asymptotic bounds on frameproof codes we study the asymptotic behavior of frameproof codes some lower bounds are derived from the theory of error correcting codes in particular the lower bound obtained directly by applying algebraic geometry codes is improved by employing the jacobian group structure of algebraic curves

microwave imaging of nonsparse domains using born iterative method with wavelet transform and block sparse bayesian learning a microwave technique utilizing the combination of wavelet transform block sparse bayesian learning bsbl and born iterative method bim is proposed to image nonsparse domains the wavelet transform is implemented to convert the nonsparse domain into a sparse domain then bsbl framework based on expectation maximization em algorithm is applied on the bim model to reconstruct the original profile of the nonsparse domain the presented imaging results of a nonsparse model indicate that the proposed technique in comparison with traditional microwave imaging or compressive sensing cs algorithms achieve very low normalized error rate ner at a short computational time using only small number of antennas the accuracy robustness and effectiveness of the proposed method are further assessed by employing it to detect a hemorrhagic brain stroke in a realistic numerical head model which is a nonsparse domain the obtained results indicate the capability for the technique to detect an early stroke in the realistic nonsparse environment of the human head using only six antennas

directions of arrival estimation through bayesian compressive sensing strategies the estimation of the directions of arrival doas of narrow band signals impinging on a linear antenna array is addressed within the bayesian compressive sensing bcs framework unlike several state of the art approaches the voltages at the output of the receiving sensors are directly used to determine the doas of the signals thus avoiding the computation of the correlation matrix towards this end the estimation problem is properly formulated to enforce the sparsity of the solution in the linear relationships between output voltages i e the problem data and the unknown doas customized implementations exploiting the measurements collected at a unique time instant single snapshot and multiple time instants multiple snapshots are presented and discussed the effectiveness of the proposed approaches is assessed through an extensive numerical analysis addressing different scenarios signal configurations and noise conditions comparisons with state of the art methods are reported as well

adaptive importance sampling monte carlo simulation for general multivariate probability laws we establish a parametric adaptive importance sampling variance reduction method for general multivariate probability laws employing the principle of bypass distributions makes it possible to develop adaptive algorithms without relying on particular properties of the target and proposal laws both of which in the proposed framework are as general as the uniform law on the unit hypercube without changing the sampling distribution at each iteration we establish the asymptotic normality of the estimator of the desired mean and of the importance sampling parameter as the number of observations tends to infinity although implementation of the proposed methodology requires a small amount of initial work it has the potential to yield substantial improvements in estimator efficiency in various general problem settings to illustrate the applicability and effectiveness we provide numerical results throughout in which we apply exponential and normal bypass distributions as well as demonstrate that well known adaptive importance sampling formulations in the literature can be easily rewritten in the proposed framework

a probabilistic model for the nonlinear electromagnetic inverse scattering tm case electromagnetic inverse scattering emis is a noninvasive examination tool which holds the promising potential in science engineering and military applications in contrast to conventional tomography techniques the inverse scattering is a quantitative superresolution imaging method since it is capable of accommodating more realistic interactions between the wavefield and the probed scene in this paper a full probabilistic formulation of the emis is presented for the first time which is then solved by applying the well known expectation maximization method afterward the concept of the complex valued alternating direction method of multipliers has been proposed as an alternative approach to solve the resulting nonlinear optimization problem finally exemplary numerical and experimental results are provided to validate the proposed method

characterization of division algebras of minimal rank and the structure of their algorithm varieties the purpose of this paper is to show that every finite dimensional division algebra of minimal rank i e of minimal complexity with respect to the noncommutative model of computation is a finite simple field extension moreover we investigate the structure of the variety of optimal algorithms for the computation of the multiplication in such fields modulo the isotropy group of the problem

adaptive importance sampling and control variates abstract we construct and investigate an adaptive variance reduction framework in which both importance sampling and control variates are employed the three lines monte carlo averaging and two variance reduction parameter search lines run in parallel on a common sequence of uniform random vectors on the unit hypercube given that these two variance reduction techniques are effective often in a complementary way their combined application is well expected to widen the applicability of adaptive variance reduction we derive convergence rates of the theoretical estimator variance towards its minimum as a fixed computing budget increases when stochastic approximation runs with optimal constant learning rates we derive sufficient conditions for the proposed algorithm to attain the minimal estimator variance in the limit by stochastic approximation with decreasing learning rates or by sample average approximation when computing budget is unlimitedly available numerical results support our theoretical findings and illustrate the effectiveness of the proposed framework

new uniform and asymptotic upper bounds on the tensor rank of multiplication in extensions of finite fields we obtain new uniform upper bounds for the tensor rank of the multiplication in the extensions of the finite fields mathbb f q for any prime power q moreover these uniform bounds lead to new asymptotic bounds as well in addition we also give purely asymptotic bounds which are substantially better by using a family of shimura curves defined over mathbb f q with an optimal ratio of mathbb f q t rational places to their genus where q t is a square

synthesis of two dimensional antenna array using independent compression regions the synthesis of two dimensional antenna arrays that allows to optimize the number of its elements is of great interest for long term evolution lte advanced wireless systems in this communication we present a novel synthesis approach which focuses on reducing the number of antenna elements using independent compression regions icr we base our approach on the non iterative matrix pencil method mpm and the iterative bayesian compressive sampling bcs method both of these techniques have been previously used for the compression of linear arrays and now we apply them in the context of two dimensional arrays our compression method is based on the idea of segmenting the array in independent regions a set of numerical experiments small and large 2d arrays shaped beam antenna patterns are presented to assess the performance and potentialities of icr design approach

torsion limits and riemann roch systems for function fields and applications the ihara limit or constant a q has been a central problem of study in the asymptotic theory of global function fields or equivalently algebraic curves over finite fields it addresses global function fields with many rational points and so far most applications of this theory do not require additional properties motivated by recent applications we require global function fields with the additional property that their zero class divisor groups contain at most a small number of d torsion points we capture this with the notion of torsion limit a new asymptotic quantity for global function fields it seems that it is even harder to determine values of this new quantity than the ihara constant nevertheless some nontrivial upper bounds are derived apart from this new asymptotic quantity and bounds on it we also introduce riemann roch systems of equations it turns out that this type of equation system plays an important role in the study of several other problems in each of these areas arithmetic secret sharing symmetric bilinear complexity of multiplication in finite fields frameproof codes and the theory of error correcting codes finally we show how our new asymptotic quantity our bounds on it and riemann roch systems can be used to improve results in these areas

squares of random linear codes given a linear code c one can define the d th power of c as the span of all componentwise products of d elements of c a power of c may quickly fill the whole space our purpose is to answer the following question does the square of a code typically fill the whole space we give a positive answer for codes of dimension k and length roughly frac 1 2 k 2 or smaller moreover the convergence speed is exponential if the difference k k 1 2 n is at least linear in k the proof uses random coding and combinatorial arguments together with algebraic tools involving the precise computation of the number of quadratic forms of a given rank and the number of their zeros

asymptotic bound for multiplication complexity in the extensions of small finite fields in 1986 d v chudnovsky and g v chudnovsky first employed algebraic curves over finite fields to construct bilinear multiplication algorithms implicitly through supercodes introduced by shparlinski tsfasman vladut or equivalently multiplication friendly codes that we will introduce in this paper this idea was further developed by shparlinski tsfasman vladut in order to study the asymptotic behavior of multiplication complexity in extension fields later on ballet et al further investigated the method and obtained some improvements recently ballet and pieltant made use of curves over an extension field of to obtain an improvement on the complexity of multiplications in extensions of the binary field in this paper we develop the multiplication friendly splitting technique and then apply this technique to study asymptotic behavior of multiplications in extension fields by combining this with the idea of using algebraic function fields we are able to improve further the asymptotic results of multiplication complexity in particular the improvement for small fields such as the binary and ternary fields is substantial

microwave imaging within the first order born approximation by means of the contrast field bayesian compressive sensing a new approach based the contrast field cf formulation of the microwave imaging problem that exploits the bayesian compressive sampling bcs paradigm is proposed for the reconstruction of sparse distributions of weak scatterers towards this end the original inverse scattering problem is recast to a probabilistic sparseness constrained optimization by introducing suitable hierarchical priors as sparsity constraints a fast relevance vector machine rvm is then employed to reconstruct the scatterers as well as to estimate the confidence level of the inversion representative numerical results are presented to illustrate the method as well as to assess its potentialities and limitations in terms of inversion accuracy computational efficiency and robustness comparisons with state of the art deterministic and stochastic reconstruction methodologies still within the born approximation ba are discussed as well

goppa geometric codes achieving the gilbert varshamov bound based on s zeta functions of curves over finite fields we show that goppa geometry codes achieve the q ary gilbert varshamov bound for all prime powers q including q 2

wavelet based compressive imaging of sparse targets the application of the compressive sensing cs paradigm to retrieve non single pixels contrast profiles is discussed by exploiting a wavelet representation to model complex scatterer distributions with sparse vectors of coefficients an efficient bayesian cs bcs strategy is adopted to solve the arising inverse scattering problem a set of representative numerical examples is presented to illustrate the advantages and the limitations of the proposed approach also with respect to comparable state of the art inversion methods

an improvement of the construction of the d v and g v chudnovsky algorithm for multiplication in finite fields from an interpolation method on algebraic curves due to d v chudnovsky and g v chudnovsky we give a new method for the construction of bilinear algorithms for multiplication in the extensions of finite fields we obtain algorithms better than known ones

optimal algorithms for multiplication in certain finite fields using elliptic curves using the results given in d v chudnovsky and g v chudnovsky proc nat acad sci usa 84 1987 pp 1739 1743 and w c waterhouse ann sci ecole norm sup 4 1969 pp 521 560 it is proven that the rank bilinear complexity of multiplication of the finite field mathbbf q n viewed as an mathbbf q algebra is 2n if n satisfies frac12q 1 n frac12 q 1 epsilon q here epsilon q is the greatest integer leq 2sqrt q which is prime to q if q is not a perfect square and epsilon q 2sqrt q if q is a perfect square

image coding using wavelet transform a scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed this method involves two steps first a wavelet transform used in order to obtain a set of biorthogonal subclasses of images the original image is decomposed at different scales using a pyramidal algorithm architecture the decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image second according to shannon s rate distortion theory the wavelet coefficients are vector quantized using a multiresolution codebook to encode the wavelet coefficients a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed in order to allow the receiver to recognize a picture as quickly as possible at minimum cost a progressive transmission scheme is presented it is shown that the wavelet transform is particularly well adapted to progressive transmission

bayesian compressive sampling for pattern synthesis with maximally sparse non uniform linear arrays a numerically efficient technique based on the bayesian compressive sampling bcs for the design of maximally sparse linear arrays is introduced the method is based on a probabilistic formulation of the array synthesis and it exploits a fast relevance vector machine rvm for the problem solution the proposed approach allows the design of linear arrangements fitting desired power patterns with a reduced number of non uniformly spaced active elements the numerical validation assesses the effectiveness and computational efficiency of the proposed approach as a suitable complement to existing state of the art techniques for the design of sparse arrays

synthesis of sparse arrays with focused or shaped beampattern via sequential convex optimizations an iterative procedure for the synthesis of sparse arrays radiating focused or shaped beampattern is presented the algorithm consists in solving a sequence of weighted l1 convex optimization problems the method can thus be readily implemented and efficiently solved in the optimization procedure the objective is the minimization of the number of radiating elements and the constraints correspond to the pattern requirements the method can be applied to synthesize either focused or shaped beampattern and there is no restriction regarding the array geometry and individual element patterns numerical comparisons with standard benchmark problems assess the efficiency of the proposed approach whose computation time is several orders of magnitude below those of so called global optimization algorithms

on squares of cyclic codes the square c 2 of a linear error correcting code c is the linear code spanned by the component wise products of every pair of non necessarily distinct words in c squares of codes have gained attention for several applications mainly in the area of cryptography and typically in those applications one is concerned about some of the parameters dimension and minimum distance of both c 2 and c in this paper motivated mostly by the study of this problem in the case of linear codes defined over the binary field squares of cyclic codes are considered general results on the minimum distance of the squares of cyclic codes are obtained and constructions of cyclic codes c with a relatively large dimension of c and minimum distance of the square c 2 are discussed in some cases the constructions lead to codes c such that both c and c 2 simultaneously have the largest possible minimum distances for their length and dimensions

multi point codes from generalized hermitian curves we investigate multi point algebraic geometric codes defined from curves related to the generalized hermitian curve introduced by bassa et al our main result is to find a basis of the riemann roch space of a series of divisors which can be used to construct multi point codes explicitly these codes turn out to have nice properties similar to those of hermitian codes for example they are easy to describe to encode and decode it is shown that the duals are also such codes and an explicit formula is given in particular this formula enables one to calculate the parameters of these codes finally we apply our results to obtain linear codes attaining new records on the parameters a new record giving 234 141 59 code over mathbb f 27 is presented as one of the examples

acceleration on adaptive importance sampling with sample average approximation we construct and analyze acceleration techniques for adaptive monte carlo simulations for general multivariate probability laws when the sample average approximation is employed for optimal parameter search our goal is to accelerate the adaptive monte carlo estimation by leading the parameter search line based on the sample average approximation to reach a nearly optimal realm at its small sample size stage first we introduce an auxiliary parameter into the parameter search line and update it wisely to aim for small sample convergence all three lines of the algorithm the monte carlo averaging the importance sampling parameter search and the auxiliary parameter updating run concurrently in a fully automated manner with a common set of random vectors without ad hoc tuning of the simulation system we next propose and examine various criteria for the auxiliary parameter updating all under which the asymptotic normality of the estimator of the desired mean and of the importance sampling parameter hol

minimum distance decoding of general algebraic geometry codes via lists algebraic geometry codes are defined by divisors d and g on a curve over a finite field f often g is supported by a single f rational point and the resulting code is called a one point code recently there has been interest in allowing the divisor g to be more general as this can result in superior codes in particular one may obtain a code with better parameters by allowing g to be supported by m distinct f rational points where m 1 in this paper we demonstrate that a multipoint algebraic geometry code c may be embedded in a one point code c exploiting this fact we obtain a minimum distance decoding algorithm for the multipoint code c this is accomplished via list decoding in the one point code c

asymptotically good binary linear codes with asymptotically good self intersection spans if c is a binary linear code let c 2 be the linear code spanned by intersections of pairs of codewords of c we construct an asymptotically good family of binary linear codes such that for c ranging in this family c 2 also form an asymptotically good family for this we use algebraic geometry codes concatenation and a fair amount of bilinear algebra more precisely the two main ingredients used in our construction are first a description of the symmetric square of an odd degree extension field in terms only of field operations of small degree and second a recent result of garcia stichtenoth bassa beelen on the number of points of curves on such an odd degree extension field

algebraic geometry codes with asymptotic parameters better than the gilbert varshamov and the tsfasman vladut zink bounds in this correspondence we show that both the gilbert varshamov and the tsfasman vladut zink bounds can be improved by goppa geometric codes around two points where these two bounds intersect

a note on further improvements of the tvz bound in this note we present improvements of recent asymptotic results on constructions of nonlinear codes using algebraic geometry the main constructions involve an adaptation of recent constructions by niederreiter and oumlzbudak and stichtenoth and xing

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

an explicit tower of function fields over cubic finite fields and zink s lower bound for a function field f f l over a finite field of cardinality l denote by g f resp n f the genus resp the number of rational places of f fl in this paper we present an explicit tower of function fields f 1 subset of f 2 subset of f 3 subset of over f l for l q 3 such that lim r infinity n f r g f r 2 q 2 1 q 2

sparsening conformal arrays through a versatile bcs based method sparsening conformal arrangements is carried out through a versatile multi task bayesian compressive sensing mt bcs strategy the problem formulated in a probabilistic fashion as a pattern matching synthesis is that of determining the sparsest excitation set locations and weights fitting a reference pattern subject to user defined geometrical constraints results from a set of representative numerical experiments are presented to illustrate the key features of the proposed approach as well as to assess also through comparisons its potentials in terms of matching accuracy element saving and computational costs

algebraic complexities and algebraic curves over finite fields abstract we consider the problem of minimal multiplicative complexity of polynomial multiplication and multiplication in finite extensions of fields for infinite fields minimal complexities are known winograd s 1977 math syst theory 10 169 180 we prove lower and upper bounds on minimal complexities over finite fields both linear in the number of inputs using the relationship with linear coding theory and algebraic curves over finite fields

a tower of artin schreier extensions of function fields attaining the drinfeld vladut bound for an algebraic function fieldf having a finite constant field letg f resp n f denote the genus off resp the number of places off of degree one we construct a tower of function fields f 1 subseteq f 2 subseteq f 3 subseteq ldots over mathbb f q 2 such that the ration fi g fi tends to the drinfeld vladut boundq 1

adaptive wavelet thresholding for image denoising and compression the first part of this paper proposes an adaptive data driven threshold for image denoising via wavelet soft thresholding the threshold is derived in a bayesian framework and the prior used on the wavelet coefficients is the generalized gaussian distribution ggd widely used in image processing applications the proposed threshold is simple and closed form and it is adaptive to each subband because it depends on data driven estimates of the parameters experimental results show that the proposed method called bayesshrink is typically within 5 of the mse of the best soft thresholding benchmark with the image assumed known it also outperforms sureshrink donoho and johnstone 1994 1995 donoho 1995 most of the time the second part of the paper attempts to further validate claims that lossy compression can be used for denoising the bayesshrink threshold can aid in the parameter selection of a coder designed with the intention of denoising and thus achieving simultaneous denoising and compression specifically the zero zone in the quantization step of compression is analogous to the threshold value in the thresholding function the remaining coder design parameters are chosen based on a criterion derived from rissanen s minimum description length mdl principle experiments show that this compression method does indeed remove noise significantly especially for large noise power however it introduces quantization noise and should be used only if bitrate were an additional concern to denoising

improvement on parameters of goppa geometry codes from maximal curves using the vla spl breve dut xing method in the present correspondence an idea of xing and chen is used to improve the parameters of goppa geometry codes from maximal curves it is shown that we can improve the parameters of goppa geometry codes almost up to the genus of a maximal curve

on the algorithmic complexity of associative algebras abstract the complexity l a of a finite dimensional associative algebra a is the number of non scalar multiplications divisions of an optimal algorithm to compute the product of two elements of the algebra we show l a 2ddim a t where t is the number of maximal two sided ideals of a

improvements on parameters of one point ag codes from hermitian curves by choosing specific divisors we show that some algebraic geometry ag codes from the hermitian curves have better parameters than one point hermitian codes the general lower bound is discussed

complex weight sparse linear array synthesis by bayesian compressive sampling an innovative method for the synthesis of maximally sparse linear arrays matching arbitrary reference patterns is proposed in the framework of sparseness constrained optimization the approach exploits the multi task mt bayesian compressive sensing bcs theory to enable the design of complex non hermitian layouts with arbitrary radiation and geometrical constraints by casting the pattern matching problem into a probabilistic formulation a relevance vector machine rvm technique is used as solution tool the numerical assessment points out the advances of the proposed implementation over the extension to complex patterns of and it gives some indications about the reliability flexibility and numerical efficiency of the mt bcs approach also in comparison with state of the art sparse arrays synthesis methods

improvements on parameters of algebraic geometry codes from hermitian curves using the vladut xing method we refine a construction of xu to improve the parameters of algebraic geometry codes based on hermitian curves the parameters of these hermitian codes are arbitrarily close to the singleton bound provided that the length of the code is sufficiently large we also exhibit a class of hermitian codes over any finite field bbfq 2 q 2 with good parameters

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed