the equivalence between mann ishikawa iterations and multistep iteration abstract we show that the convergence of mann ishikawa iterations are equivalent to the convergence of a multistep iteration for various classes of operators

convergence and stability of iterative algorithms of generalized set valued variational like inclusions in banach spaces abstract in this paper we give the notion of p proximal mapping an extension of p proximal mapping given by ding and xia j comput appl math 147 2002 369 for a nonconvex lower semicontinuous subdifferentiable proper functional on banach space and prove its existence and lipschitz continuity further we consider a class of generalized set valued variational like inclusions in banach space and show its equivalence with a class of implicit wiener hopf equations using the concept of p proximal mapping using this equivalence we propose a new class of iterative algorithms for the class of generalized set valued variational like inclusions furthermore we prove the existence of solution of generalized set valued variational like inclusions and discuss the convergence criteria and the stability of the iterative algorithm

strong convergence for the modified mann s iteration of λ strict pseudocontraction abstract in this paper for an strict pseudocontraction t we prove strong convergence of the modified mann s iteration defined by x n 1 n u n x n 1 n n n tx n 1 n x n where n n and n in 0 1 satisfy i 0 n k 2 with lim inf n n k 2 n 0 ii lim n n 0 and n 1 n iii lim sup n n 1 our results unify and improve some existing results

gaussian beams and legendre polynomials as invariants of the time reversal operator for a large rigid cylinder the dort method french acronym for decomposition of the time reversal operator is an active remote sensing technique using an array of antennas for the detection and localization of scatterers this method is based on the singular value decomposition of the interelement response matrix in this paper an analytical expression of the singular vectors due to the reflection from a large rigid cylinder is provided depending on the array aperture two asymptotic regimes are described it is shown that the singular vectors correspond to hermite gaussian modes for large apertures and legendre polynomials for small ones using perturbation theory the corresponding singular values are deduced theoretical predictions are in good agreement with experimental results

new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

the van cittert zernike theorem in pulse echo measurements a classical theorem of statistical optics the van cittert zernike theorem is generalized to pulse echo ultrasound this theorem fully describes the second order statistics of the spatial fluctuations the spatial covariance of the field produced by an incoherent source as a random scattering medium is insonified it behaves as an incoherent source the van cittert zernike theorem can thus predict the spatial covariance of the pressure field backscattered by a random medium it is shown that this spatial covariance and the incident energy diagram are fourier pairs in the case of a focused illumination the spatial covariance of the backscattered pressure field is proportional to the autocorrelation of the transmitting aperture function this is independent of frequency and of f number experimental results obtained with a linear array are in good agreement with theoretical expectations the implications of this theorem in speckle reduction and in focusing in nonhomogenous media are discussed

three step iterations for nonlinear accretive operator equations abstract in this paper we suggest and analyze a three step iterative scheme for solving nonlinear strongly accretive operator equation tx f without continuous condition in a uniformly smooth banach space our results include the ishikawa mann and noor iterations as special cases the results presented in this paper improve and extend almost all the current results in the more general setting

multiterminal source coding with high resolution we consider separate encoding and joint decoding of correlated continuous information sources subject to a difference distortion measure we first derive a multiterminal extension of the shannon lower bound for the rate region then we show that this shannon outer bound is asymptotically tight for small distortions these results imply that the loss in the sum of the coding rates due to the separation of the encoders vanishes in the limit of high resolution furthermore lattice quantizers followed by slepian wolf lossless encoding are asymptotically optimal we also investigate the high resolution rate region in the remote coding case where the encoders observe only noisy versions of the sources for the quadratic gaussian case we establish a separation result to the effect that multiterminal coding aimed at reconstructing the noisy sources subject to the rate constraints followed by estimation of the remote sources from these reconstructions is optimal under certain regularity conditions on the structure of the coding scheme

convergence criteria of modified noor iterations with errors for asymptotically nonexpansive mappings in this paper weak and strong convergence theorems of the modified noor iterations with errors are established for asymptotically nonexpansive mappings in banach spaces the results obtained in this paper extend and improve the several recent results in this area

approximating fixed points of φ hemicontractive mappings by the ishikawa iteration process with errors in uniformly smooth banach spaces abstract let e be a uniformly smooth banach space and t e e be a continuous and strongly o hemicontractive mapping this paper proves that under suitable conditions the ishikawa iterative sequence with errors strongly converges to the unique fixed point of t the related result deals with the strong convergence of the ishikawa iterative sequence with errors to the unique solution of the equation t x f when t e e is o strongly accretive these results generalize the results of ding 1 into more general o hemicontractive operators and extend a recent paper written by osilike 2 in two ways 1 i the lipschitzian continuity is replaced by the continuity on mapping t 2 ii if the errors u n v n 0 for all n n our theorems of this paper extend results of osilike 2 to the more general class of real uniformly smooth banach spaces

some problems and results in the study of nonlinear analysis this paper is presented as a survey of the latest and new results on some topics in the study of nonlinear analysis which were obtained by the author and some chinese mathematicians

iterative processes with mixed errors for nonlinear equations with perturbed m accretive operators in banach spaces let x be a real uniformly smooth banach space of which the dual x has a frechet differentiable norm let a d a x 2 x be an m accretive operator with closed domain d a and bounded range r a and s x x a continuous and a strongly accretive operator with bounded range r i s it is proved that the ishikawa and mann iterative processes with mixed errors converge strongly to the unique solution of the equation z sx lax for given z x and l 0

convergence and certain control conditions for hybrid iterative algorithms very recently yao et al 2010 4 proposed a hybrid iterative algorithm under the parameter sequences satisfying some quite restrictive conditions they derived a strong convergence theorem in a hilbert space in this paper under the weaker conditions we prove the strong convergence of the sequence generated by their iterative algorithm to a common fixed point of an infinite family of nonexpansive mappings which solves a variational inequality an appropriate example such that all conditions of this result that are satisfied and that other conditions are not satisfied is provided moreover the method of our paper is different from the method in yao et al 2010 4

iterative process with errors to locally strictly pseudocontractive maps in banach spaces abstract let k be a nonempty subset of a uniformly smooth banach space x and a k x be a locally strickly pseudocontractive map with bounded range the mann and ishikawa iterative sequences with errors which strongly converge to the unique fixed point of a are given under weaker conditions these results answer positively the open problems mentioned by deng and ding 1 p 122 and chidume 2 p 550 the related results deal with the problems that the mann and ishikawa iterative sequences with errors strongly converge to the unique solution of the equation tx f when t x x is locally strongly accretive such that the range of i t is bounded

the direct estimation of sound speed using pulse echo ultrasound a method for the direct estimation of the longitudinal speed of sound in a medium is presented this estimator derives the speed of sound through analysis of pulse echo data received across a single transducer array following a single transmission and is analogous to methods used in exploration seismology a potential application of this estimator is the dynamic correction of beamforming errors in medical imaging that result from discrepancy between the assumed and actual biological tissue velocities the theoretical basis of this estimator is described and its function demonstrated in phantom experiments using a wire target sound speed estimates in water methanol ethanol and n butanol are compared to published values sound speed estimates in two speckle generating phantoms are also compared to expected values the mean relative errors of these estimates are all less than 0 4 and under the most ideal experimental conditions are less than 0 1 the relative errors of estimates based on independent regions of speckle generating phantoms have a standard deviation on the order of 0 5 simulation results showing the relative significance of potential sources of estimate error are presented the impact of sound speed errors on imaging and the potential of this estimator for phase aberration correction and tissue characterization are also discussed

mann and ishikawa iterations with errors for asymptotically nonexpansive mappings abstract in a recent paper rhoades 1 presented some generalizations of schu 2 on the convergence of the mann and ishikawa iterations of asymptotically nonexpansive mappings in uniformly convex banach spaces we continue the study on the ishikawa and mann iteration process with errors and prove that if x is a uniformly convex banach space o e x closed bounded and convex and t e e is an asymptotically nonexpansive mapping then the ishikawa and mann iteration process with errors converges strongly to some fixed point of t

eigenfunction analysis of stochastic backscatter for characterization of acoustic aberration in medical ultrasound imaging presented here is a characterization of aberration in medical ultrasound imaging the characterization is optimal in the sense of maximizing the expected energy in a modified beamformer output of the received acoustic backscatter aberration correction based on this characterization takes the form of an aberration correction filter the situation considered is frequently found in applications when imaging organs through a body wall aberration is introduced in a layer close to the transducer and acoustic backscatter from a scattering region behind the body wall is measured at the transducer surface the scattering region consists of scatterers randomly distributed with very short correlation length compared to the acoustic wavelength of the transmit pulse the scatterer distribution is therefore assumed to be delta correlated this paper shows how maximizing the expected energy in a modified beamformer output signal naturally leads to eigenfunctions of a fredholm integral operator where the associated kernel function is a spatial correlation function of the received stochastic signal aberration characterization and aberration correction are presented for simulated data constructed to mimic aberration introduced by the abdominal wall the results compare well with what is obtainable using data from a simulated point source

convergence of iterative processes with errors for set valued pseudocontractive and accretive type mappings in banach spaces abstract in this paper some new results on convergence of iterative processes with errors for set valued pseudocontractive and accretive mappings in banach spaces are obtained our results extend and improve a number of the recent results

iterative solution of nonlinear equations involving set valued uniformly accretive operators abstract let e be a real normed linear space and let a e 2 e be a uniformly continuous and uniformly quasi accretive multivalued map with nonempty closed values such that the range of i a is bounded and the inclusion f ax has a solution x e it is proved that ishikawa and mann type iteration processes converge strongly to x further if t e 2 e is a uniformly continuous and uniformly hemicontractive set valued map with bounded range and a fixed point x e it is proved that both the mann and ishikawa type iteration processes converge strongly to x the strong convergence of these iteration processes with errors is also proved

on the equivalence of the convergence criteria between modified mann ishikawa and multi step iterations with errors for successively strongly pseudo contractive operators abstract in this paper the equivalence of the convergence between the modified mann ishikawa and multi step noor iterations with errors is proven for the successively strongly pseudo contractive operators without lipschitzian assumption our results generalize the recent results of the paper b e rhoades s m soltuz the equivalence between mann ishikawa iterations and multi step iteration nonlinear anal 58 2004 219 228 b e rhoades s m soltuz the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudo contractive maps j math anal appl 289 2004 266 278 by extending to the more generalized multi step iterations with errors and hence improve the corresponding results of all the references in bibliography by providing the equivalences of convergence between all of these up to date iteration schemes

local speed of sound estimation in tissue using pulse echo ultrasound model based approach a model and method to accurately estimate the local speed of sound in tissue from pulse echo ultrasound data is presented the model relates the local speeds of sound along a wave propagation path to the average speed of sound over the path and allows one to avoid bias in the sound speed estimates that can result from overlying layers of subcutaneous fat and muscle tissue herein the average speed of sound using the approach by anderson and trahey is measured and then the authors solve the proposed model for the local sound speed via gradient descent the sound speed estimator was tested in a series of simulation and ex vivo phantom experiments using two layer media as a simple model of abdominal tissue the bias of the local sound speed estimates from the bottom layers is less than 6 2 m s while the bias of the matched anderson s estimates is as high as 66 m s the local speed of sound estimates have higher standard deviation than the anderson s estimates when the mean local estimate is computed over a 5 by 5 mm region of interest its standard deviation is reduced to less than 7 m s

on a mann type implicit iteration process for continuous pseudo contractive mappings abstract let k be a nonempty closed convex subset of a banach space e t k k a continuous pseudo contractive mapping suppose that n is a real sequence in 0 1 satisfying appropriate conditions then for arbitrary x 0 k the mann type implicit iteration process x n given by x n n x n 1 1 n t x n n 0 strongly and weakly converges to a fixed point of t respectively

weak and strong convergence criteria of noor iterations for asymptotically nonexpansive mappings in this paper weak and strong convergence theorems are established for a three step iterative scheme for asymptotically nonexpansive mappings in banach spaces mann type and ishikawa type iterations are included by the new iterative scheme the results obtained in this paper extend and improve the recent ones announced by xu and noor glowinski and le tallec noor ishikawa and many others

strong convergence of an explicit iterative algorithm for continuous pseudo contractions in banach spaces let c be a nonempty closed convex subset of a real banach space x whose norm is uniformly g teaux differentiable and t c c be a continuous pseudo contraction with a nonempty fixed point set f t for arbitrary given element u c and for t 0 1 let yt be the unique continuous path such that yt 1 t tyt tu assume that yt p f t as t 0 let n n and n be three real sequences in 0 1 satisfying the following conditions i n n n 1 ii limn n limn n 0 iii limn n1 n 0 or iii n 0 n1 n let n be a summable sequence of positive numbers for arbitrary initial datum x0 x00 c and a fixed n 0 construct elements xnm as follows xnm 1 nu nxn ntxnm m 0 1 2 suppose that there exists a least positive integer n n satisfying the following condition txnn n 1 txnn n n 1 1 n n define iteratively a sequence xn in an explicit manner as follows xn 1 xn 10 xnn n 1 nu nxn ntxnn n n 0 then xn converges strongly to a fixed point of t for all the continuous pseudo contractive mappings for which is possible to construct the sequence xn this result improves and extends a recent result of yao et al yonghong yao yeong cheng liou rudong chen strong convergence of an iterative algorithm for pseudocontractive mapping in banach spaces nonlinear anal 67 2007 3311 3317

equivalence theorems of the convergence between ishikawa and mann iterations with errors for generalized strongly successively φ pseudocontractive mappings without lipschitzian assumptions abstract in this paper the equivalence of the strong convergence between the modified mann and ishikawa iterations with errors in two different schemes by xu y g xu ishikawa and mann iteration process with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and liu l s liu ishikawa and mann iterative process with errors for nonlinear strongly accretive mappings in banach spaces j math anal appl 194 1995 114 125 respectively is proven for the generalized strongly successively pseudocontractive mappings without lipschitzian assumption our results generalize the recent results of the papers zhenyu huang f bu the equivalence between the convergence of ishikawa and mann iterations with errors for strongly successively pseudocontractive mappings without lipschitzian assumption j math anal appl 325 1 2007 586 594 b e rhoades s m soltuz the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps j math anal appl 289 2004 266 278 b e rhoades s m soltuz the equivalence between mann ishikawa iterations and multi step iteration nonlinear anal 58 2004 219 228 by extending to the most general class of the generalized strongly successively pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points u 1 x 1 in uniformly smooth banach spaces

convergence theorems for ψ expansive and accretive mappings abstract let e be a real banach space and let a d a e e be a lipschitz expansive and accretive mapping such that c o d a 0 r i a suppose that there exists x 0 d a where one of the following holds i there exists r 0 such that r 2 a x 0 or ii there exists a bounded neighborhood u of x 0 such that t x x 0 a x for x u d a and t 0 an iterative sequence x n is constructed to converge strongly to a zero of a related results deal with the strong convergence of this iteration process to fixed points of expansive and pseudocontractive mappings in real banach spaces the convergence results established in this paper are new for this more general class of expansive and accretive or pseudocontractive mappings

convergence of ishikawa iterates of quasi nonexpansive mappings abstract this paper deals with a necessary and sufficient condition for the convergence of ishikawa iterates of quasi nonexpansive mapping in a banach space the convergence of ishikawa iterates for nonexpansive mappings in a uniformly convex banach space is also discussed

on characterizations of common fixed points in general quasi metric spaces abstract necessary and sufficient conditions for the existence of common fixed points of certain commuting mappings in general quasi metric spaces are proved the results of this paper generalize improve and unify some recent results

simpler is also better in approximating fixed points in this paper we demonstrate that a number of fixed point iteration problems can be solved using a modified krasnoselskij iteration process which is much simpler to use than the other iteration schemes that have been defined

convergence of composite iterative methods for finding zeros of accretive operators abstract strong convergence theorems on composite iterative schemes by the viscosity approximation methods for finding a zero of an accretive operator are established in banach spaces the main results generalize the recent corresponding results of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 ceng et al l c ceng a r khan q h ansari j c yao strong convergence of composite iterative schemes for zeros of m accretive operators in banach spaces nonlinear anal 70 2009 1830 1840 kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 to viscosity methods in a strictly convex and reflexive banach space having a uniformly g teaux differentiable norm our results also improve the corresponding results of t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory appl 2006 2006 1 10 s kamimura w takahashi approximation solutions of maximal monotone operators in hilbert spaces j approx theory 106 2000 226 240 p e mainge viscosity methods for zeroes of accretive operators j approx theory 140 2 2006 127 140 k nakajo strong convergence to zeros of accretive operators in banach spaces j nonlinear convex anal 7 2006 71 81

iterative algorithms for a new class of extended general nonconvex set valued variational inequalities abstract some new classes of extended general nonconvex set valued variational inequalities and the extended general wiener hopf inclusions are introduced by the projection technique equivalence between the extended general nonconvex set valued variational inequalities and the fixed point problems as well as the extended general nonconvex wiener hopf inclusions is proved then by using this equivalent formulation we discuss the existence of solutions of the extended general nonconvex set valued variational inequalities and construct some new perturbed finite step projection iterative algorithms with mixed errors for approximating the solutions of the extended general nonconvex set valued variational inequalities we also verify that the approximate solutions obtained by our algorithms converge to the solutions of the extended general nonconvex set valued variational inequalities the results presented in this paper extend and improve some known results from the literature

on generalized set valued variational inclusions abstract we point out a basic flaw made by m a noor 1998 j math anal appl 228 206 220 construct a new iterative algorithm for a class of variational inclusions involving non monotone set valued mappings with noncompact values and study the convergence of the perturbed ishikawa iterative process for solving a class of the generalized single valued variational inclusions

the prolate spheroidal wave functions as invariants of the time reversal operator for an extended scatterer in the fraunhofer approximation the decomposition of the time reversal operator known by the french acronym dort is widely used to detect locate and focus on scatterers in various domains such as underwater acoustics medical ultrasound and nondestructive evaluation in the case of point scatterers the theory is well understood the number of nonzero eigenvalues is equal to the number of scatterers and the eigenvectors correspond to the scatterers green s function in the case of extended objects however the formalism is not as simple it is shown here that in the fraunhofer approximation analytical solutions can be found and that the solutions are functions called prolate spheroidal wave functions these functions have been studied in information theory as a basis of band limited and time limited signals they also arise in optics the theoretical solutions are compared to simulation results most importantly the intuition that for an extended objects the number of nonzero eigenvalues is proportional to the number of resol

the equivalence between the convergences of ishikawa and mann iterations for an asymptotically pseudocontractive map the convergence of mann iteration is equivalent to the convergence of ishikawa iterations when t is an asymptotically nonexpansive and asymptotically pseudocontractive map

multiterminal source encoding with one distortion criterion the authors unify earlier investigations concerning the encoding of two correlated sources x sub k y sub k by means of separate encoders decoding is done by a single decoder which receives the outputs from both encoders the reconstruction of x sub k is required to be perfect in the usual shannon sense the authors determine the admissible rate region r d where d is the distortion of the reconstruction of y sub k the binary hamming case is investigated explicitly

on the stability of the effective apodization of the nonlinearly generated second harmonic with respect to range the concept of an effective apodization was introduced to describe the field pattern for the nonlinearly generated second harmonic 2f within the focal zone using a linear propagation model our objective in this study was to investigate the validity of the concept of an effective apodization at 2f as an approach to approximating the field of the second harmonic over a wide range of depths two experimental setups were employed a vascular imaging array with a water path and an adult cardiac imaging array with an attenuating liver path in both cases the spatial dependencies of the ultrasonic fields were mapped by scanning a point like hydrophone within a series of planes orthogonal to the propagation direction the sampling distances were located before within and beyond the focal zone the signals were fourier transformed and the complex values at 2f were linearly backpropagated to the transmit plane in order to obtain an effective apodization the measured results demonstrated a relatively constant

information bottleneck for gaussian variables the problem of extracting the relevant aspects of data was previously addressed through the information bottleneck ib method through soft clustering one variable while preserving information about another relevance variable the current work extends these ideas to obtain continuous representations that preserve relevant information rather than discrete clusters for the special case of multivariate gaussian variables while the general continuous ib problem is difficult to solve we provide an analytic solution for the optimal representation and tradeoff between compression and relevance for the this important case the obtained optimal representation is a noisy linear projection to eigenvectors of the normalized regression matrix x y x 1 which is also the basis obtained in canonical correlation analysis however in gaussian ib the compression tradeoff parameter uniquely determines the dimension as well as the scale of each eigenvector through a cascade of structural phase transitions this introduces a novel interpretation where solutions of different ranks lie on a continuum parametrized by the compression level our analysis also provides a complete analytic expression of the preserved information as a function of the compression the information curve in terms of the eigenvalue spectrum of the data as in the discrete case the information curve is concave and smooth though it is made of different analytic segments for each optimal dimension finally we show how the algorithmic theory developed in the ib framework provides an iterative algorithm for obtaining the optimal gaussian projections

convergence theorems for φ strongly accretive and φ hemicontractive operators suppose that x is an arbitrary real banach space and t x x is a continuous strongly accretive operator it is shown that the nonlinear equation tx f has a unique solution and under certain conditions both the mann and ishikawa iteration methods with errors introduced by y xu 1998 j math anal appl 224 91 101 converge strongly to the solution a related result deals with the approximation of fixed points of hemicontractive operators

angular coherence in ultrasound imaging theory and applications the popularity of plane wave transmits at multiple transmit angles for synthetic transmit aperture or coherent compounding has spawned a number of adaptations and new developments of ultrasonic imaging however the coherence properties of backscattered signals with plane wave transmits at different angles are unknown and may impact a subset of these techniques to provide a framework for the analysis of the coherence properties of such signals this article introduces the angular coherence theory in medical ultrasound imaging the theory indicates that the correlation function of such signals forms a fourier transform pair with autocorrelation function of the receive aperture function this conclusion can be considered as an extended form of the van cittert zernike theorem the theory is validated with simulation and experimental results obtained on speckle targets on the basis of the angular coherence of the backscattered wave a new short lag angular coherence beamformer is proposed and compared with an existing spatial coherence based beamformer an application of the theory in phase shift estimation and speed of sound estimation is also presented

variance analysis of arrival time and amplitude estimates from random speckle signal an aberration estimation algorithm previously developed in the frequency domain is implemented in the time domain the algorithm is used to estimate arrival time and amplitude fluctuations with signals from random scatterers simulations have been performed to investigate the variance of the estimates stability differences between the two implementations are also explored eight body wall models emulating the human abdominal wall were used for this purpose the variance was investigated as a function of the number of independent scatterer realizations used to obtain an estimate such signals may be acquired by imaging moving scatterers e g blood or contrast agent alternatively they can be obtained by using different nonoverlapping beams from a sector linear scan the results show only minor differences between the two implementations with respect to stability this means that the algorithm can be readily implemented in the time domain for real time applications the standard deviation of arrival

convergence theorem for fixed points of nearly uniformly l lipschitzian asymptotically generalized φ hemicontractive mappings abstract in this paper we introduce the new class of asymptotically generalized hemicontractive mappings and establish a strong convergence theorem of the iterative sequence generated by these mappings in a general banach space the main result of this paper is the improvement of the well known corresponding result

the equivalence of the convergence of four kinds of iterations for a finite family of uniformly asymptotically o pseudocontractive mappings in this paper we prove the equivalences of the strong convergence each other the modified mann iterative process with errors the modified ishikawa iterative process with errors the implicit iterative process with errors and the composite implicit iterative process with errors for a finite family of uniformly asymptotically o pseudocontractive mappings in arbitrary real banach space the results presented in this paper generalize and improve the corresponding results of roades soltuz and huang

spatial coherence analysis applied to aberration correction using a two dimensional array system complex degree of coherence functions are computed using synthetic and measured ultrasound data to demonstrate noteworthy aspects of coherence analysis in the context of aberration correction coherence functions calculated from synthetic data illustrate the importance of proper normalization of the constituent cross correlation integrals when weak elements and receiver directivity are significant factors the synthetic data also show that a spike can occur at the zero lag position of the coherence function when the signal to noise ratio is reduced by element directivity near the edges of a large aperture the latter observation is confirmed by experimental data acquired through tissue mimicking distributed aberration phantoms using a low f number two dimensional array system the coherence of data acquired at neighboring elements is not changed by time shift compensation of transmit and receive focusing but time shift compensation does improve the coherence of echoes measured over larger separations the resulting increase in coherence widths evaluated at levels between 0 2 and 0 5 is correlated with narrower 10 db and 20 db effective widths in focuses visualized using single transmit images iterative focus compensation methods may benefit from aberration estimation algorithms that take advantage of these longer range correlations in random scattering waveforms

measurement and correction of ultrasonic pulse distortion produced by the human breast ultrasonic wavefront distortion produced by transmission through breast tissue specimens was measured in a two dimensional aperture differences in arrival time and energy level between the measured waveforms and references that account for geometric delay and spreading were calculated also calculated was a waveform similarity factor that is decreased from 1 0 by changes in waveform shape for nine different breast specimens the arrival time fluctuations had an average s d rms value of 66 8 12 6 ns and an associated correlation length of 4 3 1 1 mm while the energy level fluctuations had an average rms value of 5 0 0 5 db and a correlation length of 3 4 0 8 mm the corresponding waveform similarity factor was 0 910 0 023 the effect of the wavefront distortion on focusing and the ability of time shift compensation to remove the distortion were evaluated by comparing parameters such as the 30 db effective radius the 10 db peripheral energy ratio and the level at which the effectiv

approximation of common fixed points of weakly compatible pairs using the jungck iteration abstract we show that the jungck iteration scheme can be used to approximate the common fixed points of some weakly compatible pairs of generalized quasicontractive operators defined on metric spaces the existence of coincidence points are also discussed for those pair of maps the results are generalizations of well known results of the convergence of picard iterations for single self maps of banach spaces in particular the results improve generalize and extend the recent results of berinde v berinde a common fixed point theorem for compatible quasi contractive self mappings in metric spaces applied mathematics and computation 213 2009 348 354 and answers the open question posed in the paper

the equivalence between the convergences of ishikawa and mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps the convergence of modified mann iteration is equivalent to the convergence of modified ishikawa iterations when t is an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive map

ishikawa and mann iteration methods with errors for nonlinear equations of the accretive type abstract let e be an arbitrary banach space and t e e a lipschitz strongly accretive operator it is proved that for a given f e the ishikawa and the mann iteration methods with errors introduced by 18 converge strongly to the solution of the equation tx f furthermore if e is a uniformly smooth banach space and t e e is demicontinuous and strongly accretive it is also proved that both the ishikawa and the mann iteration methods with errors converge strongly to the solution of the equation tx f related results deal with the iterative approximation of fixed points of strongly pseudocontractive operators and the solution of the equation x tx f f e when t e e is m accretive

convergence theorems for multivalued φ hemicontractive operators and φ strongly accretive operators abstract suppose e is a uniformly smooth banach space and t e 2e is a multivalued hemicontractive operator with bounded range suppose an bn cn and an bn cn are real sequences in 0 1 satisfying the following conditions i a n b n c n a n b n c n 1 for all n n ii lim n b n lim n b n lim n c n 0 iii n 1 b n iv c n o b n for arbitrary xi u1 v1 e define the sequence xn n 1 by xn 1 anxn bn n cnun n tyn n n yn a nxn b n n c nvn n txn n n where un n 1 vn n 1 are arbitrary bounded sequences in e then xn n 1 converges strongly to the unique fixed point of t related results deal with the iterative solutions of nonlinear multivalued accretive operator equation f tx

coherence factor and wiener postfilter in synthetic aperture ultrasound imaging the coherence factor cf and wiener postfilter methods have been proposed as effective approaches for reducing the output noise of the delay and sum das beamformer in ultrasound imaging the theoretical framework between them was also established however past researches about the cf and wiener postfilter methods mainly focused on the summation of an array signal this paper analyzes the cf and wiener postfilter in the synthetic aperture sa imaging mode where two dimensional echo data are recorded different cf definitions in the sa imaging are first given and the corresponding wiener postfilter methods are then proposed including a wiener postfilter especially for the sa imaging named as wienersa the performances of different cf and wiener postfilter methods were evaluated on both simulated and experimental sa data results showed that the proposed wienersa outperformed the other wiener postfilters in reducing the sidelobe noise level it obtained the highest contrast ratio among the wiener postfilter methods which was even higher than some of the cf methods meanwhile it could benefit a much higher contrast to noise ratio than those cf methods with further suppression of incoherent noises consequently the wienersa is believed to be a promising approach in enhancing the sa image quality

experimental subwavelength localization of scatterers by decomposition of the time reversal operator interpreted as a covariance matrix the d o r t method french acronym for decomposition of the time reversal operator is an active remote sensing technique using arrays of antennas for the detection and localization of scatterers prada et al j acoust soc am 99 2067 2076 1996 the analogy between the time reversal operator and the covariance matrix used for classical sources separation in passive remote sensing bienvenu et al ieee trans assp 31 1235 1247 1983 is established then an experiment of subwavelength detection and localization of point like scatterers with a linear array of transducers is presented using classical estimators in reception like maximum likelihood and multiple signal characterization music two point like scatterers separated by 3 and placed at 100 from the array of transducers are resolved in these experiments the role of multiple scattering and the existence of additional eigenvectors associated with dipolar and monopolar radiation of each scatterer is discussed

graph convergence for the h accretive operator in banach spaces with an application abstract in this paper a concept of graph convergence concerned with the h accretive operator is introduced in banach spaces and some equivalence theorems between of graph convergence and resolvent operator convergence for the h accretive operator sequence are proved as an application a perturbed algorithm for solving a class of variational inclusions involving the h accretive operator is constructed under some suitable conditions the existence of the solution for the variational inclusions and the convergence of iterative sequence generated by the perturbed algorithm are also given

the equivalence between the convergence of ishikawa and mann iterations with errors for strongly successively pseudocontractive mappings without lipschitzian assumption abstract in this paper we prove some new equivalences between convergence of the ishikawa and mann iteration sequences with errors in two schemes by xu y g xu ishikawa and mann iteration process with errors for nonlinear strongly accretive operator equations j math anal appl 224 1998 91 101 and liu l s liu ishikawa and mann iterative process with errors for nonlinear strongly accretive mappings in banach spaces j math anal appl 194 1995 114 125 respectively for strongly successively pseudocontractive mappings our main results improve and extend the corresponding results of the all references listed in this article

overdetermined least squares aberration estimates using common midpoint signals as medical ultrasound imaging moves to larger apertures and higher frequencies tissue sound speed variations continue to limit resolution in geophysical imaging a standard approach for estimating near surface aberrating delays is to analyze the time shifts between common midpoint signals this requires complete data echoes from every source receiver pair in the array unfocused common midpoint signals remain highly correlated in the presence of delay aberrations there is also tremendous redundancy in the data in medical ultrasound this technique has been impaired by the wide angle random scattering nature of tissue this has made it difficult to estimate azimuth dependent aberration profiles or to harness the full redundancy in the complete data prefiltering the data with two dimensional fan filters mitigates these problems permitting highly overdetermined least squares solutions for the aberration profiles at many steering angles in experiments with a tissue mimicking phantom target and silicone rubber aberrators at nonzero stand off distances from a one dimensional phased array this overdetermined fan filtering algorithm significantly outperformed other phase screen algorithms based on nearest neighbor cross correlation speckle brightness maximization and common midpoint signal analysis our results imply that there is still progress to be made in imaging with single valued focusing operators it also appears that the signal to noise penalty for using complete data sets is partially compensated by the overdetermined nature of the problem

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

the rate loss in the wyner ziv problem the rate distortion function for source coding with side information at the decoder the wyner ziv problem is given in terms of an auxiliary random variable which forms a markov chain with the source and the side information this markov chain structure typical to the solution of multiterminal source coding problems corresponds to a loss in coding rate with respect to the conditional rate distortion function i e to the case where the encoder is fully informed we show that for difference or balanced distortion measures this loss is bounded by a universal constant which is the minimax capacity of a suitable additive noise channel furthermore in the worst case this loss is equal to the maximin redundancy over the rate distortion function of the additive noise test channel for example the loss in the wyner ziv problem is less than 0 5 bit sample in the squared error distortion case and it is less than 0 22 bit for a binary source with hamming distance these results have implications also in universal quantization with side information and in more general multiterminal source coding problems

steepest descent approximations for accretive operator equations a necessary and sufficient condition is established for the strong convergence of the steepest descent approximation to a solution of equations involving quasi accretive operators defined on a uniformly smooth banach space miramare trieste march 1993

time reversal imaging with multiple signal classification considering multiple scattering between the targets the time reversal imaging with multiple signal classification method for the location of point targets developed within the framework of the born approximation in lehman and devaney transmission mode time reversal super resolution imaging j acoust soc am 113 2742 2753 2003 is generalized to incorporate multiple scattering between the targets it is shown how the same method can be used in the location of point targets even if there is multiple scattering between them on the other hand both the conventional images and the calculated values of the target scattering amplitudes are scattering model dependent

rate distortion for correlated sources with partially separated encoders we resolve some open problems concerning the encoding of a pair of correlated sources with respect to a fidelity criterion two encoders are used one encoder observes only the output of the first source while the other is supplied both with the second source output and with partial information about the first source at some predetermined rate a general coding theorem is proved which established that cal s ast a certain region defined in terms of single letter information theoretic quantities is an inner bound to the region of all attainable vectors of rates and distortions for certain cases of interest the converse is proved too thereby establishing the rate distortion region for these cases

general a monotone operators and perturbed iterations for nonlinear set valued relaxed cocoercive operator inclusion problems in this paper we introduce the notion of general a monotone operators in banach spaces study some properties of general a monotone operator and the new proximal mapping associated with the general a monotone operators by using alber s inequalities nalder s results and the new proximal mapping technique we also construct two new class of perturbed iterative algorithms with mixed errors for solving a new class of nonlinear set valued relaxed cocoercive operator inclusions and study applications of general a monotone operators to the approximation solvability of the nonlinear set valued relaxed cocoercive operator inclusion problems in banach spaces furthermore the general a monotone operators are illustrated by some examples the results presented in this paper improve and generalize the corresponding results on strongly monotone quasi variational inclusions and nonlinear implicit quasi variational inclusions

estimation of ultrasound wave aberration with signals from random scatterers a method for estimating waveform aberration from random scatterers in medical ultrasound imaging has been derived and its properties investigated using two dimensional simulations the method uses a weighted and modified cross spectrum in order to estimate arrival time and amplitude fluctuations from received signals the arrival time and amplitude fluctuations were used in a time delay and a time delay and amplitude aberration correction filter for evaluation of the retransmitted aberration corrected signal different types of aberration have been used in this study first aberration was concentrated on the plane of the transmitting receiving array second aberration was generated with a distributed aberrator both conditions emulated aberration from the human abdominal wall results show that for the concentrated aberrator arrival time and amplitude fluctuations were estimated in close agreement with reference values the reference values were obtained from simulations with a point source in the focal point of the array correction of the transmitted signal with a time delay and a time delay and amplitude filter produced approximately equal correction as with point source estimates for the distributed aberrator the estimator performance degraded significantly arrival time and amplitude fluctuations deviated from reference values leading to a limited correction of the retransmitted signal

iterative solution of nonlinear equations of the φ strongly accretive type abstract letq 1 and letebe a realq uniformly smooth banach space lett e ebe a lipschitz strongly accretive operator and suppose the equationtx f f e has a solution it is proved that under suitable conditions on the real sequences n n 0 and n n 0 the iteration process formula converges strongly to the unique solution of the equationtx f a related result deals with the approximation of fixed points of hemicontractive operators a class of operators which is much more general than the important class of strongly pseudocontractive operators

a semi continuous version of the berger yeung problem we present a continuous dual of multiterminal source encoding with one distortion criterion the berger yeung 1989 problem a continuous source x is encoded with high resolution d sub x spl rarr 0 with the aid of a helper i e a correlated discrete or continuous source y that is encoded separately subject to some arbitrary distortion criterion d sub y we find the asymptotic form of the set of achievable coding rates r d sub x d sub y of the x and y encoders as d sub x spl rarr 0 two extreme cases of our result provide high resolution interpretations to the classical work of wyner 1975 1978 ahlswede 1975 korner 1975 and ziv 1976 on source coding with side information

ishikawa and mann iterative processes with errors for nonlinear strongly accretive operator equations abstract the purpose of this paper is to revise the definitions of ishikawa and mann iterative processes with errors by using a new inequality to study the unique solution of the nonlinear strongly accretive operator equationtx fand the convergence problem of ishikawa and mann iterative sequences for strongly pseudo contractive mappings without the lipschitz condition the results presented in this paper improve and extend the corresponding results in 4 5 7 10 12 15 16 in the more general setting in particular the open problem mentioned by chidume in 5 has been given an affirmative answer

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

modified noor iterations for nonlinear equations in banach spaces the purpose of this paper is to analyze the modified three step iterative scheme for solving nonlinear operator equations in real banach spaces our results can be viewed as an extension of three step and two step iterative schemes of glowinski and le tallec r glowinski p le tallec augemented lagrangian and operator splitting methods in nonlinear mechanics siam publishing co philadelphia 1989 noor m a noor three step iterative algorithms for multivalued quasi variational inclusions j math anal appl 255 2001 589 604 m a noor some predictor corrector algorithms for multivalued variational inequalities j optim theory appl 108 3 2001 659 670 m a noor t m rassias z huang three step iterations for nonlinear accretive operator equations j math anal appl 274 2002 59 68 and ishikawa s ishikawa fixed points by a new iteration method proc amer math soc 44 1974 147 150

global existence and mann iterative algorithms of positive solutions for first order nonlinear neutral delay differential equations abstract this paper deals with the first order nonlinear neutral delay differential equation d dt x t p t x t f t x 1 t x 2 t x n t 0 t t 0 where 0 p c t 0 r f c t 0 r n r and l c t 0 r with limt l t for l 1 2 n by using the banach fixed point theorem we prove the global existence of uncountably many bounded positive solutions for the above equation relative to all ranges of the function p construct some mann type iterative algorithms with errors to approximate these positive solutions and discuss several error estimates between the sequences generated by the iterative algorithms and these positive solutions seven examples are presented to illuminate the results obtained in this paper

strong convergence of viscosity approximation methods for finding zeros of accretive operators in banach spaces abstract in this paper we introduce a composite iterative scheme by viscosity approximation method for finding a zero of an accretive operator in banach spaces then we establish strong convergence theorems for the composite iterative scheme the main theorems improve and generalize the recent corresponding results of kim and xu t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 2005 51 60 qin and su x qin y su approximation of a zero point of accretive operator in banach spaces j math anal appl 329 2007 415 424 and xu h k xu strong convergence of an iterative method for nonexpansive and accretive operators j math anal appl 314 2006 631 643 as well as aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in banach spaces nonlinear anal 67 2007 2350 2360 benavides et al t d benavides g l acedo h k xu iterative solutions for zeros of accretive operators math nachr 248 249 2003 62 71 chen and zhu r chen z zhu viscosity approximation fixed points for nonexpansive and m accretive operators fixed point theory and appl 2006 2006 1 10 and kamimura and takahashi s kamimura w takahashi approximation solutions of maximal monotone operators in hilberts spaces j approx theory 106 2000 226 240

green s function estimation in speckle using the decomposition of the time reversal operator application to aberration correction in medical imaging the fdort method french acronym for decomposition of the time reversal operator using focused beams is a time reversal based method that can detect point scatterers in a heterogeneous medium and extract their green s function it is particularly useful when focusing in a heterogeneous medium this paper generalizes the theory of the fdort method to random media speckle and shows that it is possible to extract green s functions from the speckle signal using this method therefore it is possible to achieve a good focusing even if no point scatterers are present moreover a link is made between fdort and the van cittert zernike theorem it is deduced from this interpretation that the normalized first eigenvalue of the focused time reversal operator is a well known focusing criterion the concept of an equivalent virtual object is introduced that allows the random problem to be replaced by an equivalent deterministic problem and leads to an intuitive understanding of fdort in speckle applications to aberration correction are presented the reduction of the variance of the green s function estimate is discussed finally it is shown that the method works well in the presence of strong interfering scatterers

the ceo problem multiterminal source coding we consider a new problem in multiterminal source coding motivated by the following decentralized communication estimation task a firm s chief executive officer ceo is interested in the data sequence x t sub t 1 sup spl infin which cannot be observed directly perhaps because it represents tactical decisions by a competing firm the ceo deploys a team of l agents who observe independently corrupted versions of x t sub t 1 sup spl infin because x t is only one among many pressing matters to which the ceo must attend the combined data rate at which the agents may communicate information about their observations to the ceo is limited to say r bits per second if the agents were permitted to confer and pool their data then in the limit as l spl rarr spl infin they usually would be able to smooth out their independent observation noises entirely then they could use their r bits per second to provide the ceo with a representation of x t with fidelity d r where d spl middot is the distortion rate function of x t in particular with such data pooling d can be made arbitrarily small if r exceeds the entropy rate h of x t suppose however that the agents are not permitted to convene agent i having to send data based solely on his own noisy observations y sub i t we show that then there does not exist a finite value of r for which even infinitely many agents can make d arbitrarily small furthermore in this isolated agents case we determine the asymptotic behavior of the minimal error frequency in the limit as l and then r tend to infinity

equivalency of convergence between one step iteration algorithm and two step iteration algorithm of variational inclusions for h monotone mappings the aim of this paper is to establish the equivalence of convergence for h monotone mappings of variational inclusions between the one step iteration algorithm of the paper y p fang n j huang h monotone opertor and resolvent operator technique for variational inclusions appl math comput 145 2003 795 803 and the two step iteration algorithm of the paper l c zeng s m guu j c yao characterization of h monotone operators with applications to variational inclusions comput math appl 50 2005 329 337 it is clear from this paper that the one step iteration algorithm with easy implement and small computational workload has more advantages than the two step iteration algorithm

a general iterative scheme for k strictly pseudo contractive mappings and optimization problems in this paper we introduce a new general iterative scheme for finding fixed points of a strictly pseudo contractive mapping and then prove that the sequence generated by the proposed iterative scheme converges strongly to a fixed point of the mapping which is a solution of a certain optimization problem related to a strongly positive bounded linear operator additional results of the main result are also obtained