microwave image reconstruction utilizing log magnitude and unwrapped phase to improve high contrast object recovery reconstructing images of large high contrast objects with microwave methods has proved difficult successful images have generally been obtained by using a priori information to constrain the image reconstruction to recover the correct electromagnetic property distribution in these situations the measured electric field phases as a function of receiver position around the periphery of the imaging field of view vary rapidly often undergoing changes of greater than spl pi radians especially when the object contrast and illumination frequency increase here the authors introduce a modified form of a maxwell equation model based image reconstruction algorithm which directly incorporates log magnitude and phase of the measured electric field data by doing so measured phase variation can be unwrapped and distributed over more than one rieman sheet in the complex plane simulation studies and microwave imaging experiments demonstrate that significant image quality enhancements occur with this approach for large high contrast objects simple strategies for visualizing and unwrapping phase values as a function of the transmitter and receiver positions within our microwave imaging array are described metrics of the degree of phase variation expressed in terms of the amount and extent of phase wrapping are defined and found to be figures of merit which estimate when it is critical to deploy the new image reconstruction approach in these cases the new algorithm recovers high quality images without resorting to the use of a priori information on object contrast and or size as previously required

continuum percolation in two dimensions monte carlo tests of scaling and universality for non interacting discs detailed results are reported for the connectivity properties of a system of discs of unit radius free to be situated anywhere within a square of area 2l2 ordinary lattke percolation would correspond to the discs being situated on the vertices of a j2l x j2l lattice computer simulations are carried out for a sequence of increasing system sizes ranging from l 20 to l 1000 for each value of l a large number of realisations are generated for 25 values of the disc concentration x we calculate a variety of estimates for the threshold parameter x as well as the critical exponents p y t and v our exponent estimates are in close agreement with accepted values for ordinary lattice percolation therefore this continuum system appears to be in the same universality class as lattice percolation

iterative construction of fixed points of asymptotically nonexpansive mappings abstract let t be a completely continuous and asymptotically nonexpansive self mapping of a nonempty closed bounded and convex subset of a hilbert space then under certain conditions the sequence defined by xn 1 ntn xn 1 n x n converges strongly to some fixed point of t a similar result is obtained for asymptotically pseudocontractive mappings whose iterates are lipschitz continuous with respect to some common lipschitz constant

approximating common fixed points of asymptotically nonexpansive maps in uniformly convex banach spaces we introduce three step iterative schemes with errors for two and three nonexpansive maps and establish weak and strong convergence theorems for these schemes mann type and ishikawa type convergence results are included in the analysis of these new iteration schemes the results presented in this paper substantially improve and extend the results due to s h khan h fukhar ud din weak and strong convergence of a scheme with errors for two nonexpansive mappings nonlinear anal 8 2005 1295 1301 n shahzad approximating fixed points of non self nonexpansive mappings in banach spaces nonlinear anal 61 2005 1031 1039 w takahashi t tamura convergence theorems for a pair of nonexpansive mappings j convex anal 5 1995 45 58 k k tan h k xu approximating fixed points of nonexpansive mappings by the ishikawa iteration process j math anal appl 178 1993 301 308 and h f senter w g dotson approximating fixed points of nonexpansive mappings proc amer math soc 44 1974 375 380

a mathematical framework to analyze the achievable resolution from microwave tomography a mathematical framework is proposed to investigate how different parameters affect the achievable resolution from microwave tomography mwt this framework attempts to incorporate multiple scattering events within the object of interest oi into its analysis by taking into account the effect of the induced total field within the oi to this end a linearized operator which maps the oi s permittivity profile to the measured data is first constructed the framework then revolves around the number of the right singular vectors of this operator and their spatial frequency contents that can be utilized in reconstruction furthermore this framework is used to introduce the best possible reconstruction that can be achieved in a given mwt system when imaging a typical oi this concept can then provide some insights and guidelines for mwt system design

piecewise smoothed value picking regularization applied to 2 d tm and te inverse scattering the stepwise relaxed value picking srvp regularization technique proposed earlier for the iterative reconstruction of piecewise quasi homogeneous objects is a non spatial technique whereby the reconstruction unknowns are clustered around a limited number of a priori unknown reference values artifacts have been observed in some 2 d and 3d complex permittivity reconstructions this paper therefore combines the non spatial srvp technique with a spatial smoothing technique whereby the reference values provided by the former in each iteration are employed by the latter to define separate smoothing regions this way edges are preserved since the spatial smoothing constraints in the cost function are active within but not across the region boundaries this combined technique denoted as stepwise relaxed piecewise smoothed value picking srpsvp regularization is formulated for the 2 5d microwave inverse scattering problem and is illustrated with reconstructions from the institut fresnel 2 d scattering database

the fractal dimension of percolation cluster hulls large simulations of 2d site percolation on a square lattice provide several estimates of the fractal dimension dh of the hull or outer boundary of percolation clusters close to criticality statistical estimates based on an ensemble of more than 106 clusters with varying sizes yield dh 1 74 or 0 02 geometrical measurements of the hull two point correlation for individual clusters with more than 105 sites give dh 1 76 or 0 01 the observed scaling behaviour is the same both slightly above and below pc

overview and classification of some regularization techniques for the gauss newton inversion method applied to inverse scattering problems different regularization techniques used in conjunction with the gauss newton inversion method for electromagnetic inverse scattering problems are studied and classified into two main categories the first category attempts to regularize the quadratic form of the nonlinear data misfit cost functional at different iterations of the gauss newton inversion method this can be accomplished by utilizing penalty methods or projection methods the second category tries to regularize the nonlinear data misfit cost functional before applying the gauss newton inversion method this type of regularization may be applied via additive multiplicative or additive multiplicative terms we show that these two regularization strategies can be viewed from a single consistent framework

demiclosed principle and δ convergence theorems for total asymptotically nonexpansive mappings in cat 0 spaces abstract the purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove the demiclosed principle for this kind of mappings in cat 0 spaces as a consequence we obtain a convergence theorem of the krasnoselskii mann type iteration for total asymptotically nonexpansive mappings in this setting our results extend and improve the corresponding recent results announced by many authors

some logical metatheorems with applications in functional analysis in previous papers we have developed proof theoretic techniques for extracting effective uniform bounds from large classes of ineffective existence proofs in functional analysis here uniform means independence from parameters in compact spaces a recent case study in fixed point theory systematically yielded uniformity even w r t parameters in metrically bounded but noncompact subsets which had been known before only in special cases in the present paper we prove general logical metatheorems which cover these applications to fixed point theory as special cases but are not restricted to this area at all our theorems guarantee under general logical conditions such strong uniform versions of non uniform existence statements moreover they provide algorithms for actually extracting effective uniform bounds and transforming the original proof into one for the stronger uniformity result our metatheorems deal with general classes of spaces like metric spaces hyperbolic spaces cat 0 spaces normed linear spaces uniformly convex spaces as well as inner product spaces

monte carlo renormalisation group approach to percolation on a continuum test of universality it is shown that a monte carlo renormalisation group technique can be employed for direct renormalisation of a system on a continuum i e without restriction to a periodic lattice for the problem of overlapping discs the authors find the critical area fraction sc 0 688 or 0 005 and the correlation length critical exponent nu 1 33 or 0 07 the latter result indicates the regular irregular lattice universality

a concept of convergence in geodesic spaces abstract a cat 0 space is a geodesic space for which each geodesic triangle is at least as thin as its comparison triangle in the euclidean plane a notion of convergence introduced independently several years ago by lim and kuczumow is shown in cat 0 spaces to be very similar to the usual weak convergence in banach spaces in particular many banach space results involving weak convergence have precise analogues in this setting at the same time many questions remain open

inverse scattering an iterative numerical method for electromagnetic imaging the authors propose a spatial iterative algorithm for electromagnetic imaging based on a newton kantorovich procedure for the reconstruction of the complex permittivity of inhomogeneous lossy dielectric objects with arbitrary shape starting from integral representation of the electric field and using the moment method this technique has been developed for 2 d for tm and te polarization cases objects as well as for 3 d objects its performance has been compared with spectral techniques of classical diffraction tomography the modified newton method and the pseudo inverse method

microwave image reconstruction from 3 d fields coupled to 2 d parameter estimation an efficient gauss newton iterative imaging technique utilizing a three dimensional 3 d field solution coupled to a two dimensional 2 d parameter estimation scheme 3 d 2 d is presented for microwave tomographic imaging in medical applications while electromagnetic wave propagation is described fully by a 3 d vector field a 3 d scalar model has been applied to improve the efficiency of the iterative reconstruction process with apparently limited reduction in accuracy in addition the image recovery has been restricted to 2 d but is generalizable to three dimensions image artifacts related primarily to 3 d effects are reduced when compared with results from an entirely two dimensional inversion 2 d 2 d important advances in terms of improving algorithmic efficiency include use of a block solver for computing the field solutions and application of the dual mesh scheme and adjoint approach for jacobian construction methods which enhance the image quality such as the log magnitude unwrapped phase minimization were also applied results obtained from synthetic measurement data show that the new 3 d 2 d algorithm consistently outperforms its 2 d 2 d counterpart in terms of reducing the effective imaging slice thickness in both permittivity and conductivity images over a range of inclusion sizes and background medium contrasts

nonexpansive iterations in hyperbolic spaces one of the most active research areas in nonlinear functional analysis is the asymptotics of nonexpansive mappings most of the results however have been obtained in normed linear spaces it is natural therefore to try to develop a theory of nonexpansive iterations in more general infinite dimensional manifolds this is the purpose of the present paper more specifically we propose the class of hyperbolic spaces as an appropriate background for the study of operator theory in general and of iterative processes for nonexpansive mappings in particular this class of metric spaces which is defined in section 2 includes all normed linear spaces and hadamard manifolds as well as the hilbert ball and the cartesian product of hilbert balls in section 3 we introduce co accretive operators and their resolvents and present some of their properties in the fourth section we discuss the concept of uniform convexity for hyperbolic spaces section 5 is devoted to two new geometric properties of infinite dimensional banach spaces theorem 5 6 provides a characterization of banach spaces having these properties in terms of nonlinear accretive operators in sections 6 7 and 8 we study explicit implict and continuous iterations repectively using the same approach in all three sections we illustrate this common approach with the following special case let c be a closed convex subset of a hyperbolic space x p let t c f c be a nonexpansive mapping and let x be a point in c in order to study the iteration t x n 0 1 2 we set z 1 l n x 0 l n t x k clco zj j i l and d inf p y ty y e c the first step is to show that p x k lim p x t x n d this leads to the convergence m of lz when x is uniformly convex and to the weak convergence of z when x is a banach space which is reflexive and strictly convex when t is an averaged mapping we are also able to establish the following triple equality for all k 2 1

ultrasound tomography for simultaneous reconstruction of acoustic density attenuation and compressibility profiles a fast and efficient forward scattering solver is developed for use in ultrasound tomography the solver is formulated so as to enable the calculation of scattering from large and relatively high contrast objects with inhomogeneous physical properties that vary simultaneously in acoustic attenuation compressibility and density it is based on the method of moments in conjunction with a novel implementation of the conjugate gradient algorithm which requires the use of the adjoints of the scattering operators the solver takes advantage of the symmetric block toeplitz matrix with symmetric toeplitz blocks property of the green s function matrix to increase efficiency and only stores the first row of this matrix to reduce memory requirements this row is then used for the matrix vector multiplication using the fast fourier transform technique thus resulting in the computational complexity of o n log n the marching on source technique is also used to provide a good initial guess which allows the conjugate gradient technique to converge faster than initializing with an arbitrary guess this feature is important in tomographic inversion algorithms which require that the object to be imaged be interrogated via several incident fields forward scattering and inversion examples based on the conjugate gradient least squares regularized born iterative method are shown in two dimensions for objects varying in all three physical properties

deterministic edge preserving regularization in computed imaging many image processing problems are ill posed and must be regularized usually a roughness penalty is imposed on the solution the difficulty is to avoid the smoothing of edges which are very important attributes of the image in this paper we first give conditions for the design of such an edge preserving regularization under these conditions we show that it is possible to introduce an auxiliary variable whose role is twofold first it marks the discontinuities and ensures their preservation from smoothing second it makes the criterion half quadratic the optimization is then easier we propose a deterministic strategy based on alternate minimizations on the image and the auxiliary variable this leads to the definition of an original reconstruction algorithm called artur some theoretical properties of artur are discussed experimental results illustrate the behavior of the algorithm these results are shown in the field of 2d single photon emission tomography but this method can be applied in a large number of applications in image processing

percolation in a symmetric random potential abstract we study percolation in a two dimensional random gaussian potential and calculate p c the critical exponents the fractal dimension of the percolating equipotential lines and the amplitude ratio c c of the perlocation susceptibility these quantities including the amplitude ratio match the known results of the two dimensional lattice percolation models

a quadratic rate of asymptotic regularity for cat 0 spaces abstract in this paper we obtain a quadratic bound on the rate of asymptotic regularity for the krasnoselski mann iterations of nonexpansive mappings in cat 0 spaces whereas previous results guarantee only exponential bounds the method we use is to extend to the more general setting of uniformly convex hyperbolic spaces a quantitative version of a strengthening of groetsch s theorem obtained by kohlenbach using methods from mathematical logic so called proof mining

strong convergence of a general iteration scheme in cat 0 spaces abstract we introduce and study strong convergence of a general iteration scheme for a finite family of asymptotically quasi nonexpansive maps in convex metric spaces and c a t 0 spaces the new iteration scheme includes modified mann and ishikawa iterations the three step iteration scheme of xu and noor and the scheme of khan domlo and fukhar ud din as special cases in banach spaces our results are refinements and generalizations of several recent results from the current literature

nonlinear microwave imaging for breast cancer screening using gauss newton s method and the cgls inversion algorithm breast cancer screening using microwave imaging is emerging as a new promising technique as a supplement to x ray mammography to create tomographic images from microwave measurements it is necessary to solve a nonlinear inversion problem for which an algorithm based on the iterative gauss newton method has been developed at dartmouth college this algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the tikhonov algorithm in this paper a new algorithm for determining the iteration update values in the gauss newton algorithm is presented which is based on the conjugate gradient least squares cgls algorithm the iterative cgls algorithm is capable of solving the update problem by operating on just the jacobian and the regularizing effects of the algorithm can easily be controlled by adjusting the number of iterations the new algorithm is compared to the gauss newton algorithm with tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations

a prescaled multiplicative regularized gauss newton inversion a prescaled multiplicative regularized gauss newton inversion gni algorithm is proposed which utilizes a priori information about the expected ratio between the average magnitude of the real and imaginary parts of the true contrast as well as the expected ratio between the average magnitude of the gradient of the real and imaginary parts of the true contrast using both synthetically and experimentally collected data sets we show that this prescaled inversion algorithm is successful in reconstructing both real and imaginary parts of the contrast when there is a large imbalance between the average magnitude of these two parts where the standard multiplicative regularized gauss newton inversion algorithm fails we further show that the proposed prescaled inversion algorithm is robust and does not require the a priori information to be exact

a novel method of calculating amplitude ratios by series expansions the author introduces a new method of calculating critical amplitude ratios using series which is both simple and powerful this method which gives estimates for the amplitude ratios that are neither biased by the values of the critical points nor by the critical exponents is applied to several models it is shown that this method produces results where no reliable estimates from series expansion exist in particular one finds 0 025 or 0 001 for at b2 for the 3d ising model and 220 or 10 for c c for the two dimensional percolation model in agreement with and with more accuracy than values obtained by other methods

concentration gradient approach to continuum percolation in two dimensions the author has investigated percolation properties of a system of overlapping discs randomly distributed with a gradient of concentration fractal properties and critical exponents of this system appear to be identical to their counterparts on a lattice this is in agreement with the universality of critical exponents of percolation the concentration gradient approach permits a precise calculation of the percolation threshold corresponding to a critical area fraction of 0 6766 or 0 0005 he has investigated the part of the external perimeter of the percolation cluster which is accessible to discs of various sizes the fractal dimension of this accessible perimeter is found to decrease abruptly as a function of the radius of invading discs from 1 75 or 0 02 to 1 35 or 0 02

on kirk s strong convergence theorem for multivalued nonexpansive mappings on cat 0 spaces abstract we prove a strong convergence theorem for multivalued nonexpansive mappings which includes kirk s convergence theorem on cat 0 spaces the theorem properly contains a result of jung for hilbert spaces we then apply the result to approximate a common fixed point of a countable family of single valued nonexpansive mappings and a compact valued nonexpansive mapping

enhancement of the krylov subspace regularization for microwave biomedical imaging although krylov subspace methods provide fast regularization techniques for the microwave imaging problem they cannot preserve the edges of the object being imaged and may result in an oscillatory reconstruction to suppress these spurious oscillations and to provide an edge preserving regularization we use a multiplicative regularizer which improves the reconstruction results significantly while adding little computational complexity to the inversion algorithm we show the inversion results for a real human forearm assuming the 2 d transverse magnetic illumination and a cylindrical object assuming the 2 d transverse electric illumination

2 5d forward and inverse modeling for interpreting low frequency electromagnetic measurements we present 2 5d fast and rigorous forward and inversion algorithms for deep electromagnetic em applications that include crosswell and controlled source em measurements the forward algorithm is based on a finite difference approach in which a multifrontal lu decomposition algorithm simulates multisource experiments at nearly the cost of simulating one single source experiment for each frequency of operation when the size of the linear system of equations is large the use of this noniterative solver is impractical hence we use the optimal grid technique to limit the number of unknowns in the forward problem the inversion algorithm employs a regularized gauss newton minimization approach with a multiplicative cost function by using this multiplicative cost function we do not need a priori data to determine the so called regularization parameter in the optimization process making the algorithm fully automated the algorithm is equipped with two regularization cost functions that allow us to reconstruct either a smooth or a sharp conductivity image to increase the robustness of the algorithm we also constrain the minimization and use a line search approach to guarantee the reduction of the cost function after each iteration to demonstrate the pros and cons of the algorithm we present synthetic and field data inversion results for crosswell and controlled source em measurements

δ convergence theorems for multi valued nonexpansive mappings in hyperbolic spaces the purpose of this paper is to introduce the mixed agarwal o regan sahu type iterative scheme agarwal et al 2007 for finding a common fixed point of the multi valued nonexpansive mappings in the setting of hyperbolic spaces under suitable conditions some convergence theorems of the iterative sequence generated by the proposed scheme to approximate a common fixed point of multi valued nonexpansive mappings are proved the results presented in the paper extend and improve some recent results announced in the current literature