estimation of distributions via multilevel monte carlo with stratified sampling abstract we design and implement a novel algorithm for computing a multilevel monte carlo mlmc estimator of the joint cumulative distribution function cdf of a vector valued quantity of interest in problems with random input parameters or initial conditions our approach combines mlmc with stratified sampling of the input sample space by replacing standard monte carlo at each level with stratified monte carlo initialized with proportionally allocated samples we show that the resulting stratified mlmc smlmc algorithm is more efficient than its standard mlmc counterpart due to the additional variance reduction provided by the stratification of the random parameter s domain especially at the coarsest levels additional computational cost savings are obtained by smoothing the indicator function with a gaussian kernel which proves to be an efficient and robust alternative to recently developed polynomial based techniques

a new weighted mean filter with a two phase detector for removing impulse noise abstract this paper proposes a new weighted mean filter with a two phase noise detector for image denoising operations are carried out by the detection followed by filtering strategy for detection a two phase noise detector is presented to detect impulse noise in in the first phase a rank ordered difference of road rod road scheme is introduced for detecting noise candidates different from most of the existing in detectors the proposed detector identifies a pixel by a fuzzy rule that matches the stochastic nature of in and greatly improves the denoising performance in the second phase a local image statistic minimum edge pixels difference mepd is proposed to identify edge pixels from noise candidates this preserves edges from being wrongly detected as noise therefore improves the detection accuracy for filtering we design a new weighted mean filter wmf that is more suitable for in to suppress the detected noisy pixels finally an iterative denoising algorithm is presented by combining the proposed two phase noise detector and the new wmf the proposed method is accessible and easy to implement experimental results show that the proposed method outperforms all the tested state of the art denoising methods with respect to the visual effects and quantitative measure results

new exact solutions for a free boundary system a method for constructing explicit exact solutions to nonlinear evolution equations is further developed the method is based on consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation the method is then applied to a free boundary problem based on the process of precipitant assisted protein crystal growth

structure based low rank model with graph nuclear norm regularization for noise removal nonlocal image representation methods including group based sparse coding and block matching 3 d filtering have shown their great performance in application to low level tasks the nonlocal prior is extracted from each group consisting of patches with similar intensities grouping patches based on intensity similarity however gives rise to disturbance and inaccuracy in estimation of the true images to address this problem we propose a structure based low rank model with graph nuclear norm regularization we exploit the local manifold structure inside a patch and group the patches by the distance metric of manifold structure with the manifold structure information a graph nuclear norm regularization is established and incorporated into a low rank approximation model we then prove that the graph based regularization is equivalent to a weighted nuclear norm and the proposed model can be solved by a weighted singular value thresholding algorithm extensive experiments on additive white gaussian noise removal and mixed noise removal demonstrate that the proposed method achieves a better performance than several state of the art algorithms

image denoising via sparse and redundant representations over learned dictionaries we address the image denoising problem where zero mean white and homogeneous gaussian additive noise is to be removed from a given image the approach taken is based on sparse and redundant representations over trained dictionaries using the k svd algorithm we obtain a dictionary that describes the image content effectively two training options are considered using the corrupted image itself or training on a corpus of high quality image database since the k svd is limited in handling small image patches we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image we show how such bayesian treatment leads to a simple and effective denoising algorithm this leads to a state of the art denoising performance equivalent and sometimes surpassing recently published leading alternative denoising methods

new non lie ansatze and exact solutions of nonlinear reaction diffusion convection equations a constructive method for obtaining new exact solutions of nonlinear evolution equations is further developed the method is based on the consideration of a fixed nonlinear partial differential equation together with an additional generating condition in the form of a linear high order ordinary differential equation using this method new non lie ansatze and exact solutions are obtained for two classes of diffusion equations with power and exponential nonlinearities which describe real processes in physics chemistry and biology the analysis of the found solutions and the relation of the proposed method to some approaches which have been suggested in several recently published papers are presented

mixed noise removal by weighted encoding with sparse nonlocal regularization mixed noise removal from natural images is a challenging task since the noise distribution usually does not have a parametric model and has a heavy tail one typical kind of mixed noise is additive white gaussian noise awgn coupled with impulse noise in many mixed noise removal methods are detection based methods they first detect the locations of in pixels and then remove the mixed noise however such methods tend to generate many artifacts when the mixed noise is strong in this paper we propose a simple yet effective method namely weighted encoding with sparse nonlocal regularization wesnr for mixed noise removal in wesnr there is not an explicit step of impulse pixel detection instead soft impulse pixel detection via weighted encoding is used to deal with in and awgn simultaneously meanwhile the image sparsity prior and nonlocal self similarity prior are integrated into a regularization term and introduced into the variational encoding framework experimental results show that the proposed wesnr method achieves leading mixed noise removal performance in terms of both quantitative measures and visual quality

from local kernel to nonlocal multiple model image denoising we review the evolution of the nonparametric regression modeling in imaging from the local nadaraya watson kernel estimate to the nonlocal means and further to transform domain filtering based on nonlocal block matching the considered methods are classified mainly according to two main features local nonlocal and pointwise multipoint here nonlocal is an alternative to local and multipoint is an alternative to pointwise these alternatives though obvious simplifications allow to impose a fruitful and transparent classification of the basic ideas in the advanced techniques within this framework we introduce a novel single and multiple model transform domain nonlocal approach the block matching and 3 d filtering bm3d algorithm which is currently one of the best performing denoising algorithms is treated as a special case of the latter approach

weighted couple sparse representation with classified regularization for impulse noise removal many impulse noise in reduction methods suffer from two obstacles the improper noise detectors and imperfect filters they used to address such issue in this paper a weighted couple sparse representation model is presented to remove in in the proposed model the complicated relationships between the reconstructed and the noisy images are exploited to make the coding coefficients more appropriate to recover the noise free image moreover the image pixels are classified into clear slightly corrupted and heavily corrupted ones different data fidelity regularizations are then accordingly applied to different pixels to further improve the denoising performance in our proposed method the dictionary is directly trained on the noisy raw data by addressing a weighted rank one minimization problem which can capture more features of the original data experimental results demonstrate that the proposed method is superior to several state of the art denoising methods

fast sampling of parameterised gaussian random fields abstract gaussian random fields are popular models for spatially varying uncertainties arising for instance in geotechnical engineering hydrology or image processing a gaussian random field is fully characterised by its mean function and covariance operator in more complex models these can also be partially unknown in this case we need to handle a family of gaussian random fields indexed with hyperparameters sampling for a fixed configuration of hyperparameters is already very expensive due to the nonlocal nature of many classical covariance operators sampling from multiple configurations increases the total computational cost severely in this report we employ parameterised karhunen loeve expansions for sampling to reduce the cost we construct a reduced basis surrogate built from snapshots of karhunen loeve eigenvectors in particular we consider matern type covariance operators with unknown correlation length and standard deviation we suggest a linearisation of the covariance function and describe the associated online offline decomposition in numerical experiments we investigate the approximation error of the reduced eigenpairs as an application we consider forward uncertainty propagation and bayesian inversion with an elliptic partial differential equation where the logarithm of the diffusion coefficient is a parameterised gaussian random field in the bayesian inverse problem we employ markov chain monte carlo on the reduced space to generate samples from the posterior measure all numerical experiments are conducted in 2d physical space with non separable covariance operators and finite element grids with 1 0 4 degrees of freedom

a new class of detail preserving filters for image processing a new class of median type filters for image processing is proposed in the filters linear fir substructures are used in conjunction with the median operation the root signals and noise attenuation properties of the fir median hybrid filters are analyzed and compared to representative edge preserving filtering operations the concept of multilevel median operation is introduced to improve the detail preserving property of conventional median and the fir median hybrid filters in the multilevel filters there exists a tradeoff between noise attenuation and detail preservation the analysis and examples indicate that fir median hybrid filters preserve details better and are computationally much more efficient than the conventional median and the k nearest neighbor averaging filters

a universal noise removal algorithm with an impulse detector we introduce a local image statistic for identifying noise pixels in images corrupted with impulse noise of random values the statistical values quantify how different in intensity the particular pixels are from their most similar neighbors we continue to demonstrate how this statistic may be incorporated into a filter designed to remove additive gaussian noise the result is a new filter capable of reducing both gaussian and impulse noises from noisy images effectively which performs remarkably well both in terms of quantitative measures of signal restoration and qualitative judgements of image quality our approach is extended to automatically remove any mix of gaussian and impulse noise

convergence analysis of multifidelity monte carlo estimation the multifidelity monte carlo method provides a general framework for combining cheap low fidelity approximations of an expensive high fidelity model to accelerate the monte carlo estimation of statistics of the high fidelity model output in this work we investigate the properties of multifidelity monte carlo estimation in the setting where a hierarchy of approximations can be constructed with known error and cost bounds our main result is a convergence analysis of multifidelity monte carlo estimation for which we prove a bound on the costs of the multifidelity monte carlo estimator under assumptions on the error and cost bounds of the low fidelity approximations the assumptions that we make are typical in the setting of similar monte carlo techniques numerical experiments illustrate the derived bounds

a new efficient approach for the removal of impulse noise from highly corrupted images a new framework for removing impulse noise from images is presented in which the nature of the filtering operation is conditioned on a state variable defined as the output of a classifier that operates on the differences between the input pixel and the remaining rank ordered pixels in a sliding window as part of this framework several algorithms are examined each of which is applicable to fixed and random valued impulse noise models first a simple two state approach is described in which the algorithm switches between the output of an identity filter and a rank ordered mean rom filter the technique achieves an excellent tradeoff between noise suppression and detail preservation with little increase in computational complexity over the simple median filter for a small additional cost in memory this simple strategy is easily generalized into a multistate approach using weighted combinations of the identity and rom filter in which the weighting coefficients can be optimized using image training data extensive simulations indicate that these methods perform significantly better in terms of noise suppression and detail preservation than a number of existing nonlinear techniques with as much as 40 impulse noise corruption moreover the method can effectively restore images corrupted with gaussian noise and mixed gaussian and impulse noise finally the method is shown to be extremely robust with respect to the training data and the percentage of impulse noise

exact solutions of a class of nonlinear boundary value problems with moving boundaries presents a method for the construction of the exact solutions of nonlinear bvps in melting and evaporation processes the case of smooth functions of thermal conductivity is studied and illustrations of some specific nonlinearities given

a detection statistic for random valued impulse noise this paper proposes an image statistic for detecting random valued impulse noise by this statistic we can identify most of the noisy pixels in the corrupted images combining it with an edge preserving regularization we obtain a powerful two stage method for denoising random valued impulse noise even for noise levels as high as 60 simulation results show that our method is significantly better than a number of existing techniques in terms of image restoration and noise detection

tri state median filter for image denoising a novel nonlinear filter called tri state median tsm filter is proposed for preserving image details while effectively suppressing impulse noise we incorporate the standard median sm filter and the center weighted median cwm filter into a noise detection framework to determine whether a pixel is corrupted before applying filtering unconditionally extensive simulation results demonstrate that the proposed filter consistently outperforms other median filters by balancing the tradeoff between noise reduction and detail preservation

optimal model management for multifidelity monte carlo estimation this work presents an optimal model management strategy that exploits multifidelity surrogate models to accelerate the estimation of statistics of outputs of computationally expensive high fidelity models existing acceleration methods typically exploit a multilevel hierarchy of surrogate models that follow a known rate of error decay and computational costs however a general collection of surrogate models which may include projection based reduced models data fit models support vector machines and simplified physics models does not necessarily give rise to such a hierarchy our multifidelity approach provides a framework to combine an arbitrary number of surrogate models of any type instead of relying on error and cost rates an optimization problem balances the number of model evaluations across the high fidelity and surrogate models with respect to error and costs we show that a unique analytic solution of the model management optimization problem exists under mild conditions on the models ou

switching bilateral filter with a texture noise detector for universal noise removal in this paper we propose a switching bilateral filter sbf with a texture and noise detector for universal noise removal operation was carried out in two stages detection followed by filtering for detection we propose the sorted quadrant median vector sqmv scheme which includes important features such as edge or texture information this information is utilized to allocate a reference median from sqmv which is in turn compared with a current pixel to classify it as impulse noise gaussian noise or noise free the sbf removes both gaussian and impulse noise without adding another weighting function the range filter inside the bilateral filter switches between the gaussian and impulse modes depending upon the noise classification result simulation results show that our noise detector has a high noise detection rate as well as a high classification rate for salt and pepper uniform impulse noise and mixed impulse noise unlike most other impulse noise filters the proposed sbf achieves high peak signal to noise ratio and great image quality by efficiently removing both types of mixed noise salt and pepper with uniform noise and salt and pepper with gaussian noise in addition the computational complexity of sbf is significantly less than that of other mixed noise filters

new exact solutions of a nonlinear cross diffusion system a system of two reaction diffusion equations with cross diffusion and quadratic nonlinearities is considered the system is a particular case the well known model proposed by shigesada et al 1979 j theor biol 79 83 new non lie ansatze special type substitutions reducing the system to systems of first order ordinary differential equations are obtained and applied to find its exact solutions several families of exact solutions are constructed their asymptotic behavior is investigated and some biological interpretation of the solutions is provided lie symmetry of this system is also discussed

image denoising by sparse 3 d transform domain collaborative filtering we propose a novel image denoising strategy based on an enhanced sparse representation in transform domain the enhancement of the sparsity is achieved by grouping similar 2d image fragments e g blocks into 3d data arrays which we call groups collaborative altering is a special procedure developed to deal with these 3d groups we realize it using the three successive steps 3d transformation of a group shrinkage of the transform spectrum and inverse 3d transformation the result is a 3d estimate that consists of the jointly filtered grouped image blocks by attenuating the noise the collaborative filtering reveals even the finest details shared by grouped blocks and at the same time it preserves the essential unique features of each individual block the filtered blocks are then returned to their original positions because these blocks are overlapping for each pixel we obtain many different estimates which need to be combined aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy a significant improvement is obtained by a specially developed collaborative wiener filtering an algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail an extension to color image denoising is also developed the experimental results demonstrate that this computationally scalable algorithm achieves state of the art denoising performance in terms of both peak signal to noise ratio and subjective visual quality

selective removal of impulse noise based on homogeneity level information we propose a decision based signal adaptive median filtering algorithm for removal of impulse noise our algorithm achieves accurate noise detection and high snr measures without smearing the fine details and edges in the image the notion of homogeneity level is defined for pixel values based on their global and local statistical properties the cooccurrence matrix technique is used to represent the correlations between a pixel and its neighbors and to derive the upper and lower bound of the homogeneity level noise detection is performed at two stages noise candidates are first selected using the homogeneity level and then a refining process follows to eliminate false detections the noise detection scheme does not use a quantitative decision measure but uses qualitative structural information and it is not subject to burdensome computations for optimization of the threshold values empirical results indicate that our scheme performs significantly better than other median filters in terms of noise suppression and detail preservation

non linear reaction diffusion systems with variable diffusivities lie symmetries ansatze and exact solutions abstract this work first considers the classical lie symmetry analysis of a class of systems of two quasilinear reaction diffusion equations having variable diffusivities subsequently non lie reductions to systems of first order ordinary differential equations are obtained for a subclass of these systems in particular families of exact solutions of a diffusive lotka volterra type system are constructed

positivity versus localization in degenerate diffusion equations on considere le probleme de cauchy u t u m f u 0 dans s r n o u x o u 0 x x r n ou m 1 n 1 et les fonctions f et u 0 satisfont les hypotheses 1 f c 1 o f o 0 2 u 0 est une fonction continue non negative definie sur r n a support borne

restoration of images corrupted by gaussian and uniform impulsive noise many approaches to image restoration are aimed at removing either gaussian or uniform impulsive noise this is because both types of degradation processes are distinct in nature and hence they are easier to manage when considered separately nevertheless it is possible to find them operating on the same image which produces a hard damage this happens when an image already contaminated by gaussian noise in the image acquisition procedure undergoes impulsive corruption during its digital transmission here we propose a principled method to remove both types of noise it is based on a bayesian classification of the input pixels which is combined with the kernel regression framework

a bi fidelity method for the multiscale boltzmann equation with random parameters abstract in this paper we study the multiscale boltzmann equation with multi dimensional random parameters by a bi fidelity stochastic collocation sc method developed in 52 70 71 by choosing the compressible euler system as the low fidelity model we adapt the bi fidelity sc method to combine computational efficiency of the low fidelity model with high accuracy of the high fidelity boltzmann model with only a small number of high fidelity asymptotic preserving solver runs for the boltzmann equation the bi fidelity approximation can capture well the macroscopic quantities of the solution to the boltzmann equation in the random space a priori estimate on the accuracy between the high and bi fidelity solutions together with a convergence analysis is established finally we present extensive numerical experiments to verify the efficiency and accuracy of our proposed method

a universal denoising framework with a new impulse detector and nonlocal means impulse noise detection is a critical issue when removing impulse noise and impulse gaussian mixed noise in this paper we propose a new detection mechanism for universal noise and a universal noise filtering framework based on the nonlocal means nl means the operation is carried out in two stages i e detection followed by filtering for detection first we propose the robust outlyingness ratio ror for measuring how impulselike each pixel is and then all the pixels are divided into four clusters according to the ror values second different decision rules are used to detect the impulse noise based on the absolute deviation to the median in each cluster in order to make the detection results more accurate and more robust the from coarse to fine strategy and the iterative framework are used in addition the detection procedure consists of two stages i e the coarse and fine detection stages for filtering the nl means are extended to the impulse noise by introducing a reference image then a universal denoising framework is proposed by combining the new detection mechanism with the nl means ror nlm finally extensive simulation results show that the proposed noise detector is superior to most existing detectors and the ror nlm produces excellent results and outperforms most existing filters for different noise models unlike most of the other impulse noise filters the proposed ror nlm also achieves high peak signal to noise ratio and great image quality by efficiently removing impulse gaussian mixed noise

goal oriented adaptive modeling of random heterogeneous media and model based multilevel monte carlo methods abstract methods for generating sequences of surrogates approximating fine scale models of two phase random heterogeneous media are presented that are designed to adaptively control the modeling error in key quantities of interest qois for specificity the base models considered involve stochastic partial differential equations characterizing for example steady state heat conduction in random heterogeneous materials and stochastic elastostatics problems in linear elasticity the adaptive process involves generating a sequence of surrogate models defined on a partition of the solution domain into regular subdomains and then based on estimates of the error in the qois assigning homogenized effective material properties to some subdomains and full random fine scale properties to others to control the error so as to meet a preset tolerance new model based multilevel monte carlo mbmlmc methods are presented that exploit the adaptive sequencing and are designed to reduce variances and thereby accelerate convergence of monte carlo sampling estimates of cost and mean squared error of the method are presented the results of several numerical experiments are discussed that confirm that substantial saving in computer costs can be realized through the use of controlled surrogate models and the associated mbmlmc algorithms

a robust bi sparsity model with non local regularization for mixed noise reduction sparse representation model srm has been widely used in many image processing and computer vision tasks however the conventional srm usually neglects the prior knowledge about similar signals considering the fact that similar signals also have subtle differences in this paper we propose a robust bi sparsity model rbsm to effectively exploit the prior knowledge about the similarities and the distinctions of signals in rbsm similar signals are encouraged to be coded on the same sub dictionary but the distinctiveness of similar signals is also addressed by imposing the l0 norm regularization on the difference between each coefficient and its non local means in addition a weight vector is incorporated into the loss function to make the proposed model robust to outliers we apply rbsm for mixed noise reduction and experimental results show that our proposed model is superior to several state of the art mixed noise removal methods