a branch and bound algorithm for quadratically constrained sparse filter design this paper presents an exact algorithm for sparse filter design under a quadratic constraint on filter performance the algorithm is based on branch and bound a combinatorial optimization procedure that can either guarantee an optimal solution or produce a sparse solution with a bound on its deviation from optimality to reduce the complexity of branch and bound several methods are developed for bounding the optimal filter cost bounds based on infeasibility yield incrementally accumulating improvements with minimal computation while two convex relaxations referred to as linear and diagonal relaxations are derived to provide stronger bounds the approximation properties of the two relaxations are characterized analytically as well as numerically design examples involving wireless channel equalization and minimum variance distortionless response beamforming show that the complexity of obtaining certifiably optimal solutions can often be significantly reduced by incorporating diagonal relaxations especially in more difficult instances in the case of early termination due to computational constraints diagonal relaxations strengthen the bound on the proximity of the final solution to the optimum

peak error constrained sparse fir filter design using iterative socp in this paper a novel algorithm is proposed to design sparse fir filters it is known that this design problem is highly nonconvex due to the existence of norm of a filter coefficient vector in its objective function to tackle this difficulty an iterative procedure is developed to search a potential sparsity pattern which is then used to compute the final solution by solving a convex optimization problem in each iterative step the original sparse filter design problem is successively transformed to a simpler subproblem it can be proved that under a weak condition globally optimal solutions of these subproblems can be attained by solving their dual problems in this case the overall iterative procedure converges to a locally optimal solution of the original design problem the design procedure described above can be repeated for several times to further improve the sparsity of design results the output of the previous stage can be used as the initial point of the subsequent design the performance of the proposed algorithm is evaluated by two sets of design examples and compared to other sparse fir filter design algorithms

new initialization methods for discrete coefficient fir filter design with coefficient scaling and the use of scale factor in the design process the initialization of filter coefficients in discrete coefficient finite impulse response fir filter design with coefficient scaling using coefficient value assignment based optimization techniques is considered a common weakness of existing initialization measures a total square error tse measure and a maximum error me measure is described new tse and me measures that overcome the weakness are introduced as opposed to the current knowledge it is revealed that tse and me measures do not necessarily provide different initial coefficient set information and that the initial coefficient set information by the me measure is not unique in general on a parallel track the treatment of coefficient scaling in the optimization process is considered the closed form expression of the objective function normalized peak ripple magnitude nprm which was defined implicitly in the literature is given in contrast to existing methods the computation of nprm accordingly does not require a scale factor parameter independent of filter coefficients although coefficient scaling persists then tse and me measures become practically equivalent although in general they indicate different initial scale factors since an explicit scale factor parameter is no longer needed

boundary effects in a phase field approach to topology optimization a phase field based topology optimization approach is considered for the maximum stiffness or minimum compliance problem the objective functional to be minimized consists in addition to the compliance a cost for gray solutions and a cost for interfaces between void and full material since the interfaces between void and full material are penalized via a volume integral in the original phase field formulation there is no penalty associated with interfaces along the external boundaries in the present contribution an additional term representing the cost of interfaces at external boundaries is added to the functional subject to minimization it is shown that the new boundary term enters the optimization as a robin boundary condition the method is implemented in a finite element setting and numerical simulations of typical structures are considered the results indicate that the optimal designs are influenced by the cost of interfaces to a large less

topology optimization using regularized intermediate density control abstract we consider topology optimization of elastic continua the elasticity tensor is assumed to depend linearly on the design function density as in the variable thickness sheet problem in order to get black white design pictures the intermediate density values are controlled by an explicit constraint this constraint is regularized by including a compact and linear operator s to guarantee existence of solutions a proof of convergence of the finite element fe discretized optimization problem s solutions to exact ones is also given so the method is not prone to numerical anomalies such as mesh dependence or checkerboards the procedure is illustrated in some minimum compliance examples where s is chosen to be a classical convolution type operator the fe discretized optimization problems are solved by sequential convex approximations

phase unwrapping via graph cuts phase unwrapping is the inference of absolute phase from modulo 2pi phase this paper introduces a new energy minimization framework for phase unwrapping the considered objective functions are first order markov random fields we provide an exact energy minimization algorithm whenever the corresponding clique potentials are convex namely for the phase unwrapping classical lp norm with pges1 its complexity is kt n 3n where k is the length of the absolute phase domain measured in 2pi units and t n m is the complexity of a max flow computation in a graph with n nodes and m edges for nonconvex clique potentials often used owing to their discontinuity preserving ability we face an np hard problem for which we devise an approximate solution both algorithms solve integer optimization problems by computing a sequence of binary optimizations each one solved by graph cut techniques accordingly we name the two algorithms puma for phase unwrapping max flow min cut a set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state of the art phase unwrapping algorithms

some convergence results for howard s algorithm this paper deals with convergence results of howard s algorithm for the resolution of min a in mathcal a b a x c a 0 where b a is a matrix c a is a vector and mathcal a is a compact set we show a global superlinear convergence result under a monotonicity assumption on the matrices b a extensions of howard s algorithm for a max min problem of the form max b in mathcal b min a in mathcal a b a b x c a b 0 are also proposed in the particular case of an obstacle problem of the form min ax b x g 0 where a is an n times n matrix satisfying a monotonicity assumption we show the convergence of howard s algorithm in no more than n iterations instead of the usual 2 n bound still in the case of an obstacle problem we establish the equivalence between howard s algorithm and a primal dual active set algorithm m hintermuller k ito and k kunisch siam j optim 13 2002 pp 865 888 the algorithms are illustrated on the discretization of nonlinear pdes arising in the context of mathematical finance american option and merton s portfolio problem of front propagation problems and for the double obstacle problem

interpolated finite impulse response filters a new approach to implement computationally efficient finite impulse response fir digital filters is presented the filter structure is a cascade of two sections the first section generates a sparse set of impulse response samples and the other section generates the remaining samples by using interpolation the method can be used to implement most practical fir filters with significant savings in the number of arithmetic operations typically 1 2 to 1 8 of the number of multipliers and adders of conventional fir filters are required in the implementation the saving is achieved both in the linear phase and the non linear phase cases in addition the new implementation gives smaller coefficient sensitivities and better roundoff noise properties than conventional implementations

results on nonrecursive digital filters with nonequidistant taps a new method in nonrecursive digial filter design with nonequidistant taps is presented with characteristic examples the method consists of increasing the number of taps progressively and optimizing their positions at every addition of a new tap the efficiency of the method manifests itself in the drastic reduction of the number of taps and in the reduction dynamic range of tap weights as compared to the equally spaced case for the same filter performance

large strain phase field based multi material topology optimization summary a multi material topology optimization scheme is presented the formulation includes an arbitrary number of phases with different mechanical properties to ensure that the sum of the volume fractions is unity and in order to avoid negative phase fractions an obstacle potential function which introduces infinity penalty for negative densities is utilized the problem is formulated for nonlinear deformations and the objective of the optimization is the end displacement the boundary value problems associated with the optimization problem and the equilibrium equation are solved using the finite element method to illustrate the possibilities of the method it is applied to a simple boundary value problem where optimal designs using multiple phases are considered copyright 2015 john wiley sons ltd

filters in topology optimization in this article a modified filtered version of the minimum compliance topology optimization problem is studied the direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field by the mean of a convolution operator in this setting it is possible to establish the existence of solutions moreover convergence of an approximation by means of finite elements can be obtained this is illustrated through some numerical experiments the filtering technique is also shown to cope with two important numerical problems in topology optimization checkerboards and mesh dependent designs copyright 2001 john wiley sons ltd

topology optimization utilizing inverse motion based form finding topology optimization at finite strain setting using the concept of inverse motion based form finding is introduced this novel procedure allows boundary conditions and shape of the structure in the operating deformed state to be prescribed the outcome of the optimization algorithm will be the shape of the undeformed structure i e the state in which the structure should be manufactured the objective of the optimization considered is to find the stiffest structure for a given amount of material the problem is regularized using a helmholtz filter which is formulated in the deformed configuration both the elastic boundary value problem and the partial differential equation associated with the helmholtz filter are solved using the finite element method the optimization problem is solved using a sequence of convex separable approximations the paper is closed by 2d as well as 3d numerical examples that clearly illustrates that the method is able to find optimal solutions for inverse motion finite strain topology optimization problems

improved filter sharpening we propose a natural extension to kaiser hamming 1977 filter sharpening methods to allow for a piecewise linear desired amplitude change function acf the primary advantages of the proposed acf over piecewise constant acfs is that we obtain better control of selective improvement or degradation in either the passband or stopband or both and we are not restricted to applying our methods to filters with piecewise constant pass and stopbands since linear segments of slope 1 can be used to retain existing filter performance in either passband or stopband the proposed acf approximating polynomial ap is easy to compute may be constrained to have simple or integer coefficients and may be expressed as the ap of kaiser and hamming plus a correction polynomial we also provide applications for motivation

linear programming algorithms for sparse filter design in designing discrete time filters the length of the impulse response is often used as an indication of computational cost in systems where the complexity is dominated by arithmetic operations the number of nonzero coefficients in the impulse response may be a more appropriate metric to consider instead and computational savings are realized by omitting arithmetic operations associated with zero valued coefficients this metric is particularly relevant to the design of sensor arrays where a set of array weights with many zero valued entries allows for the elimination of physical array elements resulting in a reduction of data acquisition and communication costs however designing a filter with the fewest number of nonzero coefficients subject to a set of frequency domain constraints is a computationally difficult optimization problem this paper describes several approximate polynomial time algorithms that use linear programming to design filters having a small number of nonzero coefficients i e filters that are sparse specifically we present two approaches that have different computational complexities in terms of the number of required linear programs the first technique iteratively thins the impulse response of a non sparse filter until frequency domain constraints are violated the second minimizes the 1 norm of the impulse response of the filter using the resulting design to determine the coefficients that are constrained to zero in a subsequent re optimization stage the algorithms are evaluated within the contexts of array design and acoustic equalization

phase field relaxation of topology optimization with local stress constraints we introduce a new relaxation scheme for structural topology optimization problems with local stress constraints based on a phase field method in the basic formulation we have a pde constrained optimization problem where the finite element and design analysis are solved simultaneously the starting point of the relaxation is a reformulation of the material problem involving linear and 0 1 constraints only the 0 1 constraints are then relaxed and approximated by a cahn hilliard type penalty in the objective functional which yields convergence of minimizers to 0 1 designs as the penalty parameter decreases to zero a major advantage of this kind of relaxation opposed to standard approaches is a uniform constraint qualification that is satisfied for any positive value of the penalization parameter the relaxation scheme yields a large scale optimization problem with a high number of linear inequality constraints we discretize the problem by finite elements and solve the arising finite dimensional programming problems by a primal dual interior point method numerical experiments for problems with local stress constraints based on different criteria indicate the success and robustness of the new approach

simultaneous phase unwrapping and removal of chemical shift spurs using graph cuts application in quantitative susceptibility mapping quantitative susceptibility mapping qsm is a magnetic resonance imaging technique that reveals tissue magnetic susceptibility it relies on having a high quality field map typically acquired with a relatively long echo spacing and long final te applications of qsm outside the brain require the removal of fat contributions to the total signal phase however current water fat separation methods applied on typical data acquired for qsm suffer from three issues inadequacy when using large echo spacing over smoothing of the field maps and high computational cost in this paper the general phase wrap and chemical shift problem is formulated using a single species fitting and is solved using graph cuts with conditional jump moves this method is referred as simultaneous phase unwrapping and removal of chemical shift spurs the result from spurs is then used as the initial guess for a voxel wise iterative decomposition of water and fat with echo asymmetric and least squares estimation ideal the estimated 3 d field maps are used to compute qsm in body regions outside of the brain such as the liver experimental results show substantial improvements in field map estimation water fat separation and reconstructed qsm compared to two existing water fat separation methods on 1 5t and 3t magnetic resonance human data with long echo spacing and rapid field map variation

a discrete filled function method for the design of fir filters with signed powers of two coefficients in this paper we consider the optimal design of finite impulse response fir filters with coefficients expressed as sums of signed powers of two spt terms where the normalized peak ripple npr is taken as the performance measure this problem is formulated as a mixed integer programming problem based on a transformation between two different integer spaces and the computation of the optimal scaling factor for a given set of coefficients this mixed integer programming problem is transformed into an equivalent integer programming problem then an efficient algorithm based on a discrete filled function is developed for solving this equivalent problem for illustration some numerical examples are solved

a new approach to the design of discrete coefficient fir digital filters in this correspondence the iterative lagrange multiplier approach is proposed for designing discrete coefficient fir digital filters the method associates the conventional lagrange multiplier approach and a tree search algorithm for each branch of the tree the lagrange multiplier approach is used to optimize the remaining unquantized coefficients of the designed fir filter in the least squares sense when one or more of the coefficients takes on discrete values design examples including general low pass filters and nyquist filters are presented to demonstrate the effectiveness of the method also the method can be extended to design discrete coefficient 2 d fir filters

howard s algorithm in a phase field topology optimization approach abstract in undetermined the topology optimization problem is formulated in a phase field approach the solution procedure is based on the allan cahn diffusion model where the conservation of volume is enforced by a global constraint the functional defining the minimization problem is selected such that no penalization is imposed for full and void materials upper and lower bounds of the density function are enforced by infinite penalty at the bounds a gradient term that introduces cost for boundaries and thereby regularizing the problem is also included in the objective functional conditions for stationarity of the functional are derived and it is shown that the problem can be stated as a variational inequality or a max min problem both defining a double obstacle problem the numerical examples used to demonstrate the method are solved using the fem whereas the double obstacle problem is solved using howard s algorithm less

finite word length fir filter design using integer programming over a discrete coefficient space it is demonstrated that the improvement achieved by using integer programming over simple coefficient rounding in the design of finite impulse response fir filters with discrete coefficients is most significant when the discrete coefficient space is the powers of two space or when a specification is to be met with a given coefficient word length by increasing the filter length both minimax and least square error criteria are considered

topology optimization of non linear elastic structures and compliant mechanisms abstract a linear elastic response is assumed in most structural topology optimization problems while this assumption is valid for a wide variety of problems it is not valid for structures undergoing large displacements the elastic structural analysis used here accommodates geometric and material non linearities the material density field is filtered to enforce a length scale on the field variation and is penalized to remove less effective intermediate densities the filtering scheme is embedded in the structural analysis to resolve the non existent solution to the solid void topology problem in this way we know precisely what optimization problem is being solved the structural topology optimization formulation is also used to design compliant mechanisms

multimaterial topology optimization by volume constrained allen cahn system and regularized projected steepest descent method abstract a new computational algorithm is introduced in the present study to solve multimaterial topology optimization problems it is based on the penalization of the objective functional by the multiphase volume constrained ginzburg landau energy functional the update procedure is based on the gradient flow of the objective functional by a fractional step projected steepest descent method in the first step the new design is found based on the projected steepest descent method to ensure the reduction in the objective functional simultaneously satisfying the control constraints in the second step regularization step an h 1 regularity of the solution is ensured while keeping the feasibility of solution with respect to the set of control constraints the presented algorithm could be accounted as a constrained h 1 optimization algorithm which according to our knowledge has not been reported to solve such kind of problems yet the success and efficiency of the presented method are shown through several test problems numerical results show that the presented algorithm ends with a near 0 1 topology and its computational cost scales sub linearly by the number of phases for the sake of reader convenience and the ease of further extension the matlab implementation of the presented algorithm is included in the appendix

a fast iterated conditional modes algorithm for water fat decomposition in mri decomposition of water and fat in magnetic resonance imaging mri is important for biomedical research and clinical applications in this paper we propose a two phased approach for the three point water fat decomposition problem our contribution consists of two components 1 a background masked markov random field mrf energy model to formulate the local smoothness of field inhomogeneity 2 a new iterated conditional modes icm algorithm accounting for high performance optimization of the mrf energy model the mrf energy model is integrated with background masking to prevent error propagation of background estimates as well as improve efficiency the central component of our new icm algorithm is the stability tracking st mechanism intended to dynamically track iterative stability on pixels so that computation per iteration is performed only on instable pixels the st mechanism significantly improves the efficiency of icm we also develop a median based initialization algorithm to provide good initial guesses for icm iterations and an adaptive gradient based scheme for parametric configuration of the mrf model we evaluate the robust of our approach with high resolution mouse datasets acquired from 7t mri

shape and topology optimization based on the phase field method and sensitivity analysis this paper discusses a structural optimization method that optimizes shape and topology based on the phase field method the proposed method has the same functional capabilities as a structural optimization method based on the level set method incorporating perimeter control functions the advantage of the method is the simplicity of computation since extra operations such as re initialization of functions are not required structural shapes are represented by the phase field function defined in the design domain and optimization of this function is performed by solving a time dependent reaction diffusion equation the artificial double well potential function used in the equation is derived from sensitivity analysis the proposed method is applied to two dimensional linear elastic and vibration optimization problems such as the minimum compliance problem a compliant mechanism design problem and the eigenfrequency maximization problem the numerical examples provided illustrate the convergence of the various objective functions and the effect that perimeter control has on the optimal configurations

whole brain susceptibility mapping at high field a comparison of multiple and single orientation methods abstract optimisation and comparison of the performance of three different methods for calculating three dimensional susceptibility maps of the whole brain from gradient echo phase and modulus image data acquired at 7 t is described the methods studied are a multiple orientation method in which image data acquired with the head at several different angles to the main field are combined and two methods which use data acquired at a single orientation the first of these is based on exclusion of some k space data from the calculation through thresholding of the dipolar field kernel while the second incorporates a regularisation method that is based on using information from the modulus images the methods were initially optimised via analysis of data from a phantom containing different compartments of known susceptibility as part of this work a novel high pass filtering methodology was introduced to remove background fields from field maps based on phase data the optimised methods were successfully applied to high resolution 0 7 mm isotropic whole brain modulus and phase data acquired in vivo from five healthy male subjects 25 30 years of age the multiple orientation method yielded high quality susceptibility maps out performing the single orientation methods venous blood vessels as well as the substantia nigra and globus pallidus brain regions showed particularly high positive susceptibility offsets relative to surrounding tissue consistent with high deoxyhemoglobin and non heme iron content respectively to compare the performance of the different methods regions of interest were drawn in deep grey matter structures and in cortical grey and white matter the threshold based approach was fast and simple to use but underestimated susceptibility differences and showed significant artefacts due to noise amplification in difficult regions of k space the regularised single orientation method yielded contrast dependent on the choice of spatial priors but demonstrated the potential to yield susceptibility maps of a similar quality to those calculated using data acquired at multiple orientations to the field

design of nonuniformly spaced linear phase fir filters using mixed integer linear programming an optimization problem for designing a nonuniformly spaced linear phase fir filter with minimal complexity is formulated and solved by mixed integer linear programming milp examples illustrate that the proposed method is useful for designing a wide range of filter types and can outperform subset selection based design methods

fir filter design over a discrete powers of two coefficient space fir digital filters with discrete coefficient values selected from the powers of two coefficient space are designed using the methods of integer programming the frequency responses obtained are shown to be superior to those obtained by simply rounding the coefficients both the weighted minimax and the weighted least square error criteria are considered using a weighted least square error criterion it is shown that it is possible to predict the improvement that can be expected when integer quadratic programming is used instead of simple coefficient rounding

on the use of cyclotomic polynomial prefilters for efficient fir filter design the authors present an efficient fir finite impulse response filter design algorithm that generalizes existing cascaded fir prefilter equalizer methods they propose using cyclotomic polynomial building blocks to form a multiplierless prefilter with impressive stopband performance and they provide a straightforward strategy for choosing the polynomials to match filter specification two options for design of the equalizer are provided a uniformly spaced equalizer can be optimally l sub infinity designed via a modified parks mcclellan algorithm a new algorithm based on complex basis function subset selection methods is also proposed for optimal design of a more efficient nonuniformly spaced equalizer the techniques which can be applied to a broad class of filter design problems typically provide a 35 85 reduction in the number of additions and multiplications required with a cost of 10 45 additional delays the methods also provide reduced coefficient quantization sensitivity and reduced roundoff noise