antenna array pattern synthesis via convex optimization we show that a variety of antenna array pattern synthesis problems can be expressed as convex optimization problems which can be numerically solved with great efficiency by recently developed interior point methods the synthesis problems involve arrays with arbitrary geometry and element directivity constraints on far and near field patterns over narrow or broad frequency bandwidth and some important robustness constraints we show several numerical simulations for the particular problem of constraining the beampattern level of a simple array for adaptive and broadband arrays

noise estimation and filtering using block based singular value decomposition preprocessing of image and video sequences with spatial filtering techniques usually improves the image quality and compressibility we present a block based nonlinear filtering algorithm based on singular value decomposition and compression based filtering experiments show that the proposed filter preserves edge details and can significantly improve the compression performance

ideal spatial adaptation by wavelet shrinkage summary with ideal spatial adaptation an oracle furnishes information about how best to adapt a spatially variable estimator whether piecewise constant piecewise polynomial variable knot spline or variable bandwidth kernel to the unknown function estimation with the aid of an oracle offers dramatic advantages over traditional linear estimation by nonadaptive kernels however it is a priori unclear whether such performance can be obtained by a procedure relying on the data alone we describe a new principle for spatially adaptive estimation selective wavelet reconstruction we show that variable knot spline fits and piecewise polynomial fits when equipped with an oracle to select the knots are not dramatically more powerful than selective wavelet reconstruction with an oracle we develop a practical spatially adaptive method riskshrink which works by shrinkage of empirical wavelet coefficients riskshrink mimics the performance of an oracle for selective wavelet reconstruction as well as it is possible to do so a new inequality in multivariate normal decision theory which we call the oracle inequality shows that attained performance differs from ideal performance by at most a factor of approximately 2 log n where n is the sample size moreover no estimator can give a better guarantee than this within the class of spatially adaptive procedures riskshrink is essentially optimal relying only on the data it comes within a factor log 2 n of the performance of piecewise polynomial and variableknot spline methods equipped with an oracle in contrast it is unknown how or if piecewise polynomial methods could be made to function this well when denied access to an oracle and forced to rely on data alone

mdl denoising revisited we refine and extend an earlier minimum description length mdl denoising criterion for wavelet based denoising we start by showing that the denoising problem can be reformulated as a clustering problem where the goal is to obtain separate clusters for informative and noninformative wavelet coefficients respectively this suggests two refinements adding a code length for the model index and extending the model in order to account for subband dependent coefficient distributions a third refinement is the derivation of soft thresholding inspired by predictive universal coding with weighted mixtures we propose a practical method incorporating all three refinements which is shown to achieve good performance and robustness in denoising both artificial and natural signals

fast pencil beam pattern synthesis of large unequally spaced antenna arrays reducing the computational cost of large array pattern synthesis is attractive in many applications in this paper a fast pencil beam pattern synthesis method for large nonuniform antenna arrays is proposed this method is based on an interpolation in a least square sense and iterative fast fourier transform fft i e interpolate the nonuniform distributed elements into uniform virtual elements and then apply fft to synthesis the uniform array thanks to the efficiency of fft the proposed method is much faster and can handle much larger arrays than the existing methods to guarantee the interpolation accuracy the choice of the interpolation parameters is discussed both linear and planar nonuniform array examples are shown to validate the advantages of the proposed method

bounding the equivariant betti numbers of symmetric semi algebraic sets abstract let r be a real closed field the problem of obtaining tight bounds on the betti numbers of semi algebraic subsets of r k in terms of the number and degrees of the defining polynomials has been an important problem in real algebraic geometry with the first results due to ole nik and petrovski thom and milnor these bounds are all exponential in the number of variables k motivated by several applications in real algebraic geometry as well as in theoretical computer science where such bounds have found applications we consider in this paper the problem of bounding the equivariant betti numbers of symmetric algebraic and semi algebraic subsets of r k we obtain several asymptotically tight upper bounds in particular we prove that if s r k is a semi algebraic subset defined by a finite set of s symmetric polynomials of degree at most d then the sum of the s k equivariant betti numbers of s with coefficients in q is bounded by s k d o d unlike the classical bounds on the ordinary betti numbers of real algebraic varieties and semi algebraic sets the above bound is polynomial in k when the degrees of the defining polynomials are bounded by a constant as an application we improve the best known bound on the ordinary betti numbers of the projection of a compact algebraic set improving for any fixed degree the best previously known bound for this problem due to gabrielov vorobjov and zell

spatial spectral filtering with linearly constrained minimum variance beamformers in this paper orthogonal low dimension models for broad band sources as observed by an array delay line structure are developed the models are termed broad band source representation spaces and are subspaces of the observation space they are generated from eigenstructures of source sample covariance matrices and represent sources efficiently in the 2nd order statistical sense for a single broad band source propagating in a pure delay environment and observed with an isotropic array an accurate indication of the model dimension is derived which is independent on the array configuration being a function of the observed source time bandwidth product only using these representations procedures are described for controlling the spatial and spectral response of linearly constrained minimum variance broad band array beamformers the procedures employ linear constraints to control complex gain characteristics over selected bands of frequency for multiple points of 3 d regions of source locations and do not require the use of steering delays the constraints are derived from source representation spaces and are termed eigenvector constraints simulations are presented which illustrate the effectiveness of the new linear constraints

constrained least squares optimization in conformal array antenna synthesis the least mean square error of the constrained least squares optimization method is studied the phases of non zero goal values and the phases of non zero constraint values can be selected by a fast iteration for optimum fit to the goal function amplitude this kind of modified least squares optimization method opens up a fast and robust synthesis method for large conformal antenna arrays constraints can be written also for the element excitation amplitudes and a phase synthesis with predefined amplitudes can be done iterative weight correction technique is used for accurate sidelobe control synthesis examples of two dimensional elliptical and large three dimensional conformal antenna arrays are presented

iterative reweighted least squares design of fir filters develops a new iterative reweighted least squares algorithm for the design of optimal l sub p approximation fir filters the algorithm combines a variable p technique with a newton s method to give excellent robust initial convergence and quadratic final convergence details of the convergence properties when applied to the l sub p optimization problem are given the primary purpose of l sub p approximation for filter design is to allow design with different error criteria in pass and stopband and to design constrained l sub 2 approximation filters the new method can also be applied to the complex chebyshev approximation problem and to the design of 2d fir filters

pattern optimization of a reflector antenna with planar array feeds and cluster feeds we study pattern optimization of a parabolic reflector with planar array feeds and cluster feeds the optimization is carried out within the conjugate gradient method cgm in which the optimum weight vector of a linearly constrained minimum variance lcmv beam former is used as the initial condition optimization with the cgm to determine element weights is found to yield better sidelobe suppression and true settlement of desired scan direction compared to the lcmv beam former and conjugate field matching cfm techniques for the continuous beam scanning case the proposed method is also applied to multibeam reflector antenna design

optimal narrow beam low sidelobe synthesis for arbitrary arrays the classical narrow main beam and low sidelobe synthesis problem is addressed and extended to arbitrary sidelobe envelopes in both one and two dimensional scenarios the proposed approach allows also to handle arbitrary arrays this extended basic synthesis problem is first rewritten as a convex optimization problem this problem is then transformed into either a linear program or a second order cone program that can be solved efficiently by readily available software the convex formulation is not strictly equivalent to the initial synthesis problem but arguments are given that establish that the obtained optimum is either identical or can be made as close as wanted to the desired one finally numerical applications and a comparison with a classical solution are presented to both confirm the optimality of the solution and illustrate the potentialities of the proposed approach

application of convex relaxation to array synthesis problems a general procedure to solve efficiently non convex array synthesis problems is presented it is based on the semidefinite relaxation sdr technique the way to properly relax the constraints in order to formulate the synthesis of shaped beams phase only arrays and reconfigurable arrays as semidefinite programming problems is detailed these so approximated array synthesis problems are then convex easy to implement and can be efficiently solved using off the shelf numerical routines the conditions under which the relaxed problems provide the optimal solution to the original non convex synthesis problems are specified various representative numerical comparisons with arrays designed by other approaches show the validity of the proposed method and illustrate its potentialities

optimal far field focusing of uniformly spaced arrays subject to arbitrary upper bounds in nontarget directions a new approach providing new theoretical results to the optimal far field focusing of uniformly spaced arrays subject to a completely arbitrary mask for sidelobe bounds is presented and discussed in both cases of linear or planar arrays with rectangular boundaries it is first shown that the problem can be formulated without any loss to performances on the maximum as a linear programming one guaranteeing a globally optimal solution second a sufficient uniqueness criterion for the solution of the overall problem is also developed which shows how the solution may not be unique as is actually the case when planar arrays are considered in addition further globally effective optimization procedures are proposed for the latter case in order to optimize directivity smoothness of excitations or other performance parameters in the set of equivalent solutions last an extension to planar arrays with a nonrectangular boundary is also given a thorough numerical analysis confirms the effectiveness of the approach proposed and of the solution codes developed

systems of quadratic inequalities we present a spectral sequence which efficiently computes betti numbers of a closed semi algebraic subset of rp defined by a system of quadratic inequalities and the image of the homology homomorphism induced by the inclusion of this subset in rpn we do not restrict ourselves to the term e2 of the spectral sequence and give a simple explicit formula for the differential d2

a simple algorithm to achieve desired patterns for arbitrary arrays a simple iterative algorithm which can be used to find array weights that produce array patterns with a given look direction and an arbitrary sidelobe specification is presented the method can be applied to nonuniform array geometries in which the individual elements have arbitrary and differing radiation patterns the method is iterative and uses sequential updating to ensure that peak sidelobe levels in the array meet the specification computation of each successive pattern is based on the solution of a linearly constrained least squares problem the constraints ensure that the magnitude of the sidelobes at the locations of the previous peaks takes on the prespecified values phase values for the sidelobes do not change during this process and problems associated with choosing a specific phase value are therefore avoided experimental evidence suggests that the procedure terminates in remarkably few iterations even for arrays with significant numbers of elements

the empirical distribution of rate constrained source codes let x x sub 1 be a stationary ergodic finite alphabet source x sup n denote its first n symbols and y sup n be the codeword assigned to x sup n by a lossy source code the empirical kth order joint distribution q spl circ sup k x sup n y sup n spl rceil x sup k y sup k is defined as the frequency of appearances of pairs of k strings x sup k y sup k along the pair x sup n y sup n our main interest is in the sample behavior of this random distribution letting i q sup k denote the mutual information i x sup k y sup k when x sup k y sup k spl sim q sup k we show that for any sequence of lossy source code s of rate spl les r lim sup sub n spl rarr spl infin 1 k i q spl circ sup k x sup n y sup n spl rfloor spl les r 1 k h x sub 1 sup k h x a s where h x denotes the entropy rate of x this is shown to imply for a large class of sources including all independent and identically distributed i i d sources and all sources satisfying the shannon lower bound with equality that for any sequence of codes which is good in the sense of asymptotically attaining a point on the rate distortion curve q spl circ sup k x sup n y sup n spl rfloor spl rarr sup d p x sup k y sup k a s whenever p sub x sup k sub y sup k is the unique distribution attaining the minimum in the definition of the kth order rate distortion function consequences of these results include a new proof of kieffer s sample converse to lossy source coding as well as performance bounds for compression based denoisers

a new set of linear constraints for broad band time domain element space processors a new set of linear constraints for designing broad band time domain element space antenna array processors is presented the set of linear constraints is used to ensure that a desired look direction response of the processor over a frequency band of interest can be closely approximated the design technique is posed in such a way that three types of presteering can be handled no presteering coarse presteering and exact presteering the elimination of presteering time delays or the possibility to use coarse presteering is an attractive feature in a digital implementation of antenna array processors the relationship that the new processor has to other broad band processors is also established furthermore the approach enables various types of errors and mismatches between signal model and actual scenario to be incorporated in the problem formulation

distortion program size complexity with respect to a fidelity criterion and rate distortion function a novel concept of distortion kolmogorov chaitin complexity is proposed bearing analogy to ordinary kolmogorov chaitin complexity that represents the information content of a single message distortion kolmogorov chaitin complexity can be regarded as the amount of information about a single message that must be conveyed in order to reproduce it with a bounded distortion this explanation is justified by the properties of distortion kolmogorov chaitin complexity and the equivalences between distortion kolmogorov chaitin complexity and the rate distortion function which are analogous to those between ordinary kolmogorov chaitin complexity and the shannon entropy some implications for universal almost sure data compression are also discussed

kolmogorov s contributions to information theory and algorithmic complexity briefly information theory says a random object x p x has complexity entropy h xp x log p x with the attendant interpretation that h bits are sufficient to describe x on the average algorithmic complexity says an object x has a complexity k x equal to the length of the shortest binary program that describes x it is a beautiful fact that these ideas are much the same in fact it is roughly true that ek x h moreover if we let pu x pr u prints x be the probability that a given computer u prints x when given a random program it can be shown that log 1 pu x k x for all x thus establishing a vital link between the universal probability measure pu and the universal complexity k more on this later the relationship of these ideas to probability theory was summed up in kolmogorov s 1983 paper which was based on his 1970 talk in nice perhaps only

beampattern synthesis via a matrix approach for signal power estimation we present new beampattern synthesis approaches based on semidefinite relaxation sdr for signal power estimation the conventional approaches use weight vectors at the array output for beampattern synthesis which we refer to as the vector approaches va instead of this we use weight matrices at the array output which leads to matrix approaches ma we consider several versions of ma including a data adaptive ma ama as well as several data independent ma designs for all of these ma designs globally optimal solutions can be determined efficiently due to the convex optimization formulations obtained by sdr numerical examples as well as theoretical evidence are presented to show that the optimal weight matrix obtained via sdr has few dominant eigenvalues and often only one when the number of dominant eigenvalues of the optimal weight matrix is equal to one ma reduces to va and the main advantage offered by sdr in this case is to determine the globally optimal solution efficiently moreover we show that the ama allows for strict control of main beam shape and peak sidelobe level while retaining the capability of adaptively nulling strong interferences and jammers numerical examples are also used to demonstrate that better beampattern designs can be achieved via the data independent ma than via its va counterpart

restoration by compression in this paper we study the topic of signal restoration using complexity regularization quantifying the compression bit cost of the signal estimate while complexity regularized restoration is an established concept solid practical methods were suggested only for the gaussian denoising task leaving more complicated restoration problems without a generally constructive approach here we present practical methods for complexity regularized restoration of signals accommodating deteriorations caused by a known linear degradation operator of an arbitrary form our iterative procedure obtained using the alternating direction method of multipliers admm approach addresses the restoration task as a sequence of simpler problems involving ell 2 regularized estimations and rate distortion optimizations considering the squared error criterion we replace the rate distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression additionally we propose a shift invariant complexity regularizer measuring the bit cost of all the shifted forms of the estimate extending our method to use averaging of decompressed outputs gathered from compression of shifted signals on the theoretical side we present an analysis of complexity regularized restoration of a cyclo stationary gaussian signal from deterioration by a linear shift invariant operator and an additive white gaussian noise the theory shows that optimal complexity regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter these ideas are realized also in the proposed practical methods finally we present experiments showing good results for image deblurring and inpainting using the jpeg2000 and hevc compression standards

complexity regularized image denoising we study a new approach to image denoising based on complexity regularization this technique presents a flexible alternative to the more conventional l sup 2 l sup 1 and besov regularization methods different complexity measures are considered in particular those induced by state of the art image coders we focus on a gaussian denoising problem and derive a connection between complexity regularized denoising and operational rate distortion optimization this connection suggests the use of efficient algorithms for computing complexity regularized estimates bounds on denoising performance are derived in terms of an index of resolvability that characterizes the compressibility of the true image comparisons with state of the art denoising algorithms are given

optimal array pattern synthesis using semidefinite programming we present algorithms for the solution of two problems in array pattern synthesis the first is the design of nonuniform arrays with a desired magnitude response the second is that of robust design i e design in the presence of uncertainties constraints such as power limitation can be addressed with both problems the algorithms that we present are based on semidefinite programming for which efficient software is readily available we present examples that illustrate the effectiveness of our approach

on learning functions from noise free and noisy samples via occam s razor an occam approximation is an algorithm that takes as input a set of samples of a function and a tolerance epsilon and produces as output a compact representation of a function that is within epsilon of the given samples we show that the existence of an occam approximation is sufficient to guarantee the probably approximate learnability of classes of functions on the reals even in the presence of arbitrarily large but random additive noise one consequence of our results is a general technique for the design and analysis of nonlinear filters in digital signal processing

the edge process model and its application to information hiding capacity analysis in this paper the problem of capacity analysis of data hiding techniques in a game information theoretic framework is considered capacity is determined by the stochastic model of the host image by the distortion constraints and by the side information about the watermarking channel state available at the encoder and at the decoder the importance of the proper modeling of image statistics is emphasized and for this purpose a novel stochastic nonstationary image model is proposed that is based on geometrical priors the so called edge process model being mathematically simple and tractable the edge process model outperforms the estimation quantization eq and spike process models in reference applications such as denoising finally this model allows us to obtain a realistic estimate of maximal embedding rates and in particular it is shown that the expected capacity limit of real images is significantly lower than previously reported

reduced complexity delayed decision algorithm for context based image processing systems it is well known that the performance of context based image processing systems can be improved by allowing the processor e g an encoder or a denoiser a delay of several samples before making a processing decision often however for such systems traditional delayed decision algorithms can become computationally prohibitive due to the growth in the size of the space of possible solutions in this paper we propose a reduced complexity one pass delayed decision algorithm that systematically reduces the size of the search space while also preserving its structure in particular we apply the proposed algorithm to two examples of adaptive context based image processing systems an image coding system that employs a context based entropy coder and a spatially adaptive image denoising system for these two types of widely used systems we show that the proposed delayed decision search algorithm outperforms instantaneous decision algorithms with only a small increase in complexity we also show that the performance of the proposed algorithm is better than that of other higher complexity delayed decision algorithms

approximate synthesis of nonseparable design responses for rectangular arrays a method is presented for the approximation of any real symmetrical nonseparable array design response polynomial of order m 1 by n 1 for rectangular arrays with m by n uniformly spaced elements m geq n previously a sampling method has been used to exactly synthesize response functions of a single variable by n element line arrays 1 and nonseparable functions of two variables by n times n square arrays the sampling method is extended herein to apply to rectangular arrays by deriving the element weights for an m by n rectangular array that exactly yield the values of any desired real symmetrical array response function on an m by n grid of the interelement phase shifts this would yield the designed array response exactly everywhere if the design equation were of order m 1 with respect to one dimension and of order n 1 with respect to the other dimension to approximate this condition the original design function of order n 1 in both dimensions is modified to make it of order m 1 in one dimension and of order n 1 along a single grid line in the other dimension a second function is derived with these roles reversed the resulting function has the form of the original design function exactly equaling it along the n grid lines of m points each and along the single perpendicular chosen grid line of n points and closely approximating it throughout the entire range of the variables this technique is illustrated for chebyshev response functions for which the two approximating functions are derived and evaluated for several combinations of m and n the responses are shown to have generally uniform sidelobe regions with all but a small percentage of the sidelobes within 1 db of the designed sidelobe value

minimum variance beamforming with phase independent derivative constraints a set of first and second order derivative constraints that can be used in minimum variance beamformers to achieve flat main beam response is presented efficient algorithms are derived for the implementation of these constraints in contrast to conventional derivative constraint methods which constrain both the magnitude power and phase responses of the beamformer the method only constrains the magnitude response the unnecessary constraint on the phase is a major drawback to the conventional methods since it causes the beamformer performance to vary with the particular spatial reference point used to define the array element positions this phenomenon is clearly undesirable because the choice of a reference point is generally made for notational convenience as a direct sequence of the phase constraint an inappropriately chosen reference point can easily result in a beamformer response which has undesirably high sidelobes the problem is avoided through the use of phase independent derivative constraints

pattern synthesis with multipoint accurate array response control in this paper the problem of pattern synthesis with antenna arrays is addressed and new approaches based on the recently developed accurate array response control textrm a 2 textrm rc algorithm are presented it is shown that the array weight vector obtained by the textrm a 2 textrm rc algorithm to control the normalized response at a single direction in each step belongs to a specific set thus an appropriate weight vector chosen from the intersection of weight vector sets corresponding to the desired responses at multiple directions is capable of simultaneously controlling those responses this results in the so called multipoint accurate array response control textrm ma 2 textrm rc algorithm moreover in order to avoid possible beam axis shift in pattern synthesis a modified textrm ma 2 textrm rc textrm m 2 textrm a 2 textrm rc algorithm is proposed by imposing a derivative constraint on the direction of beam axis representative numerical examples are provided to demonstrate the effectiveness of the proposed textrm ma 2 textrm rc and textrm m 2 textrm a 2 textrm rc algorithms for multipoint responses control and pattern synthesis

a flexible array synthesis method using quadratic programming a highly flexible synthesis method for an arbitrary array is proposed to best approximate a desired array pattern in a minimum mean square error sense the basic idea of the technique is to form a quadratic program with its cost function given by the mean square error between the array response and a properly selected pattern described by a known mathematical function this quadratic program can be a constrained or unconstrained optimization problem depending on the requirements of the desired array pattern in formulating the quadratic program no assumption has been made on the gain phase response or characteristics of the individual array elements therefore one can synthesize an array of arbitrary shape to any appropriate pattern with the characteristic of the array elements taken into consideration as long as one is able to model the array accurately the proposed method is used to synthesize arrays of different shapes linear as well as planar arrays including rectangular and circular planar arrays using a chebyshev polynomial or zero function as a design template to illustrate the feasibility of the proposed method

approximating rate distortion graphs of individual data experiments in lossy compression and denoising classical rate distortion theory requires specifying a source distribution instead we analyze rate distortion properties of individual objects using the recently developed algorithmic rate distortion theory the latter is based on the noncomputable notion of kolmogorov complexity to apply the theory we approximate the kolmogorov complexity by standard data compression techniques and perform a number of experiments with lossy compression and denoising of objects from different domains we also introduce a natural generalization to lossy compression with side information to maintain full generality we need to address a difficult searching problem while our solutions are therefore not time efficient we do observe good denoising and compression performance

dimension 1 sequences are close to randoms abstract we show that a sequence has effective hausdorff dimension 1 if and only if it is coarsely similar to a martin lof random sequence more generally a sequence has effective dimension s if and only if it is coarsely similar to a weakly s random sequence further for any s t every sequence of effective dimension s can be changed on density at most h 1 t h 1 s of its bits to produce a sequence of effective dimension t and this bound is optimal

optimal polarization synthesis of arbitrary arrays with focused power pattern the joint synthesis of the spatial power pattern and polarization of arbitrary arrays is addressed specifically the proposed approach gives the solution to a frequently encountered problem namely the array design i e the determination of the radiating element weightings to achieve a pattern that is arbitrarily upper bounded while its polarization is optimized in a given angular region any state of polarization elliptical circular and linear can be synthesized and there is no restriction regarding the array geometry and element patterns the synthesis problem is rewritten as a convex optimization problem that is efficiently solved using readily available software this ensures the optimality of the proposed solution various numerical results are presented to validate the proposed method and illustrate its potentialities the synthesis of a sequentially rotated array is first addressed then a linear array of equispaced randomly oriented dipoles is considered finally a conformal and a planar array of patches where the mutual coupling effects are considered are synthesized to radiate a linear and a circular polarization

a new approach to the optimization of robust antenna array processors the authors present a method for solving a class of optimization problems with nonsmooth constraints in particular they apply the method to the design of narrowband minimum power antenna array processors which are robust in the presence of errors such as array element placement look direction misalignment and frequency offset they first show that the constrained minimum power problem has a unique global minimum provided that the constraint set is nonempty then it is shown how the design problem derived directly from considerations of the sensitivity of the antenna array processor to errors can be transformed into a quadratic programming problem with linear inequality constraints which can be solved efficiently by the standard active set strategy they also present numerical results for two types of nonsmooth constraints developed to provided robustness these results confirm the effectiveness of the method

synthesis of sparse planar arrays using modified real genetic algorithm in array design the positions of sparse array elements is an important concern for optimal performance in terms of its ability to achieve minimum peak sidelobe level sll this paper proposes a modified real genetic algorithm mga based on resetting of chromosome for the element position optimization of sparse planar arrays with rectangular boundary and here the multiple optimization constraints include the number of elements the aperture and the minimum element spacing by simplifying the space between the elements from the actual distance to chebychev distance the mga searches a smaller solution space by means of indirect description of individual and it can avoid infeasible solution during the optimization process by two novel genetic operators finally the simulation results confirming the great efficiency and the robustness of the proposed method are shown in this paper

a numerical pattern synthesis algorithm for arrays a numerical technique for pattern synthesis in arrays is presented for a given set of elements the technique allows one to find a set of array coefficients that steer the main beam in a given direction and yield sidelobes meeting a specified criterion if such a set of array coefficients exists if the pattern specifications cannot be met with the given elements the algorithm finds the best attainable pattern the advantage of this technique is that it can be used with an arbitrary set of array elements different elements in the array can have different element patterns and the array can have arbitrary nonuniform spacing between elements the synthesis technique is based on adaptive array theory the given array elements are assumed to be used as the elements of an adaptive array the main beam is pointed in the proper direction by choosing the steering vector for that direction and the sidelobes are controlled by introducing a large number of interfering signals at many angles throughout the sidelobe region the algorithm iterates on the interference powers until a suitable pattern is obtained

sidelobe reduction in array pattern synthesis using genetic algorithm a simple and flexible genetic algorithm ga for pattern synthesis of antenna array with arbitrary geometric configuration is presented unlike conventional ga using binary coding and binary crossover this approach directly represents the array excitation weighting vectors as complex number chromosomes and uses decimal linear crossover without a crossover site compared with conventional gas this approach has a few advantages giving a clearer and simpler representation of the problem simplifying chromosome construction and totally avoiding binary encoding and decoding so as to simplify software programming and to reduce cpu time this method also allows us to impose constraints on phases and magnitudes of complex excitation coefficients for preferable implementation in practice using digital phase shifters and digital attenuators successful applications show that the approach can be used as a general tool for pattern synthesis of arbitrary arrays

synthesis of minimax sidelobes for arbitrary arrays this paper presents a synthesis algorithm to minimize the maximum sidelobe level for an arbitrary array similar to dolph chebyshev patterns the minimax array patterns for arbitrary arrays have uniform sidelobes

numerical synthesis of arbitrary discrete arrays a numerical algorithm for the synthesis of arbitrary discrete arrays is given the technique is based on the algorithm of c a olen and r t compton 1990 but employs a different iterative recursive algorithm yielding an optimum convergence rate it is shown that the new algorithm converges to the optimum solution in a significantly reduced number of iterations compared with the technique of olen and compton use of the technique is illustrated by applying the synthesis procedure to a ten element linear array and to a conformal array consisting of ten dipoles located on a parabolic curve

on the gaussianity of kolmogorov complexity of mixing sequences it has been proved that for all stationary and ergodic processes the average kolmogorov complexity of the first n observations converges almost surely to its shannon s conditional entropy this paper studies the convergence rate of this asymptotic result in particular we show that if the process satisfies certain mixing conditions then a central limit theorem will be respected furthermore we show that under slightly stronger mixing conditions one may obtain non asymptotic concentration bounds for the kolmogorov complexity

low dimensional sdp formulation for large antenna array synthesis bounding the sidelobe and mainlobe levels of an array with complex weights is attractive in that it allows direct control of the radiation pattern in this paper we propose an efficient beamforming technique for synthesizing the patterns of large arrays with bound constraints on the sidelobe and mainlobe levels it is shown that the pattern synthesis problem can be posed as a convex semi infinite program sip which is then turned into a semi definite program sdp via a novel linear matrix inequality lmi characterization of semi infinite trigonometric polynomial constraints in contrast to existing sdp formulations which require a large number of additional variables our sdp representation only uses a minimal number of additional variables this subsequently enables the design of patterns for arrays with several hundred elements to be efficiently achieved on a standard personal computer using existing sdp solvers

phase only shaped beam synthesis via technique of approximated beam addition a new method for phase only phased array beam pattern synthesis is derived the method is appropriate for the synthesis of coverage patterns for satellite communications where a minimax goal of maximizing the worst case beamforming gain to a set of service locations is desired the new approach called the technique of approximated beam addition is found to be computationally attractive relative to conventional methods yet offers optimal performance included are a theoretical consideration of optimality and simulation examples comparing the computational complexity and convergence quality to that of proven techniques

taylor patterns for discrete arrays the equivalent of a taylor pattern for continuous apertures is developed for discrete arrays this array factor can be realized exactly since it belongs to the appropriate class of patterns a method for determining the element excitations is also presented as an example the pattern and excitations are calculated for a 41 element array with bar n 6 and a 25 db design sidelobe level comparison is made with the patterns obtained by applying root matching and sampling of a continuous taylor aperture

wavelet thresholding via mdl for natural images we study the application of rissanen s 1989 principle of minimum description length mdl to the problem of wavelet denoising and compression for natural images after making a connection between thresholding and model selection we derive an mdl criterion based on a laplacian model for noiseless wavelet coefficients we find that this approach leads to an adaptive thresholding rule while achieving mean squared error performance comparable with other popular thresholding schemes the mdl procedure tends to keep far fewer coefficients from this property we demonstrate that our method is an excellent tool for simultaneous denoising and compression we make this claim precise by analyzing mdl thresholding in two optimality frameworks one in which we measure rate and distortion based on quantized coefficients and one in which we do not quantize but instead record rate simply as the number of nonzero coefficients

universal denoising of discrete time continuous amplitude signals we consider the problem of reconstructing a discrete time signal sequence with continuous valued components corrupted by a known memoryless channel when performance is measured using a per symbol loss function satisfying mild regularity conditions we develop a sequence of denoisers that although independent of the distribution of the underlying ldquocleanrdquo sequence is universally optimal in the limit of large sequence length this sequence of denoisers is universal in the sense of performing as well as any sliding window denoising scheme which may be optimized for the underlying clean signal our results are initially developed in a ldquosemi stochasticrdquo setting where the noiseless signal is an unknown individual sequence and the only source of randomness is due to the channel noise it is subsequently shown that in the fully stochastic setting where the noiseless sequence is a stationary stochastic process our schemes universally attain optimum performance the proposed schemes draw from nonparametric density estimation techniques and are practically implementable we demonstrate efficacy of the proposed schemes in denoising gray scale images in the conventional additive white gaussian noise awgn setting with additional promising results for less conventional noise distributions

rate distortion and denoising of individual data using kolmogorov complexity we examine the structure of families of distortion balls from the perspective of kolmogorov complexity special attention is paid to the canonical rate distortion function of a source word which returns the minimal kolmogorov complexity of all distortion balls containing that word subject to a bound on their cardinality this canonical rate distortion function is related to the more standard algorithmic rate distortion function for the given distortion measure examples are given of list distortion hamming distortion and euclidean distortion the algorithmic rate distortion function can behave differently from shannon s rate distortion function to this end we show that the canonical rate distortion function can and does assume a wide class of shapes unlike shannon s we relate low algorithmic mutual information to low kolmogorov complexity and consequently suggest that certain aspects of the mutual information formulation of shannon s rate distortion function behave differently than would an analogous formulation using algorithmic mutual information we explore the notion that low kolmogorov complexity distortion balls containing a given word capture the interesting properties of that word which is hard to formalize in shannon s theory and this suggests an approach to denoising

time frequency distribution kernels using fir filter design techniques in this correspondence time frequency distribution tfd kernels are obtained using finite impulse response fir filter design methods namely the windowing method and the equiripple approximation method based on chebyshev criterion it is shown that the class of the window designed kernels are simple to obtain and can handle most time varying environments

despeckling of medical ultrasound images using data and rate adaptive lossy compression a novel technique for despeckling the medical ultrasound images using lossy compression is presented the logarithm of the input image is first transformed to the multiscale wavelet domain it is then shown that the subband coefficients of the log transformed ultrasound image can be successfully modeled using the generalized laplacian distribution based on this modeling a simple adaptation of the zero zone and reconstruction levels of the uniform threshold quantizer is proposed in order to achieve simultaneous despeckling and quantization this adaptation is based on 1 an estimate of the corrupting speckle noise level in the image 2 the estimated statistics of the noise free subband coefficients and 3 the required compression rate the laplacian distribution is considered as a special case of the generalized laplacian distribution and its efficacy is demonstrated for the problem under consideration context based classification is also applied to the noisy coefficients to enhance the performance of the subband coder simulation results using a contrast detail phantom image and several real ultrasound images are presented to validate the performance of the proposed scheme comparison with two two stage schemes wherein the speckled image is first filtered and then compressed using the state of the art jpeg2000 encoder is presented experimental results show that the proposed scheme works better both in terms of the signal to noise ratio and the visual quality

sparse array quiescent beamformer design combining adaptive and deterministic constraints in this paper we examine sparse array quiescent beamforming for multiple sources in interference free environment to maximize the output signal to noise ratio snr the beamformer design comprises two intertwined stages the determination of beamforming weights and the reconfiguration of array structure the snr maximization may produce high sidelobe levels making the receiver vulnerable to interferences we consider the problem of achieving maximum snr beamforming subject to specified quiescent pattern constraints and as such combine both adaptive and deterministic approaches for sparse array configurations we employ two convex relaxation methods and an iterative linear fractional programming algorithm to solve the nonconvex antenna selection problem for sparse array beamformers simulation examples demonstrate that the array configuration plays a vital role in determining the beamforming performance in interference free scenarios

an adaptive generalized sidelobe canceller with derivative constraints an adaptive broad band beamforming structure is presented which employs a gradient based weight adjustment algorithm to minimize output variance subject to a set of j linear constraints on broadband directional derivatives in the desired look direction a generalized sidelobe cancelling structure is employed in which a nonadaptive conventional beamformer operates in parallel with an adaptive beamformer the conventional portion has a broad band beampattern which adheres to the specified constraints while the adaptive path is a cascade of a fixed signal blocking matrix and a set of tapped delay line filters blocking is employed to ensure that all incident waveforms which meet the specified constraints do not reach the tapped delay lines as a result an unconstrained least mean square lms power minimization algorithm is employed to adapt the delay line weights it is shown that with the addition of the directional derivative constraints the beamformer quiescent bcampattern becomes a function of the location of the phase center used to specify the constraints a design criterion for choosing this location is suggested and simulation experiments which illustrate the performance of this new adaptive beamformer are presented

lower bounds for algebraic computation trees with integer inputs let w subseteq r n be scale invariant and rationally dispersed i e tilde x in w implies lambda tilde x in w for all real lambda 0 and the rationale are dense in both w and r n w it is shown that in the algebraic computation tree model the problem of deciding whether an input tilde x in r n with integer coordinates is a member of w has complexity omega log 2 hat beta w 2n where hat beta w is the number of connected components of w that are not of measure 0 this theorem can be used to prove tight lower bounds for the integral constrained form of many basic problems such as element distinctness set disjointness finding convex hull etc through further transformations it leads to lower bounds for problems such as integer max gap and closest pair of a simple polygon the proof involves a nontrivial extension of the milnor thorn techniques for finding upper bounds on the betti numbers of algebraic varieties

finite state adaptive block to variable length noiseless coding of a nonstationary information source the author associates with a given nonstationary finite alphabet information source a certain class of stationary processes that he terms the stationary hull of the given source he shows that the optimum average rate at which the given source can be noiselessly coded by means of a finite state adaptive block to variable length coding schemes is the largest entropy rate among those processes in the stationary hull he explains what he means by an adaptive block to variable length coding scheme

a context quantization approach to universal denoising we revisit the problem of denoising a discrete time continuous amplitude signal corrupted by a known memoryless channel by modifying our earlier approach to the problem we obtain a scheme that is much more tractable than the original one and at the same time retains the universal optimality properties the universality refers to the fact that the proposed denoiser asymptotically with increasing block length of the data achieves the performance of an optimum denoiser that has full knowledge of the distribution of a source generating the underlying clean sequence the only restriction being that the distribution is stationary the optimality in a sense we will make precise of the denoiser also holds in the case where the underlying clean sequence is unknown and deterministic and the only source of randomness is in the noise the schemes involve a simple preprocessing step of quantizing the noisy symbols to generate quantized contexts the quantized context value corresponding to each sequence component is then used to partition the unquantized symbols into subsequences a universal symbol by symbol denoiser for unquantized sequences is then separately employed on each of the subsequences we identify a rate at which the context length and quantization resolution should be increased so that the resulting scheme is universal the proposed family of schemes is computationally attractive with an upper bound on complexity which is independent of the context length and the quantization resolution initial experimentation seems to indicate that these schemes are not only superior from a computational viewpoint but also achieve better denoising in practice

fixed slope universal lossy data compression corresponding to any lossless codeword length function l three universal lossy data compression schemes are presented one is with a fixed rate another is with a fixed distortion and a third is with a fixed slope the former two universal lossy data compression schemes are the generalization of yang kieffer s see ibid vol 42 no 1 p 239 45 1995 results to the general case of any lossless codeword length function l whereas the third is new in the case of fixed slope spl lambda 0 our universal lossy data compression scheme works as follows for any source sequence x sup n of length n the encoder first searches for a reproduction sequence y sup n of length n which minimizes a cost function n sup 1 l y sup n spl lambda spl rho sub n x sup n y sup n over all reproduction sequences of length n and then encodes x sup n into the binary codeword of length l y sup n associated with y sup n via the lossless codeword length function l where spl rho sub n x sup n y sup n is the distortion per sample between x sup n and y sup n under some mild assumptions on the lossless codeword length function l it is shown that when this fixed slope data compression scheme is applied to encode a stationary ergodic source the resulting encoding rate per sample and the distortion per sample converge with probability one to r sub spl lambda and d sub spl lambda respectively where d sub spl lambda r sub spl lambda is the point on the rate distortion curve at which the slope of the rate distortion function is spl lambda this result holds particularly for the arithmetic codeword length function and lempel ziv codeword length function the main advantage of this fixed slope universal lossy data compression scheme over the fixed rate fixed distortion universal lossy data compression scheme lies in the fact that it converts the encoding problem to a search problem through a trellis and then permits one to use some sequential search algorithms to implement it simulation results show that this fixed slope universal lossy data compression scheme combined with a suitable search algorithm is promising

an effective approach for the optimal focusing of array fields subject to arbitrary upper bounds a new approach to the optimal focusing of array fields subject to arbitrary upper bounds is presented the approach formulates the problem as the minimization of a linear function in a convex set unlike other approaches this one guarantees the achievement of the global optimum by using local optimization techniques and can moreover deal with any convex constraint on the unknowns such as near field constraints optimization is performed by two ad hoc developed solution algorithms which exploit the geometrical characteristics of the problem at hand thus leading to extremely effective and computationally efficient numerical codes an extensive numerical analysis has been performed in all cases of linear planar and circular arc arrays the enhanced performance of the proposed technique with respect to the solution algorithms available in the literature fully confirms the effectiveness of the approach

a new low side lobe pattern synthesis technique for conformal arrays the application of the new nonlinear optimization algorithms to array design is demonstrated by the low side lobe pattern synthesis of conformal arrays by adopting the information of array element realized gain patterns the authors formulate synthesis problems as nonlinearly constrained optimization problems and propose a direct method to solve them the technique allows them to find a set of array coefficients that yield a pattern meeting a specified side lobe level and achieving the maximum directivity if such a set of array coefficients exists if the side lobe specifications cannot be met with the given array the technique will result in a set of coefficients that yield a pattern meeting the best attainable side lobe level and having directivity as high as possible simplified synthesis problems for an axial dipole array in an infinite perfectly conducting cylinder are discussed and numerical results are given the synthesis technique works for general array patterns

synthesis of planar arrays with elements in concentric rings the circular symmetry of concentric ring arrays becomes an advantage for situations where the radiation patterns are symmetric in the azimuthal direction for planar arrays with elements in an equispaced grid the fast fourier transform can be applied in the calculations involved between the array factor and the source distribution however for circular arrays the elements are in a non equispaced grid making the application of fast computation algorithms difficult therefore two techniques are proposed to synthesize circular arrays the first one provides the control of the pattern by sampling the array factor in this case the fast fourier transform can be applied the windows technique is also utilized to control the sidelobe levels and the ripple structure of the shaped beam the second technique considers the symmetric nature of concentric circular arrays and the control of the array factor is performed imposing some specific points of the pattern

the similarity metric a new class of distances appropriate for measuring similarity relations between sequences say one type of similarity per distance is studied we propose a new normalized information distance based on the noncomputable notion of kolmogorov complexity and show that it is in this class and it minorizes every computable distance in the class that is it is universal in that it discovers all computable similarities we demonstrate that it is a metric and call it the similarity metric this theory forms the foundation for a new practical tool to evidence generality and robustness we give two distinctive applications in widely divergent areas using standard compression programs like gzip and gencompress first we compare whole mitochondrial genomes and infer their evolutionary history this results in a first completely automatic computed whole mitochondrial phylogeny tree secondly we fully automatically compute the language tree of 52 different languages

beampattern synthesis for linear and planar arrays with antenna selection by convex optimization a convex optimization based beampattern synthesis method with antenna selection is proposed for linear and planar arrays conjugate symmetric beamforming weights are used so that the upper and non convex lower bound constraints on the beampattern can be convex thus a mainlobe of an arbitrary beamwidth and response ripple can be obtained this method can achieve completely arbitrary sidelobe levels by minimizing a re weighted objective function based on the magnitudes of the elements in the beamforming weight vector iteratively the proposed method selects certain antennas in an array to satisfy the prescribed beampattern specifications precisely interestingly a sparse array with fewer antennas compared to other methods is produced this method can design non uniformly spaced arrays with inter element spacings larger than one half wavelength without the appearance of grating lobes in the resulting beampattern simulations are shown using arrays of up to a few hundred antennas to illustrate the practicality of the proposed method

kolmogorov s structure functions and model selection in 1974 kolmogorov proposed a nonprobabilistic approach to statistics and model selection let data be finite binary strings and models be finite sets of binary strings consider model classes consisting of models of given maximal kolmogorov complexity the structure function of the given data expresses the relation between the complexity level constraint on a model class and the least log cardinality of a model in the class containing the data we show that the structure function determines all stochastic properties of the data for every constrained model class it determines the individual best fitting model in the class irrespective of whether the true model is in the model class considered or not in this setting this happens with certainty rather than with high probability as is in the classical case we precisely quantify the goodness of fit of an individual model with respect to individual data we show that within the obvious constraints every graph is realized by the structure function of some data we determine the un computability properties of the various functions contemplated and of the algorithmic minimal sufficient statistic

simple universal lossy data compression schemes derived from the lempel ziv algorithm two universal lossy data compression schemes one with fixed rate and the other with fixed distortion are presented based on the well known lempel ziv algorithm in the case of fixed rate r the universal lossy data compression scheme works as follows first pick a codebook b sub n consisting of all reproduction sequences of length n whose lempel ziv codeword length is spl les nr and then use b sub n to encode the entire source sequence n block by n block this fixed rate data compression scheme is universal in the sense that for any stationary ergodic source or for any individual sequence the sample distortion performance as n spl rarr spl infin is given almost surely by the distortion rate function a similar result is shown in the context of fixed distortion lossy source coding

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

multiobjective optimization of real and coupled antenna array excitations via primal dual interior point filter method from spherical mode expansions a novel method for the multiobjective optimization of arbitrary planar array excitations is presented the optimization problem formulation which inherently takes into account every array element pattern as well as all interelement couplings is based on matrix valued functions which are computed from the generalized scattering matrix characterization of an array and spherical mode expansions of its radiated field it allows the maximization of the directive gain subject to a maximum sidelobe level a maximum crosspolar level and a minimum aperture illumination efficiency the setting of null pointing directions and the dynamic range control to solve the resulting non linear optimization problem we have developed a primal dual interior point method specifically adapted to the presented formulation which makes use of novel filtering techniques numerical examples of arrays of microstrip patches and dielectric resonator antennas covering a wide variety of requirements on these parameters are presented

sample converses in source coding theory the rate and distortion performance of a sequence of codes along a sample sequence of symbols generated by a stationary ergodic information source are studied two results are obtained 1 the source sample sequence is encoded by an arbitrary sequence of block codes which operate at a fixed rate level r and a sample converse is obtained which states that with probability one the lower limit of the code sample distortions is lower bounded by d r the value of the distortion rate function at r 2 the source sample sequence is encoded by an arbitrary sequence of variable rate codes which operate at a fixed distortion level d and a sample converse is obtained which states that with probability one the lower limit of the code sample rates is lower bounded by r d the value of the rate distortion function at d a novel ergodic theorem is used to obtain both sample converses

an on line universal lossy data compression algorithm via continuous codebook refinement i basic results a new on line universal lossy data compression algorithm is presented for finite memoryless sources with unknown statistics its performance asymptotically approaches the fundamental rate distortion limit the codebook is generated on the fly and continuously adapted by simple rules there is no separate codebook training or codebook transmission candidate codewords are randomly generated according to an arbitrary and possibly suboptimal distribution through a carefully designed gold washing or information theoretic sieve mechanism good codewords and only good codewords are promoted to permanent status with high probability we also determine the rate at which our algorithm approaches the fundamental limit

restoration of lossy compressed noisy images noise degrades the performance of any image compression algorithm however at very low bit rates image coders effectively filter noise that may he present in the image thus enabling the coder to operate closer to the noise free case unfortunately at these low bit rates the quality of the compressed image is reduced and very distinctive coding artifacts occur this paper proposes a combined restoration of the compressed image from both the artifacts introduced by the coder along with the additive noise the proposed approach is applied to images corrupted by data dependent poisson noise and to images corrupted by film grain noise when compressed using a block transform coder such as jpeg this approach has proved to be effective in terms of visual quality and peak signal to noise ratio psnr when tested on simulated and real images

rate distortion optimization for h 264 interframe coding a general framework and algorithms rate distortion rd optimization for h 264 interframe coding with complete baseline decoding compatibility is investigated on a frame basis using soft decision quantization sdq rather than the standard hard decision quantization we first establish a general framework in which motion estimation quantization and entropy coding in h 264 for the current frame can be jointly designed to minimize a true rd cost given previously coded reference frames we then propose three rd optimization algorithms a graph based algorithm for near optimal sdq in h 264 baseline encoding given motion estimation and quantization step sizes an algorithm for near optimal residual coding in h 264 baseline encoding given motion estimation and an iterative overall algorithm to optimize h 264 baseline encoding for each individual frame given previously coded reference frames with them embedded in the indicated order the graph based algorithm for near optimal sdq is the core given motion estimation and quantization step sizes it is guaranteed to perform optimal sdq if the weak adjacent block dependency utilized in the context adaptive variable length coding of h 264 is ignored for optimization the proposed algorithms have been implemented based on the reference encoder jm82 of h 264 with complete compatibility to the baseline profile experiments show that for a set of typical video testing sequences the graph based algorithm for near optimal sdq the algorithm for near optimal residual coding and the overall algorithm achieve on average 6 8 and 12 respectively rate reduction at the same psnr ranging from 30 to 38 db when compared with the rd optimization method implemented in the h 264 reference software

minimum complexity pursuit for universal compressed sensing the nascent field of compressed sensing is founded on the fact that high dimensional signals with simple structure can be recovered accurately from just a small number of randomized samples several specific kinds of structures have been explored in the literature from sparsity and group sparsity to low rankness however two fundamental questions have been left unanswered what are the general abstract meanings of structure and simplicity do there exist universal algorithms for recovering such simple structured objects from fewer samples than their ambient dimension in this paper we address these two questions using algorithmic information theory tools such as the kolmogorov complexity we provide a unified definition of structure and simplicity leveraging this new definition we develop and analyze an abstract algorithm for signal recovery motivated by occam s razor minimum complexity pursuit mcp requires approximately 2 randomized samples to recover a signal of complexity and ambient dimension n we also discuss the performance of the mcp in the presence of measurement noise and with approximately simple signals

filtering random noise from deterministic signals via data compression we present a novel technique for the design of filters for random noise leading to a class of filters called occam filters the essence of the technique is that when a lossy data compression algorithm is applied to a noisy signal with the allowed loss set equal to the noise strength the loss and the noise tend to cancel rather than add we give two illustrative applications of the technique to univariate signals we also prove asymptotic convergence bounds on the effectiveness of occam filters

computing the betti numbers of semi algebraic sets defined by partly quadratic systems of polynomials abstract let r be a real closed field q r y 1 y l x 1 x k with deg y q 2 deg x q d q q q m and p r x 1 x k with deg x p d p p p s let s r l k be a semi algebraic set defined by a boolean formula without negations with atoms p 0 p 0 p 0 p p q we describe an algorithm for computing the betti numbers of s generalizing a similar algorithm described in s basu computing the top few betti numbers of semi algebraic sets defined by quadratic inequalities in polynomial time found comput math 8 1 2008 45 80 the complexity of the algorithm is bounded by l 1 s 1 m 1 d 1 2 o m k the complexity of the algorithm interpolates between the doubly exponential time bounds for the known algorithms in the general case and the polynomial complexity in case of semi algebraic sets defined by few quadratic inequalities s basu computing the top few betti numbers of semi algebraic sets defined by quadratic inequalities in polynomial time found comput math 8 1 2008 45 80 moreover for fixed m and k this algorithm has polynomial time complexity in the remaining parameters

geodesic diameter of sets defined by few quadratic equations and inequalities we prove a bound for the geodesic diameter of a subset of the unit ball in mathbb r n described by a fixed number of quadratic equations and inequalities which is polynomial in n whereas the known bound for general degree is exponential in n our proof uses methods borrowed from d acunto and kurdyka to deal with the geodesic diameter and from barvinok to take advantage of the quadratic nature

pattern synthesis for arbitrary arrays using an adaptive array method this paper presents a new pattern synthesis algorithm for arbitrary arrays based on adaptive array theory with this algorithm the designer can efficiently control both mainlobe shaping and sidelobe levels the element weights optimize a weighted l sub 2 norm between desired and achieved patterns the values of the weighting function in the l sub 2 norm interpreted as imaginary jammers as in olen and compton s 1990 method are iterated to minimize exceedance of the desired sidelobe levels and minimize the absolute difference between desired and achieved mainlobe patterns the sidelobe control can be achieved by iteration only on sidelobe peaks in comparison to olen and compton s method the new algorithm provides a great improvement in mainlobe shaping control example simulations including both nonuniform linear and planar arrays are shown to illustrate the effectiveness of this algorithm

occam filters for stochastic sources with application to digital images an occam filter employs lossy data compression to separate signal from noise previously it was shown that occam filters can filter random noise from deterministic signals here we show that occam filters can also separate two stochastic sources depending on their relative compressibility we also compare the performance of occam filters and wavelet based denoising on digital images

linear aperiodic array synthesis using an improved genetic algorithm a novel algorithm on beam pattern synthesis for linear aperiodic arrays with arbitrary geometrical configuration is presented in this paper linear aperiodic arrays are attractive for their advantages on higher spatial resolution and lower sidelobe however the advantages are attained at the cost of solving a complex non linear optimization problem in this paper we explain the improved genetic algorithm iga that simultaneously adjusts the weight coefficients and inter sensor spacings of a linear aperiodic array in more details and extend the investigations to include the effects of mutual coupling and the sensitivity of the peak sidelobe level psl to steering angles numerical results show that the psl of the synthesized beam pattern has been successfully lowered with the iga when compared with other techniques published in the literature in addition the computational cost of our algorithm can be as low as 10 of that of a recently reported genetic algorithm based synthesis method the excellent performance of iga makes it a promising optimization algorithm where expensive cost functions are involved

pattern synthesis of narrowband conformal arrays using iterative second order cone programming a new design method is proposed for the power or shaped beam pattern synthesis problem of narrowband conformal arrays where only the magnitude response is specified the proposed method iteratively linearizes the non convex power pattern function to obtain a convex subproblem in the design variables which can be solved optimally using second order cone programming socp in addition a wide variety of magnitude constraints such as non convex lower bound magnitude constraints can be incorporated an efficient technique for determining a reasonably good initial guess to the problem is also proposed to further improve the reliability of the method computer simulations show that the initial guesses so obtained converge to satisfactory solutions while satisfying various prescribed magnitude constraints design results show that the performance of the proposed method is comparable to the optimal solution previously obtained for uniform linear arrays with isotropic elements moreover we show by means of examples that the proposed method is also applicable to general non convex power pattern synthesis problems involving arbitrary array geometries arbitrary polarization characteristics and mutual coupling effect