presented as well