optimal design of constraint following control for fuzzy mechanical systems the control problem for a mechanical system to follow a constraint is formulated the uncertainty is considered in both the system dynamics and constraint it is bounded and the knowledge of the bound only lies within a fuzzy set we propose an adaptive robust control for the mechanical system for approximate constraint following both the mechanical system model and control scheme are deterministic and not if then heuristic rules based an optimal design problem using the fuzzy description of the uncertainty is proposed we prove that the global solution to the resulting optimization problem always exists and is unique under the control the performance of the mechanical system is both deterministically guaranteed and fuzzily optimized

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

a new perspective on the tracking control of nonlinear structural and mechanical systems based on recent results from analytical dynamics this paper develops a class of tracking controllers for controlling general nonlinear structural and mechanical systems unlike most control methods that perform some kind of linearization and or nonlinear cancellation the methodology developed herein views the nonlinear control problem from a different perspective this leads to a simple and new control methodology that is capable of exactly maintaining the nonlinear system along a certain trajectory which in general may be described by a set of differential equations in the observations measurements the approach requires very little computation compared with standard approaches it is therefore useful for online real time control of nonlinear systems the methodology is illustrated with two examples

restoration of severely blurred high range images using stochastic and deterministic relaxation algorithms in compound gauss markov random fields abstract over the last few years a growing number of researchers from varied disciplines have been utilizing markov random fields mrf models for developing optimal robust algorithms for various problems such as texture analysis image synthesis classification and segmentation surface reconstruction integration of several low level vision modules sensor fusion and image restoration however no much work has been reported on the use of simulated annealing sa and iterative conditional mode icm algorithms for maximum a posteriori estimation in image restoration problems when severe blurring is present in this paper we examine the use of compound gauss markov random fields cgmrf to restore severely blurred high range images for this deblurring problem the convergence of the sa and icm algorithms has not been established we propose two new iterative restoration algorithms which can be considered as extensions of the classical sa and icm approaches and whose convergence is established finally they are tested on real and synthetic images and the results compared with the restorations obtained by other iterative schemes

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

unbiased risk estimates for singular value thresholding and spectral estimators in an increasing number of applications it is of interest to recover an approximately low rank data matrix from noisy observations this paper develops an unbiased risk estimate holding in a gaussian model for any spectral estimator obeying some mild regularity assumptions in particular we give an unbiased risk estimate formula for singular value thresholding svt a popular estimation strategy that applies a soft thresholding rule to the singular values of the noisy observations among other things our formulas offer a principled and automated way of selecting regularization parameters in a variety of problems in particular we demonstrate the utility of the unbiased risk estimation for svt based denoising of real clinical cardiac mri series data we also give new results concerning the differentiability of certain matrix valued functions

smart nonlinear diffusion a probabilistic approach in this paper a stochastic interpretation of nonlinear diffusion equations used for image filtering is proposed this is achieved by relating the problem of evolving smoothing images to that of tracking the transition probability density functions of an underlying random process we show that such an interpretation of e g perona malik equation in turn allows additional insight and sufficient flexibility to further investigate some outstanding problems of nonlinear diffusion techniques in particular upon unraveling the limitations as well as the advantages of such an equation we are able to propose a new approach which is demonstrated to improve performance over existing approaches and more importantly to lift the longstanding problem of a stopping criterion for a nonlinear evolution equation with no data term constraint substantiating examples in image enhancement and segmentation are provided

grouped coordinate ascent algorithms for penalized likelihood transmission image reconstruction presents a new class of algorithms for penalized likelihood reconstruction of attenuation maps from low count transmission scans we derive the algorithms by applying to the transmission log likelihood a version of the convexity technique developed by de pierro for emission tomography the new class includes the single coordinate ascent sca algorithm and lange s convex algorithm for transmission tomography as special cases the new grouped coordinate ascent gca algorithms in the class overcome several limitations associated with previous algorithms 1 fewer exponentiations are required than in the transmission maximum likelihood expectation maximization ml em algorithm or in the sca algorithm 2 the algorithms intrinsically accommodate nonnegativity constraints unlike many gradient based methods 3 the algorithms are easily parallelizable unlike the sca algorithm and perhaps line search algorithms we show that the gca algorithms converge faster than the sca algorithm even on conventional workstations an example from a low count positron emission tomography pet transmission scan illustrates the method

on the impact of anisotropic diffusion on edge detection content aware edge preserving smoothing techniques have gained visibility in recent years however they have had a rather limited impact on the edge detection literature compared to content unaware linear techniques often based on gaussian filters in this work we focus on anisotropic diffusion covering its initial definition by perona and malik and subsequent extensions a visual case study is used to illustrate their features we perform a quantitative evaluation of the performance of the canny method for edge detection when substituting linear gaussian smoothing filters by anisotropic diffusion highlightsreviewing the main trends in anisotropic diffusion identifying the practical scenarios on which anisotropic diffusion fails quantifying the improvement of edge detection when anisitropic diffusion is applied

reduction of noise induced streak artifacts in x ray computed tomography through spline based penalized likelihood sinogram smoothing we present a statistically principled sinogram smoothing approach for x ray computed tomography ct with the intent of reducing noise induced streak artifacts these artifacts arise in ct when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements while these approaches involve loose consideration of the measurement statistics to determine smoothing levels they do not explicitly model the statistical distributions of the measurement data we present an explicitly statistical approach to sinogram smoothing in the presence of photon starved measurements it is an extension of a nonparametric sinogram smoothing approach using penalized poisson likelihood functions that we have previously developed for emission tomography because the approach explicitly models the data statistics it is naturally adaptive it will smooth more variable measurements more heavily than it does less variable measurements we find that it significantly reduces streak artifacts and noise levels without comprising image resolution

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

radiation dose reduction in ct myocardial perfusion imaging using smart recon in this paper a newly developed statistical model based image reconstruction referred to as simultaneous multiple artifacts reduction in tomographic reconstruction smart recon is applied to low dose computer tomography ct myocardial perfusion imaging ct mpi this method uses the nuclear norm of the spatial temporal image matrix of the ct mpi images as a regularizer rather than a conventional spatial regularizer that incorporates image smoothness edge preservation or spatial sparsity into the reconstruction in addition to providing the needed noise reduction for low dose ct mpi smart recon provides images with spatial resolution and noise power spectrum nps properties which are independent of contrast and dose levels both numerical simulations and in vivo animal studies were performed to validate the proposed method in these studies it was found that 1 quantitative accuracy of perfusion maps in ct mpi was well maintained for radiation dose level as low as 10 mas per image frame compared with the reference standard of 200 mas for conventional filtered backprojection 2 flow occluded myocardium in the porcine heart was well delineated by smart recon at 10 mas per frame when compared with model based image reconstruction using spatial total variation tv as the regularizer referred to as tv sir or spatial temporal tv st tv sir the ct mpi results were confirmed with positron emission tomography imaging 3 image sharpness in smart recon images was nearly independent of image contrast level and radiation dose level in stark contrast to tv sir and st tv sir which displayed a strong dependence on both image contrast and radiation dose levels and 4 the structure of the dose normalized nps for the smart recon method did not depend on dose while the tv sir and st tv sir nps structure was dose dependent

nonlinear multiscale analysis of three dimensional echocardiographic sequences introduces a new model for multiscale analysis of space time echocardiographic sequences the proposed nonlinear partial differential equation representing the multiscale analysis filters the sequence while keeping the space time coherent structures it combines the ideas of regularized perona malik anisotropic diffusion and the galilean invariant movie multiscale analysis of alvarez et al arch rat mech anal vol 123 p 200 57 1993 a numerical method for solving the proposed partial differential equation is suggested and its stability is shown computational results on synthesized and real sequences are provided a qualitative and quantitative evaluation of the accuracy of the method is presented

diffusion tensors for processing sheared and rotated rectangles image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing however known edge preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times in this paper we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles respectively in this context we propose a new method for estimating rotation angles and shear parameters based on the so called structure tensor further we show how the knowledge of appropriate diffusion tensors can be used in variational models numerical examples including orientation estimation denoising and segmentation demonstrate the good performance of our methods

piecewise linear approximation of vector valued images and curves via second order variational model variational models are known to work well for addressing image restoration regularization problems however most of the methods proposed in the literature are defined for scalar inputs and are used on multiband images such as rgb or multispectral imagery by the composition of a simple band wise processing this involves suboptimal results and may introduce artifacts only in a few cases variational models are extended to the case of vector valued inputs however the known implementations are restricted to the first order models while the second order models are never considered thus typical problems of the first order models such as the staircasing effect cannot be overtaken this paper considers a second order functional model to function approximation with free discontinuities given by blake zisserman bz and proposes an efficient minimization algorithm in the case of vector valued inputs in the bz model the hessian of the solution is penalized outside a set of finite length therefore the solution is forced to be piecewise linear moreover the model allows the formation of free discontinuities and free gradient discontinuities the proposed algorithm is applied to difficult color image restoration regularization problems and to piecewise linear approximation of curves in space

a discrete model for an ill posed nonlinear parabolic pde we study a finite difference discretization of an ill posed nonlinear parabolic partial differential equation the pde is the one dimensional version of a simplified two dimensional model for the formation of shear bands via anti plane shear of a granular medium for the discretized initial value problem we derive analytically and observed numerically a two stage evolution leading to a steady state i an initial growth of grid scale instabilities and ii coarsening dynamics elaborating the second phase at any fixed time the solution has a piecewise linear profile with a finite number of shear bands in this coarsening phase one shear band after another collapses until a steady state with just one jump discontinuity is achieved the amplitude of this steady state shear band is derived analytically but due to the ill posedness of the underlying problem its position exhibits sensitive dependence analyzing data from the simulations we observe that the number of shear bands at time t decays like t 1 3 from this scaling law we show that the time scale of the coarsening phase in the evolution of this model for granular media critically depends on the discreteness of the model our analysis also has implications to related ill posed nonlinear pdes for the one dimensional perona malik equation in image processing and to models for clustering instabilities in granular materials 2001 elsevier science b v all rights reserved

a volterra type model for image processing we present a class of time delay anisotropic diffusion models for image restoration these models lead to asymptotic states that are selected on the basis of a contrast parameter and bear some analogy with neural networks with hebbian dynamical learning rules numerical examples show that these models are efficient in removing even high levels of noise while allowing an accurate tracking of the edges

adaptive two pass rank order filter to remove impulse noise in highly corrupted images in this paper we present an adaptive two pass rank order filter to remove impulse noise in highly corrupted images when the noise ratio is high rank order filters such as the median filter for example can produce unsatisfactory results better results can be obtained by applying the filter twice which we call two pass filtering to further improve the performance we develop an adaptive two pass rank order filter between the passes of filtering an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise the adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values these pixels are then kept unchanged during the second filtering in combination the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering as a final result the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise the idea of adaptive two pass processing can be applied to many rank order filters such as a center weighted median filter cwmf adaptive cwmf lower upper middle filter and soft decision rank order mean filter results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters

image recovery using the anisotropic diffusion equation a new approach for image recovery using the anisotropic diffusion equation is developed which is based on the first derivative of the signal in time embedded in family of images with different scales the diffusion coefficient is determined as a function of the gradient of the signal convolved with a symmetric exponential filter a new discrete realization is developed for the simultaneous removal of noise and preservation of edges

wavelet transform domain filters a spatially selective noise filtration technique wavelet transforms are multiresolution decompositions that can be used to analyze signals and images they describe a signal by the power at each scale and position edges can be located very effectively in the wavelet transform domain a spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced a high correlation is used to infer that there is a significant feature at the position that should be passed through the filter the authors have tested the technique on simulated signals phantom images and real mr images it is found that the technique can reduce noise contents in signals and images by more than 80 while maintaining at least 80 of the value of the gradient at most edges the authors did not observe any gibbs ringing or significant resolution loss on the filtered images artifacts that arose from the filtration are very small and local the noise filtration technique is quite robust there are many possible extensions of the technique the authors see its applications in spatially dependent noise filtration edge detection and enhancement image restoration and motion artifact removal they have compared the performance of the technique to that of the weiner filter and found it to be superior

a novel pde based image restoration convection diffusion equation for image denoising in this paper we present a convection diffusion equation for processing image denoising edge preservation and compression we compare it with a popular nonlinear diffusion model which has been widely implemented in image denoising for gaussian white noise here we show that this convection diffusion model effectively removes noise especially for the mixture of gaussian and salt and pepper noises we propose the modified streamline diffusion method y shih h c elman modified streamline diffusion schemes for convection diffusion problems comput methods appl mech eng 1998 for the discretization of this convection diffusion model to prevent internal layers because of the discontinuities while using the coarsening algorithm for the image compression numerical experiments have shown that our convection diffusion model for removing both gaussian and salt and pepper noises efficiently and reliably preserves edges quite satisfactorily

a method of image preprocessing based on nonlinear diffusion and information extraction thermally induced stresses play a very important role in controlling the structural reliability of microchip packages in order to evaluate the magnitude of the warpage of measured objects caused by such stresses the shadow moire technique was suggested where how the moire fringes are extracted is the key feature in this work an improved filtering algorithm based on a nonlinear diffusion equation is developed and a medial axis transformation and pruning algorithm are applied to extract the skeleton of the moire fringe in order to remove the forficate fringe and isolated noise fringe a main fringe extraction algorithm is then used and this is discussed in detail according to the moire fringe information extracted from the shadow moire pattern the three dimensional image which indicates warpage of the measured object s surface is reconstructed this demonstrates that the measuring accuracy can be improved up to 2 0 mm by using a grating of 100 lines per inch

an analysis of the perona malik scheme the perona malik scheme is a numerical procedure for de noising digital pictures in this work we investigate how it evolves piecewise smooth initial data in one space dimension by scaling a natural parameter that appears in the scheme in an appropriate way with respect to the grid size we obtain a meaningful continuum limit the resulting evolution is unusual it involves solving a system of heat equations coupled to each other through nonlinear boundary conditions that become singular at special times leading to gradient blow up for the solutions however the scheme suggests a natural continuation beyond each of the singular times that involves a change in the p d e system we give a convergence proof that applies under some technical restrictions on any bounded interval of time which might include singular times furthermore the proposed continuum limit has some of the essential features observed in applications of the numerical scheme

a global approach for solving evolutive heat transfer for image denoising and inpainting this paper proposes an alternative to partial differential equations pdes for solving problems in computer vision based on evolutive heat transfer traditionally the method for solving such physics based problems is to discretize and solve a pde by a purely mathematical process instead of using the pde we propose to use the global heat principle and to decompose it into basic laws we show that some of these laws admit an exact global version since they arise from conservative principles we also show that the assumptions made about the other basic laws can be made wisely taking into account knowledge about the problem and the domain the numerical scheme is derived in a straightforward way from the modeled problem thus providing a physical explanation for each step in the solution the advantage of such an approach is that it minimizes the approximations made during the whole process and it modularizes it allowing changing the application to a great number of problems we apply the scheme to two applications image denoising and inpainting which are modeled with heat transfer for denoising we propose a new approximation for the conductivity coefficient and we add thin lines to the features in order to block diffusion

orientation matching minimization for image denoising and inpainting in this paper we propose an orientation matching functional minimization for image denoising and image inpainting following the two step tv stokes algorithm rahman et al in scale space and variational methods in computer vision pp 473 482 springer heidelberg 2007 tai et al in image processing based on partial differential equations pp 3 22 springer heidelberg 2006 bertalmio et al in proc conf comp vision pattern rec pp 355 362 2001 a regularized tangential vector field with zero divergence condition is first obtained then a novel approach to reconstruct the image is proposed instead of finding an image that fits the regularized normal direction from the first step we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction this functional yields a new nonlinear partial differential equation pde for reconstructing denoised and inpainted images the equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field providing reconstructed images which have sharp edges and smooth regions the additive operator splitting aos scheme is used for discretizing euler lagrange equations we present the results of various numerical experiments that illustrate the improvements obtained with the new functional

ray contribution masks for structure adaptive sinogram filtering the patient dose in computed tomography ct imaging is linked to measurement noise various noise reduction techniques have been developed that adapt structure preserving filters like anisotropic diffusion or bilateral filters to ct noise properties we introduce a structure adaptive sinogram sas filter that incorporates the specific properties of the ct measurement process it uses a point based forward projector to generate a local structure representation called ray contribution mask rcm the similarities between neighboring rcms are used in an enhanced variant of the bilateral filtering concept where the photometric similarity is replaced with the structural similarity we evaluate the performance in four different scenarios the robustness against reconstruction artifacts is demonstrated by a scan of a high resolution phantom without changing the modulation transfer function mtf nor introducing artifacts the sas filter reduces the noise level by 13 6 the image sharpness and noise reduction capabilities are visually assessed on in vivo patient scans and quantitatively evaluated on a simulated phantom unlike a standard bilateral filter the sas filter preserves edge information and high frequency components of organ textures well it shows a homogeneous noise reduction behavior throughout the whole frequency range the last scenario uses a simulated edge phantom to estimate the filter mtf for various contrasts the noise reduction for the simple edge phantom exceeds 80 for low contrasts at 55 hounsfield units hu the mid frequency range is slightly attenuated at higher contrasts of approximately 100 hu and above the mtf is fully preserved

oriented speckle reducing anisotropic diffusion ultrasound imaging systems provide the clinician with noninvasive low cost and real time images that can help them in diagnosis planning and therapy however although the human eye is able to derive the meaningful information from these images automatic processing is very difficult due to noise and artifacts present in the image the speckle reducing anisotropic diffusion filter was recently proposed to adapt the anisotropic diffusion filter to the characteristics of the speckle noise present in the ultrasound images and to facilitate automatic processing of images we analyze the properties of the numerical scheme associated with this filter using a semi explicit scheme we then extend the filter to a matrix anisotropic diffusion allowing different levels of filtering across the image contours and in the principal curvature directions we also show a relation between the local directional variance of the image intensity and the local geometry of the image which can justify the choice of the gradient and the principal curvature directions as a basis for the diffusion matrix finally different filtering techniques are compared on a 2 d synthetic image with two different levels of multiplicative noise and on a 3 d synthetic image of a y junction and the new filter is applied on a 3 d real ultrasound image of the liver

mean value theorems of multiplicative functions on additive arithmetic semigroups it has been pointed out to me by r warlimont that the proof of theorem 6 4 2 in 1 has a gap and the theorem is false he has also constructed counter examples in accordance theorem 1 6 in my paper 2 quoted in the title of this correction is false too actually either of them requires more conditions on the multiplicative functions so that it can be true in this correction we supply such a condition see condition 2 below and prove the following theorem theorem suppose an additive arithmetic semigroupg satisfies the condition i or ii in theorem 1 6 in 2 let f a be a multiplicative function such that f a 1 for every a g if there exist a subset p1 of p and a constant 0 such that p p1 q p

anisotropic second and fourth order diffusion models based on convolutional virtual electric field for image denoising this paper proposes novel second order and fourth order anisotropic diffusion models for image denoising these two models are based on convolutional virtual electric field convef the proposed second order anisotropic diffusion model was introduced by introducing the convef into the perona malik p m equation and the fourth order one is coined by combining convef and the you kaveh y k equation the employment of the convef model allows to improve the estimation of high order derivatives and makes the proposed methods more robust to noise in addition the proposed convef based y k model is an anisotropic diffusion equation which can avoid the over smoothness of edges and provide better edge protection capability except for better denoising some experiments are conducted to demonstrate the efficiency of the proposed methods

local variance controlled forward and backward diffusion for image enhancement and noise reduction in order to improve signal to noise ratio snr and contrast to noise ratio this paper introduces a local variance controlled forward and backward lvcfab diffusion algorithm for edge enhancement and noise reduction in our algorithm an alternative fab diffusion algorithm is proposed the results for the alternative fab algorithm show better algorithm behavior than other existing diffusion fab approaches furthermore two distinct discontinuity measures and the alternative fab diffusion are incorporated into a lvcfab diffusion algorithm where the joint use of the two measures leads to a complementary effect for preserving edge features in digital images this lvc mechanism adaptively modifies the degree of diffusion at any image location and is dependent on both local gradient and inhomogeneity qualitative experiments based on general digital images and magnetic resonance images show significant improvements when the lvcfab diffusion algorithm is used versus the existing anisotropic diffusion and the previous fab diffusion algorithms for enhancing edge features and improving image contrast quantitative analyses based on peak snr confirm the superiority of the proposed lvcfab diffusion algorithm

automatic lung segmentation for accurate quantitation of volumetric x ray ct images segmentation of pulmonary x ray computed tomography ct images is a precursor to most pulmonary image analysis applications this paper presents a fully automatic method for identifying the lungs in three dimensional 3 d pulmonary x ray ct images the method has three main steps first the lung region is extracted from the ct images by gray level thresholding then the left and right lungs are separated by identifying the anterior and posterior junctions by dynamic programming finally a sequence of morphological operations is used to smooth the irregular boundary along the mediastinum in order to obtain results consistent with these obtained by manual analysis in which only the most central pulmonary arteries are excluded from the lung region the method has been tested by processing 3 d ct data sets from eight normal subjects each imaged three times at biweekly intervals with lungs at 90 vital capacity the authors present results by comparing their automatic method to manually traced borders from two image analysts averaged over all volumes the root mean square difference between the computer and human analysis is 0 8 pixels 0 54 mm the mean intrasubject change in tissue content over the three scans was 2 75 spl plusmn 2 29 mean spl plusmn standard deviation

automatic prior shape selection for image edge detection with modified mumford shah model abstract edge detection plays an important role in the field of image processing in this paper we propose a novel variational model to automatically and adaptively detect one or more prior shapes from the given dictionary to guide the edge detection process in that way we can effectively detect the shapes of interest from the test image moreover an efficient algorithm based on the alternating direction method of multipliers admm is proposed to solve this model with guaranteed convergence a variety of numerical experiments show that the proposed method has achieved ideal performance for edge detection in images with missing information various types of noise and complicated background and even multiple objects

combining spatial and scale space techniques for edge detection to provide a spatially adaptive wavelet based noise filtering algorithm new methods for detecting edges in an image using spatial and scale space domains are proposed a priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge an improved double thresholding technique is introduced for spatial domain filtering probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes gradient phases and edge connectivity the scale space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales a probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale space domain methods decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale these matched filters permit significant reduction in image noise without contributing to edge distortion the spatially adaptive wavelet noise filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images

strong solutions for the generalized perona malik equation for image restoration abstract in this paper we establish the existence and uniqueness of strong solutions for the generalized perona malik equation of the fourth order for image restoration in dimension one

decentralized fuzzy control of nonlinear interconnected dynamic delay systems via mixed h_2 h_ infty optimization with smith predictor each subsystem of a nonlinear interconnected dynamic delayed system is approximated by a weighted combination of l transfer function delayed systems tfdss the h2 norm of the difference between the transfer function of a reference model and the closed loop transfer function of the kth tfds of subsystem i is then minimized to obtain a suitable frequency response without incurring oscillating and sluggish phenomena because of the existence of the disturbance at the output of the kth tfds which is not only large but also contains various frequency components the h norm of the weighted sensitivity function between the output disturbance and its corresponding output of the kth tfds is simultaneously minimized to reduce its effect furthermore with proper selection of weighted sensitivity functions certain specific modes of the output disturbance can be eliminated finally two simulations are performed one is the simulation of our designed tfdss with different delays or nonminimum phases and the other is the simulation of an internet based intelligent space for the trajectory tracking of a car like wheeled robot system we demonstrate the effectiveness and efficiency of the proposed control the main contributions of this paper are twofold first the control can simultaneously attain robust performance through the mixed h2 h optimization with a smith predictor and achieve the robust stability via l2n stable with finite gain second fuzzy observer is not needed

nonlinear regularized reaction diffusion filters for denoising of images with textures denoising is always a challenging problem in natural imaging and geophysical data processing in this paper we consider the denoising of texture images using a nonlinear reaction diffusion equation and directional wavelet frames in our model a curvelet shrinkage is used for regularization of the diffusion process to preserve important features in the diffusion smoothing and a wave atom shrinkage is used as the reaction in order to preserve and enhance interesting oriented textures we derive a digital reaction diffusion filter that lives on graphs and show convergence of the corresponding iteration process experimental results and comparisons show very good performance of the proposed model for texture preserving denoising

elementary proofs of the abstract prime number theorem for algebraic function fields elementary proofs of the abstract prime number theorem of the form m q m o q m m 751 for algebraic function fields are given the proofs use a refinement of a tauberian theorem of bombieri

simultaneous design of membership functions and rule sets for fuzzy controllers using genetic algorithms this paper examines the applicability of genetic algorithms ga s in the simultaneous design of membership functions and rule sets for fuzzy logic controllers previous work using genetic algorithms has focused on the development of rule sets or high performance membership functions however the interdependence between these two components suggests a simultaneous design procedure would be a more appropriate methodology when ga s have been used to develop both it has been done serially e g design the membership functions and then use them in the design of the rule set this however means that the membership functions were optimized for the initial rule set and not the rule set designed subsequently ga s are fully capable of creating complete fuzzy controllers given the equations of motion of the system eliminating the need for human input in the design loop this new method has been applied to two problems a cart controller and a truck controller beyond the development of these controllers we also examine the design of a robust controller for the cart problem and its ability to overcome faulty rules

combined curvelet shrinkage and nonlinear anisotropic diffusion in this paper a diffusion based curvelet shrinkage is proposed for discontinuity preserving denoising using a combination of a new tight frame of curvelets with a nonlinear diffusion scheme in order to suppress the pseudo gibbs and curvelet like artifacts the conventional shrinkage results are further processed by a projected total variation diffusion in which only the insignificant curvelet coefficients or high frequency part of the signal are changed by use of a constrained projection numerical experiments from piecewise smooth to textured images show good performances of the proposed method to recover the shape of edges and important detailed components in comparison to some existing methods

a new iterated two band diffusion equation theory and its application we propose an iterated two band filtering method to solve the selective image smoothing problem we prove that a discrete computation step in an iterated nonlinear diffusion based filtering algorithm is equivalent to a sequence of operations including decomposition regularization and then reconstruction in the proposed two band filtering scheme to correctly separate the high frequency components from the low frequency ones in the decomposition process we adopt a dyadic wavelet based approximation scheme in the regularization process we use a diffusivity function as a guide to retain useful data and suppress noises finally the signal of the next stage which is a smoother version of the signal at the previous stage can be computed by reconstructing the decomposed low frequency component and the regularized high frequency component based on the proposed scheme the smoothing operation can be applied to the correct targets experimental results show that our new approach is really efficient in noise removing

processing textured surfaces via anisotropic geometric diffusion a multiscale method in surface processing is presented which carries over image processing methodology based on nonlinear diffusion equations to the fairing of noisy textured parametric surfaces the aim is to smooth noisy triangulated surfaces and accompanying noisy textures as they are delivered by new scanning technology while enhancing geometric and texture features for an initial textured surface a fairing method is described which simultaneously processes the texture and the surface considering an appropriate coupling of the two smoothing processes one can take advantage of the frequently present strong correlation between edge features in the texture and on the surface edges the method is based on an anisotropic curvature evolution of the surface itself and an anisotropic diffusion on the processed surface applied to the texture here the involved diffusion tensors depends on a regularized shape operator of the evolving surface and on regularized texture gradients a spatial finite element discretization on arbitrary unstructured triangular grids and a semi implicit finite difference discretization in time are the building blocks of the corresponding numerical algorithm a normal projection is applied to the discrete propagation velocity to avoid tangential drifting in the surface evolution different applications underline the efficiency and flexibility of the presented surface processing tool

robust controllability of t s fuzzy model based control systems with parametric uncertainties the robust controllability problem for the takagi sugeno t s fuzzy model based control systems is studied in this paper under the assumption that the nominal t s fuzzy model based control systems are locally controllable i e each fuzzy rule of the nominal t s fuzzy model based control systems has a full row rank for its controllability matrix a sufficient condition is proposed to preserve the assumed property when the parameter uncertainties are added into the nominal t s fuzzy model based control systems the proposed sufficient condition can provide the explicit relationship of the bounds on parameter uncertainties to preserve the assumed property besides a robustly global controllability condition and the related robustly global stabilizability condition of the uncertain t s fuzzy model based control systems are also presented in this paper a nonlinear mass spring damper mechanical system with parameter uncertainties is given as an example to illustrate the application of the proposed sufficient conditions

tensor based dictionary learning for spectral ct reconstruction spectral computed tomography ct produces an energy discriminative attenuation map of an object extending a conventional image volume with a spectral dimension in spectral ct an image can be sparsely represented in each of multiple energy channels and are highly correlated among energy channels according to this characteristics we propose a tensor based dictionary learning method for spectral ct reconstruction in our method tensor patches are extracted from an image tensor which is reconstructed using the filtered backprojection fbp to form a training dataset with the candecomp parafac decomposition a tensor based dictionary is trained in which each atom is a rank one tensor then the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process and the alternating minimization scheme is adapted for optimization the effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets the results demonstrate that the proposed tensor based method generally produces superior image quality and leads to more accurate material decomposition than the currently popular popular methods

a well balanced flow equation for noise removal and edge detection an anisotropic nonlinear diffusion equation for image restoration is presented the model has two terms the diffusion term and the forcing term the balance between these terms is made in a selective way in which boundary points and interior points of the objects that make up the image are treated differently the optimal smoothing time concept which allows for finding the ideal stop time for the evolution of the partial differential equation is also proposed numerical results show the proposed model s high performance

efficient image segmentation using partial differential equations and morphology the goal of this paper is to investigate segmentation methods that combine fast preprocessing algorithms using partial differential equations pdes with a watershed transformation with region merging we consider two well founded pde methods a nonlinear isotropic diffusion filter that permits edge enhancement and a convex nonquadratic variational image restoration method which gives good denoising for the diffusion filter an efficient algorithm is applied using an additive operator splitting aos that leads to recursive and separable filters for the variational restoration method a novel algorithm is developed that uses aos schemes within a gaussian pyramid decomposition examples demonstrate that preprocessing by these pde techniques significantly improves the watershed segmentation and that the resulting segmentation method gives better results than some traditional techniques the algorithm has linear complexity and it can be used for arbitrary dimensional data sets the typical cpu time for segmenting a 256 image on a modern pc is far below one second

a new nonlocal nonlinear diffusion of image processing abstract a novel nonlocal nonlinear diffusion is analyzed which has proven useful as a denoising tool in image processing the equation can be viewed as a new paradigm for the regularization of the well known perona malik equation the regularization is implemented via nonlinearity intensity reduction through fractional derivatives well posedness in the weak setting is established global existence and convergence to the average holds in the purely diffusive limit whereas an interesting dynamic behavior is engendered by the presence of nontrivial equilibria as the intensity of the nonlinearity is increased and comes close to the one of perona malik

penalized likelihood sinogram restoration for computed tomography we formulate computed tomography ct sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy degraded measurements ct measurement data are degraded by a number of factors including beam hardening and off focal radiation that produce artifacts in reconstructed images unless properly corrected currently such effects are addressed by a sequence of sinogram preprocessing steps including deconvolution corrections for off focal radiation that have the potential to amplify noise noise itself is generally mitigated through apodization of the reconstruction kernel which effectively ignores the measurement statistics although in high noise situations adaptive filtering methods that loosely model data statistics are sometimes applied as an alternative we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function we consider three different strategies for estimating the set of ideal line integrals one based on direct estimation of ideal monochromatic line integrals that have been corrected for single material beam hardening one based on estimation of ideal polychromatic line integrals that can be readily mapped to monochromatic line integrals and one based on estimation of ideal transmitted intensities from which ideal monochromatic line integrals can be readily estimated the first two approaches involve maximization of a penalized poisson likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares pwls objective applied in the transmitted intensity domain we find that at low exposure levels typical of those being considered for screening ct the poisson likelihood based approaches outperform the pwls objective as well as a standard approach based on adaptive filtering followed by deconvolution at higher exposure levels the approaches all perform similarly

wavelet based noise reduction in ct images using correlation analysis the projection data measured in computed tomography ct and consequently the slices reconstructed from these data are noisy we present a new wavelet based structure preserving method for noise reduction in ct images that can be used in combination with different reconstruction methods the approach is based on the assumption that data can be decomposed into information and temporally uncorrelated noise in ct two spatially identical images can be generated by reconstructions from disjoint subsets of projections using the latest generation dual source ct scanners one image can be reconstructed from the projections acquired at the first the other image from the projections acquired at the second detector for standard ct scanners the two images can be generated by splitting up the set of projections into even and odd numbered projections the resulting images show the same information but differ with respect to image noise the analysis of correlations between the wavelet representations of the input images allows separating information from noise down to a certain signal to noise level wavelet coefficients with small correlation are suppressed while those with high correlations are assumed to represent structures and are preserved the final noise suppressed image is reconstructed from the averaged and weighted wavelet coefficients of the input images the proposed method is robust of low complexity and adapts itself to the noise in the images the quantitative and qualitative evaluation based on phantom as well as real clinical data showed that high noise reduction rates of around 40 can be achieved without noticeable loss of image resolution

explicit equations of motion for constrained mechanical systems with singular mass matrices and applications to multi body dynamics we present the new general explicit form of the equations of motion for constrained mechanical systems applicable to systems with singular mass matrices the systems may have holonomic and or non holonomic constraints which may or may not satisfy d alembert s principle at each instant of time the equation provides new insights into the behaviour of constrained motion and opens up new ways of modelling complex multi body systems examples are provided and applications of the equation to such systems are illustrated

local noise weighted filtering for emphysema scoring of low dose ct images computed tomography ct has become the new reference standard for quantification of emphysema the most popular measure of emphysema derived from ct is the pixel index pi which expresses the fraction of the lung volume with abnormally low intensity values as pi is calculated from a single fixed threshold on intensity this measure is strongly influenced by noise this effect shows up clearly when comparing the pi score of a high dose scan to the pi score of a low dose i e noisy scan of the same subject in this paper the noise variance nova filter is presented a general framework for iterative nonlinear filtering which uses an estimate of the spatially dependent noise variance in an image the nova filter iteratively estimates the local image noise and filters the image for the specific purpose of emphysema quantification of low dose ct images a dedicated noniterative nova filter is constructed by using prior knowledge of the data to obtain a good estimate of the spatially dependent noise in an image the performance of the nova filter is assessed by comparing characteristics of pairs of high dose and low dose scans the compared characteristics are the pi scores for different thresholds and the size distributions of emphysema bullae after filtering the pi scores of high dose and low dose images agree to within 2 3 points the reproducibility of the high dose bullae size distribution is also strongly improved nova filtering of a ct image of typically 400 spl times 512 spl times 512 voxels takes only a couple of minutes which makes it suitable for routine use in clinical practice

variational denoising of partly textured images by spatially varying constraints denoising algorithms based on gradient dependent regularizers such as nonlinear diffusion processes and total variation denoising modify images towards piecewise constant functions although edge sharpness and location is well preserved important information encoded in image features like textures or certain details is often compromised in the process of denoising we propose a mechanism that better preserves fine scale features in such denoising processes a basic pyramidal structure texture decomposition of images is presented and analyzed a first level of this pyramid is used to isolate the noise and the relevant texture components in order to compute spatially varying constraints based on local variance measures a variational formulation with a spatially varying fidelity term controls the extent of denoising over image regions our results show visual improvement as well as an increase in the signal to noise ratio over scalar fidelity term processes this type of processing can be used for a variety of tasks in partial differential equation based image processing and computer vision and is stable and meaningful from a mathematical viewpoint

graph spectral image smoothing using the heat kernel a new method for smoothing both gray scale and color images is presented that relies on the heat diffusion equation on a graph we represent the image pixel lattice using a weighted undirected graph the edge weights of the graph are determined by the gaussian weighted distances between local neighboring windows we then compute the associated laplacian matrix the degree matrix minus the adjacency matrix anisotropic diffusion across this weighted graph structure with time is captured by the heat equation and the solution i e the heat kernel is found by exponentiating the laplacian eigensystem with time image smoothing is accomplished by convolving the heat kernel with the image and its numerical implementation is realized by using the krylov subspace technique the method has the effect of smoothing within regions but does not blur region boundaries we also demonstrate the relationship between our method standard diffusion based pdes fourier domain signal processing and spectral clustering experiments and comparisons on standard images illustrate the effectiveness of the method

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