vector sparse representation of color image using quaternion matrix analysis traditional sparse image models treat color image pixel as a scalar which represents color channels separately or concatenate color channels as a monochrome image in this paper we propose a vector sparse representation model for color images using quaternion matrix analysis as a new tool for color image representation its potential applications in several image processing tasks are presented including color image reconstruction denoising inpainting and super resolution the proposed model represents the color image as a quaternion matrix where a quaternion based dictionary learning algorithm is presented using the k quaternion singular value decomposition qsvd generalized k means clustering for qsvd method it conducts the sparse basis selection in quaternion space which uniformly transforms the channel images to an orthogonal color space in this new color space it is significant that the inherent color structures can be completely preserved during vector reconstruction moreover the proposed sparse model is more efficient comparing with the current sparse models for image restoration tasks due to lower redundancy between the atoms of different color channels the experimental results demonstrate that the proposed sparse image model avoids the hue bias issue successfully and shows its potential as a general and powerful tool in color image analysis and processing domain

color sparse representations for image processing review models and prospects sparse representations have been extended to deal with color images composed of three channels a review of dictionary learning based sparse representations for color images is made here detailing the differences between the models and comparing their results on the real and simulated data these models are considered in a unifying framework that is based on the degrees of freedom of the linear filtering transformation of the color channels moreover this allows it to be shown that the scalar quaternionic linear model is equivalent to constrained matrix based color filtering which highlights the filtering implicitly applied through this model based on this reformulation the new color filtering model is introduced using unconstrained filters in this model spatial morphologies of color images are encoded by atoms and colors are encoded by color filters color variability is no longer captured in increasing the dictionary size but with color filters this gives an efficient color representation

dual geometric neighbor embedding for image super resolution with sparse tensor neighbors embedding ne technology has proved its efficiency in single image super resolution sisr however image patches do not strictly follow the similar structure in the low resolution and high resolution spaces consequently leading to a bias to the image restoration in this paper considering that patches are a set of data with multiview characteristics and spatial organization we advance a dual geometric neighbor embedding dgne approach for sisr in dgne multiview features and local spatial neighbors of patches are explored to find a feature spatial manifold embedding for images we adopt a geometrically motivated assumption that for each patch there exists a small neighborhood in which only the patches that come from the same feature spatial manifold will lie approximately in a low dimensional affine subspace formulated by sparse neighbors in order to find the sparse neighbors a tensor simultaneous orthogonal matching pursuit algorithm is advanced to realize a joint sparse coding of feature spatial image tensors some experiments are performed on realizing a 3x amplification of natural images and the recovered results prove its efficiency and superiority to its counterparts

a note on the sample complexity of the er spud algorithm by spielman wang and wright for exact recovery of sparsely used dictionaries we consider the problem of recovering an invertible n n matrix a and a sparse n p random matrix x based on the observation of y ax up to a scaling and permutation of columns of a and rows of x using only elementary tools from the theory of empirical processes we show that a version of the er spud algorithm by spielman wang and wright with high probability recovers a and x exactly provided that p cn log n which is optimal up to the constant c

single image super resolution via adaptive high dimensional non local total variation and adaptive geometric feature single image super resolution sr is very important in many computer vision systems however as a highly ill posed problem its performance mainly relies on the prior knowledge among these priors the non local total variation nltv prior is very popular and has been thoroughly studied in recent years nevertheless technical challenges remain because nltv only exploits a fixed non shifted target patch in the patch search process a lack of similar patches is inevitable in some cases thus the non local similarity cannot be fully characterized and the effectiveness of nltv cannot be ensured based on the motivation that more accurate non local similar patches can be found by using shifted target patches a novel multishifted similar patch search msps strategy is proposed with this strategy nltv is extended as a newly proposed super high dimensional nltv shnltv prior to fully exploit the underlying non local similarity however as shnltv is very high dimensional applying it directly to sr is very difficult to solve this problem a novel statistics based dimension reduction strategy is proposed and then applied to shnltv thus shnltv becomes a more computationally effective prior that we call adaptive high dimensional non local total variation ahnltv in ahnltv a novel joint weight strategy that fully exploits the potential of the msps based non local similarity is proposed to further boost the performance of ahnltv the adaptive geometric duality agd prior is also incorporated finally an efficient split bregman iteration based algorithm is developed to solve the ahnltv agd driven minimization problem extensive experiments validate the proposed method achieves better results than many state of the art sr methods in terms of both objective and subjective qualities

single image super resolution using local geometric duality and non local similarity super resolution sr from a single image plays an important role in many computer vision applications it aims to estimate a high resolution hr image from an input low resolution lr image to ensure a reliable and robust estimation of the hr image we propose a novel single image sr method that exploits both the local geometric duality gd and the non local similarity of images the main principle is to formulate these two typically existing features of images as effective priors to constrain the super resolved results in consideration of this principle the robust soft decision interpolation method is generalized as an outstanding adaptive gd agd based local prior to adaptively design weights for the agd prior a local non smoothness detection method and a directional standard deviation based weights selection method are proposed after that the agd prior is combined with a variational framework based non local prior furthermore the proposed algorithm is speeded up by a fast gd matrices construction method which primarily relies on the selective pixel processing the extensive experimental results verify the effectiveness of the proposed method compared with several state of the art sr 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

nonconvex nonsmooth low rank minimization via iteratively reweighted nuclear norm the nuclear norm is widely used as a convex surrogate of the rank function in compressive sensing for low rank matrix recovery with its applications in image recovery and signal processing however solving the nuclear norm based relaxed convex problem usually leads to a suboptimal solution of the original rank minimization problem in this paper we propose to use a family of nonconvex surrogates of l 0 norm on the singular values of a matrix to approximate the rank function this leads to a nonconvex nonsmooth minimization problem then we propose to solve the problem by an iteratively reweighted nuclear norm irnn algorithm irnn iteratively solves a weighted singular value thresholding problem which has a closed form solution due to the special properties of the nonconvex surrogate functions we also extend irnn to solve the nonconvex problem with two or more blocks of variables in theory we prove that the irnn decreases the objective function value monotonically and any limit point is a stationary point extensive experiments on both synthesized data and real images demonstrate that irnn enhances the low rank matrix recovery compared with the state of the art convex algorithms

a novel face hallucination scheme based on singular value decomposition abstract in this paper an efficient mapping model based on singular value decomposition svd is proposed for face hallucination we can observe and prove that the main singular values of an image at one resolution have approximately linear relationships with their counterparts at other resolutions this makes the estimation of the singular values of the corresponding high resolution hr face images from a low resolution lr face image more reliable from the signal processing point of view this can effectively preserve and reconstruct the dominant information in the hr face images interpolating the other two matrices obtained from the svd of the lr image does not change either the primary facial structure or the pattern of the face image the corresponding two matrices for the hr face images can be constructed in a coarse to fine manner using global reconstruction our proposed method retains the holistic structure of face images while the learned mapping matrices which are represented as embedding coefficients of the individual mapping matrices learned from lr hr training pairs can be seen as holistic constraints in the reconstruction of hr images compared to state of the art algorithms experiments show that our proposed face hallucination scheme is effective in terms of producing plausible hr images with both a holistic structure and high frequency details

compressive sensing for monostatic scattering from 3 d nurbs geometries compressive sensing cs proposes to capture compressible signals at a rate significantly smaller than the nyquist shannon rate yet allows accurate signal reconstruction cs exploits the fact that the signal of interest is compressible by a known transform e g fourier wavelet etc and it employs nonadaptive linear projections that preserve the structure of the signal approximate reconstruction is then obtained from these measurements by solving an optimization problem in this paper a new method that introduces ideas from cs to the method of moments mom is proposed to solve electromagnetic monostatic scattering from conducting bodies of arbitrary shape efficiently modeled by nonuniform rational b spline nurbs surfaces the new method is applied to obtain monostatic induced currents and radar cross section values of several objects modeled with nurbs surfaces the efficiency and accuracy of the new method are verified by comparing it against the multilevel fast multipole algorithm and the traditional mom the influences of the structure of the sparse basis functions and the number of measurements on the recovery error are also investigated

robust face recognition with kernelized locality sensitive group sparsity representation in this paper a novel joint sparse representation method is proposed for robust face recognition we embed both group sparsity and kernelized locality sensitive constraints into the framework of sparse representation the group sparsity constraint is designed to utilize the grouped structure information in the training data the local similarity between test and training data is measured in the kernel space instead of the euclidian space as a result the embedded nonlinear information can be effectively captured leading to a more discriminative representation we show that by integrating the kernelized local sensitivity constraint and the group sparsity constraint the embedded structure information can be better explored and significant performance improvement can be achieved on the one hand experiments on the orl ar extended yale b and lfw data sets verify the superiority of our method on the other hand experiments on two unconstrained data sets the lfw and the ijb a show that the utilization of sparsity can improve recognition performance especially on the data sets with large pose variation

fast image upsampling via the displacement field in this paper we present a fast image upsampling method within a two scale framework to ensure the sharp construction of upsampled image for both large scale edges and small scale structures in our approach the low frequency image is recovered via a novel sharpness preserving interpolation technique based on a well constructed displacement field which is estimated by a cross resolution sharpness preserving model within this model the distances of pixels on edges are preserved which enables the recovery of sharp edges in the high resolution result likewise local high frequency structures are reconstructed via a sharpness preserving reconstruction algorithm extensive experiments show that our method outperforms current state of the art approaches based on quantitative and qualitative evaluations as well as perceptual evaluation by a user study moreover our approach is very fast so as to be practical for real applications

single image super resolution using global regression based on multiple local linear mappings super resolution sr has become more vital because of its capability to generate high quality ultra high definition uhd high resolution hr images from low resolution lr input images conventional sr methods entail high computational complexity which makes them difficult to be implemented for up scaling of full high definition input images into uhd resolution images nevertheless our previous super interpolation si method showed a good compromise between peak signal to noise ratio psnr performances and computational complexity however since si only utilizes simple linear mappings it may fail to precisely reconstruct hr patches with complex texture in this paper we present a novel sr method which inherits the large to small patch conversion scheme from si but uses global regression based on local linear mappings glm thus our new sr method is called glm si in glm si each lr input patch is divided into 25 overlapped subpatches next based on the local properties of these subpatches 25 different local linear mappings are applied to the current lr input patch to generate 25 hr patch candidates which are then regressed into one final hr patch using a global regressor the local linear mappings are learned cluster wise in our off line training phase the main contribution of this paper is as follows previously linear mapping based conventional sr methods including si only used one simple yet coarse linear mapping to each patch to reconstruct its hr version on the contrary for each lr input patch our glm si is the first to apply a combination of multiple local linear mappings where each local linear mapping is found according to local properties of the current lr patch therefore it can better approximate nonlinear lr to hr mappings for hr patches with complex texture experiment results show that the proposed glm si method outperforms most of the state of the art methods and shows comparable psnr performance with much lower computational complexity when compared with a super resolution method based on convolutional neural nets srcnn15 compared with the previous si method that is limited with a scale factor of 2 glm si shows superior performance with average 0 79 db higher in psnr and can be used for scale factors of 3 or higher

multidimensional scaling for matching low resolution face images face recognition performance degrades considerably when the input images are of low resolution lr as is often the case for images taken by surveillance cameras or from a large distance in this paper we propose a novel approach for matching low resolution probe images with higher resolution gallery images which are often available during enrollment using multidimensional scaling mds the ideal scenario is when both the probe and gallery images are of high enough resolution to discriminate across different subjects the proposed method simultaneously embeds the low resolution probe images and the high resolution gallery images in a common space such that the distance between them in the transformed space approximates the distance had both the images been of high resolution the two mappings are learned simultaneously from high resolution training images using an iterative majorization algorithm extensive evaluation of the proposed approach on the multi pie data set with probe image resolution as low as 8 x00d7 6 pixels illustrates the usefulness of the method we show that the proposed approach improves the matching performance significantly as compared to performing matching in the low resolution domain or using super resolution techniques to obtain a higher resolution test image prior to recognition experiments on low resolution surveillance images from the surveillance cameras face database further highlight the effectiveness of the approach

nonlocally centralized sparse representation for image restoration sparse representation models code an image patch as a linear combination of a few atoms chosen out from an over complete dictionary and they have shown promising results in various image restoration applications however due to the degradation of the observed image e g noisy blurred and or down sampled the sparse representations by conventional models may not be accurate enough for a faithful reconstruction of the original image to improve the performance of sparse representation based image restoration in this paper the concept of sparse coding noise is introduced and the goal of image restoration turns to how to suppress the sparse coding noise to this end we exploit the image nonlocal self similarity to obtain good estimates of the sparse coding coefficients of the original image and then centralize the sparse coding coefficients of the observed image to those estimates the so called nonlocally centralized sparse representation ncsr model is as simple as the standard sparse representation model while our extensive experiments on various types of image restoration problems including denoising deblurring and super resolution validate the generality and state of the art performance of the proposed ncsr algorithm

optimal couple projections for domain adaptive sparse representation based classification in recent years sparse representation based classification src is one of the most successful methods and has been shown impressive performance in various classification tasks however when the training data have a different distribution than the testing data the learned sparse representation may not be optimal and the performance of src will be degraded significantly to address this problem in this paper we propose an optimal couple projections for domain adaptive src ocpd src method in which the discriminative features of data in the two domains are simultaneously learned with the dictionary that can succinctly represent the training and testing data in the projected space ocpd src is designed based on the decision rule of src with the objective to learn coupled projection matrices and a common discriminative dictionary such that the between class sparse reconstruction residuals of data from both domains are maximized and the within class sparse reconstruction residuals of data are minimized in the projected low dimensional space thus the resulting representations can well fit src and simultaneously have a better discriminant ability in addition our method can be easily extended to multiple domains and can be kernelized to deal with the nonlinear structure of data the optimal solution for the proposed method can be efficiently obtained following the alternative optimization method extensive experimental results on a series of benchmark databases show that our method is better or comparable to many state of the art methods

sparsity based image error concealment via adaptive dual dictionary learning and regularization in this paper we propose a novel sparsity based image error concealment ec algorithm through adaptive dual dictionary learning and regularization we define two feature spaces the observed space and the latent space corresponding to the available regions and the missing regions of image under test respectively we learn adaptive and complete dictionaries individually for each space where the training data are collected via an adaptive template matching mechanism based on the piecewise stationarity of natural images a local correlation model is learned to bridge the sparse representations of the aforementioned dual spaces allowing us to transfer the knowledge of the available regions to the missing regions for ec purpose eventually the ec task is formulated as a unified optimization problem where the sparsity of both spaces and the learned correlation model are incorporated experimental results show that the proposed method outperforms the state of the art techniques in terms of both objective and perceptual metrics

period doubling in a periodically forced belousov zhabotinsky reaction using an open flow reactor periodically perturbed with light we observe subharmonic frequency locking of the oscillatory belousov zhabotinsky chemical reaction at one sixth the forcing frequency 6 1 over a region of the parameter space of forcing intensity and forcing frequency where the farey sequence dictates we should observe one third the forcing frequency 3 1 in this parameter region the spatial pattern also changes from slowly moving traveling waves to standing waves with a smaller wavelength numerical simulations of the fitzhugh nagumo equations show qualitative agreement with the experimental observations and indicate that the oscillations in the experiment are a result of period doubling

super resolution reconstruction of μ ct image of rock sample using neighbour embedding algorithm abstract x ray computed tomography ct is considered to be the most effective way to obtain the inner structure of rock sample without destructions however its limited resolution hampers its ability to probe sub micro structures which is critical for flow transportation of rock sample in this study we propose an innovative methodology to improve the resolution of ct image using neighbour embedding algorithm where low frequency information is provided by ct image itself while high frequency information is supplemented by high resolution scanning electron microscopy sem image in order to obtain prior for reconstruction a large number of image patch pairs contain high and low image patches are extracted from the gaussian image pyramid generated by sem image these image patch pairs contain abundant information about tomographic evolution of local porous structures under different resolution spaces relying on the assumption of self similarity of porous structure this prior information can be used to supervise the reconstruction of high resolution ct image effectively the experimental results show that the proposed method is able to achieve the state of the art performance

inverse sparse tracker with a locally weighted distance metric sparse representation has been recently extensively studied for visual tracking and generally facilitates more accurate tracking results than classic methods in this paper we propose a sparsity based tracking algorithm that is featured with two components 1 an inverse sparse representation formulation and 2 a locally weighted distance metric in the inverse sparse representation formulation the target template is reconstructed with particles which enables the tracker to compute the weights of all particles by solving only one ell 1 optimization problem and thereby provides a quite efficient model this is in direct contrast to most previous sparse trackers that entail solving one optimization problem for each particle however we notice that this formulation with normal euclidean distance metric is sensitive to partial noise like occlusion and illumination changes to this end we design a locally weighted distance metric to replace the euclidean one similar ideas of using local features appear in other works but only being supported by popular assumptions like local models could handle partial noise better than holistic models without any solid theoretical analysis in this paper we attempt to explicitly explain it from a mathematical view on that basis we further propose a method to assign local weights by exploiting the temporal and spatial continuity in the proposed method appearance changes caused by partial occlusion and shape deformation are carefully considered thereby facilitating accurate similarity measurement and model update the experimental validation is conducted from two aspects 1 self validation on key components and 2 comparison with other state of the art algorithms results over 15 challenging sequences show that the proposed tracking algorithm performs favorably against the existing sparsity based trackers and the other state of the art methods

on solitary wave solutions of ac driven complex ginzburg landau equation a new class of periodic solutions of modified complex ginzburg landau equation phase locked to a time dependent force by applying a nonfeedback mechanism for chaos control have been found the reported solutions are necessarily of the rational form containing trigonometric and hyperbolic functions

nonnegative sparse locality preserving hashing it is a np hard problem to optimize the objective function of hash based similarity search algorithms such as spectral hashing and self taught hashing to make the problem solvable existing methods have relaxed the constraints on hash codes from binary values discrete to real values continuous then eigenvalue decomposition was employed to achieve the relaxed real solution the main problem is that the signs of the relaxed continuous solution are mixed such results may deviate severely from the true solution which has lead to significant semantic loss moreover eigenvalue decomposition confronts singularity problem when the dimension of the data is larger than the sample size to address these problems we propose a novel method named nonnegative sparse locality preserving hashing nslph nonnegative and sparse constraints are imposed for a more accurate solution which preserves semantic information well then we have applied nonnegative quadratic programming and multiplicative updating to solve the optimization problem which successfully avoids the singularity problem of the eigenvalue decomposition the extensive experiments presented in this paper demonstrate that the proposed approach outperforms the state of the art algorithms

sparse coding from a bayesian perspective sparse coding is a promising theme in computer vision most of the existing sparse coding methods are based on either l0 or l1 penalty which often leads to unstable solution or biased estimation this is because of the nonconvexity and discontinuity of the l0 penalty and the over penalization on the true large coefficients of the l1 penalty in this paper sparse coding is interpreted from a novel bayesian perspective which results in a new objective function through maximum a posteriori estimation the obtained solution of the objective function can generate more stable results than the l0 penalty and smaller reconstruction errors than the l1 penalty in addition the convergence property of the proposed algorithm for sparse coding is also established the experiments on applications in single image super resolution and visual tracking demonstrate that the proposed method is more effective than other state of the art methods

solving inverse problems with piecewise linear estimators from gaussian mixture models to structured sparsity a general framework for solving image inverse problems with piecewise linear estimations is introduced in this paper the approach is based on gaussian mixture models which are estimated via a maximum a posteriori expectation maximization algorithm a dual mathematical interpretation of the proposed framework with a structured sparse estimation is described which shows that the resulting piecewise linear estimate stabilizes the estimation when compared with traditional sparse inverse problem techniques we demonstrate that in a number of image inverse problems including interpolation zooming and deblurring of narrow kernels the same simple and computationally efficient algorithm yields results in the same ballpark as that of the state of the art

image zoom completion we consider the problem of recovering a high resolution image from a pair consisting of a complete low resolution image and a high resolution but incomplete one we refer to this task as the image zoom completion problem after discussing possible contexts in which this setting may arise we introduce a nonlocal regularization strategy giving full details concerning the numerical optimization of the corresponding energy and discussing its benefits and shortcomings we also derive two total variation based algorithms and evaluate the performance of the proposed methods on a set of natural and textured images we compare the results and get with those obtained with two recent state of the art single image super resolution algorithms

image interpolation via graph based bayesian label propagation in this paper we propose a novel image interpolation algorithm via graph based bayesian label propagation the basic idea is to first create a graph with known and unknown pixels as vertices and with edge weights encoding the similarity between vertices then the problem of interpolation converts to how to effectively propagate the label information from known points to unknown ones this process can be posed as a bayesian inference in which we try to combine the principles of local adaptation and global consistency to obtain accurate and robust estimation specially our algorithm first constructs a set of local interpolation models which predict the intensity labels of all image samples and a loss term will be minimized to keep the predicted labels of the available low resolution lr samples sufficiently close to the original ones then all of the losses evaluated in local neighborhoods are accumulated together to measure the global consistency on all samples moreover a graph laplacian based manifold regularization term is incorporated to penalize the global smoothness of intensity labels such smoothing can alleviate the insufficient training of the local models and make them more robust finally we construct a unified objective function to combine together the global loss of the locally linear regression square error of prediction bias on the available lr samples and the manifold regularization term it can be solved with a closed form solution as a convex optimization problem experimental results demonstrate that the proposed method achieves competitive performance with the state of the art image interpolation algorithms

super resolution person re identification with semi coupled low rank discriminant dictionary learning person re identification has been widely studied due to its importance in surveillance and forensics applications in practice gallery images are high resolution hr while probe images are usually low resolution lr in the identification scenarios with large variation of illumination weather or quality of cameras person re identification in this kind of scenarios which we call super resolution sr person re identification has not been well studied in this paper we propose a semi coupled low rank discriminant dictionary learning sld2l approach for sr person re identification task with the hr and lr dictionary pair and mapping matrices learned from the features of hr and lr training images sld2l can convert the features of the lr probe images into hr features to ensure that the converted features have favorable discriminative capability and the learned dictionaries can well characterize intrinsic feature spaces of the hr and lr images we design a discriminant term and a low rank regularization term for sld2l moreover considering that low resolution results in different degrees of loss for different types of visual appearance features we propose a multi view sld2l mvsld2l approach which can learn the type specific dictionary pair and mappings for each type of feature experimental results on multiple publicly available data sets demonstrate the effectiveness of our proposed approaches for the sr person re identification task

numerical solution of burgers fisher equation by cubic b spline quasi interpolation abstract in this paper numerical solution of the burgers equation is presented based on the cubic b spline quasi interpolation at first the cubic b spline quasi interpolation is introduced moreover the numerical scheme is presented by using the derivative of the quasi interpolation to approximate the spatial derivative of the dependent variable and a low order forward difference to approximate the time derivative of the dependent variable the accuracy of the proposed method is demonstrated by some test problems the numerical results are found in good agreement with exact solutions the advantage of the resulting scheme is that the algorithm is very simple so it is very easy to implement

analysis operator learning and its application to image reconstruction exploiting a priori known structural information lies at the core of many image reconstruction methods that can be stated as inverse problems the synthesis model which assumes that images can be decomposed into a linear combination of very few atoms of some dictionary is now a well established tool for the design of image reconstruction algorithms an interesting alternative is the analysis model where the signal is multiplied by an analysis operator and the outcome is assumed to be sparse this approach has only recently gained increasing interest the quality of reconstruction methods based on an analysis model severely depends on the right choice of the suitable operator in this paper we present an algorithm for learning an analysis operator from training images our method is based on lp norm minimization on the set of full rank matrices with normalized columns we carefully introduce the employed conjugate gradient method on manifolds and explain the underlying geometry of the constraints moreover we compare our approach to state of the art methods for image denoising inpainting and single image super resolution our numerical results show competitive performance of our general approach in all presented applications compared to the specialized state of the art techniques

higher order muscl scheme for transport equation originating in a neuronal model we consider a transport equation with mixed boundary conditions dirichlet and neumann originating in a neuronal model this equation contains point wise delay and advanced argument the objective of this paper is to construct and analyze higher order muscl scheme to find a numerical solution the developed scheme is stable and convergent the importance of this scheme is that it is valid for large as well as for small values of point wise delay and advance some test examples are included to examine the behavior of the solution and to verify the order of convergence the effect of point wise delay and advance arguments on the solution is shown graphically

contrast guided image interpolation in this paper a contrast guided image interpolation method is proposed that incorporates contrast information into the image interpolation process given the image under interpolation four binary contrast guided decision maps cdms are generated and used to guide the interpolation filtering through two sequential stages 1 the 45 and 135 cdms for interpolating the diagonal pixels and 2 the 0 and 90 cdms for interpolating the row and column pixels after applying edge detection to the input image the generation of a cdm lies in evaluating those nearby non edge pixels of each detected edge for re classifying them possibly as edge pixels this decision is realized by solving two generalized diffusion equations over the computed directional variation dv fields using a derived numerical approach to diffuse or spread the contrast boundaries or edges respectively the amount of diffusion or spreading is proportional to the amount of local contrast measured at each detected edge the diffused dv fields are then thresholded for yielding the binary cdms respectively therefore the decision bands with variable widths will be created on each cdm the two cdms generated in each stage will be exploited as the guidance maps to conduct the interpolation process for each declared edge pixel on the cdm a 1 d directional filtering will be applied to estimate its associated to be interpolated pixel along the direction as indicated by the respective cdm otherwise a 2 d directionless or isotropic filtering will be used instead to estimate the associated missing pixels for each declared non edge pixel extensive simulation results have clearly shown that the proposed contrast guided image interpolation is superior to other state of the art edge guided image interpolation methods in addition the computational complexity is relatively low when compared with existing methods hence it is fairly attractive for real time image applications

nonparametric bayesian dictionary learning for analysis of noisy and incomplete images nonparametric bayesian methods are considered for recovery of imagery based upon compressive incomplete and or noisy measurements a truncated beta bernoulli process is employed to infer an appropriate dictionary for the data under test and also for image recovery in the context of compressive sensing significant improvements in image recovery are manifested using learned dictionaries relative to using standard orthonormal image expansions the compressive measurement projections are also optimized for the learned dictionary additionally we consider simpler incomplete measurements defined by measuring a subset of image pixels uniformly selected at random spatial interrelationships within imagery are exploited through use of the dirichlet and probit stick breaking processes several example results are presented with comparisons to other methods in the literature

regularized label relaxation linear regression linear regression lr and some of its variants have been widely used for classification problems most of these methods assume that during the learning phase the training samples can be exactly transformed into a strict binary label matrix which has too little freedom to fit the labels adequately to address this problem in this paper we propose a novel regularized label relaxation lr method which has the following notable characteristics first the proposed method relaxes the strict binary label matrix into a slack variable matrix by introducing a nonnegative label relaxation matrix into lr which provides more freedom to fit the labels and simultaneously enlarges the margins between different classes as much as possible second the proposed method constructs the class compactness graph based on manifold learning and uses it as the regularization item to avoid the problem of overfitting the class compactness graph is used to ensure that the samples sharing the same labels can be kept close after they are transformed two different algorithms which are respectively based on ell 2 norm and ell 2 1 norm loss functions are devised these two algorithms have compact closed form solutions in each iteration so that they are easily implemented extensive experiments show that these two algorithms outperform the state of the art algorithms in terms of the classification accuracy and running time

sampling curves with finite rate of innovation in this paper we extend the theory of sampling signals with finite rate of innovation fri to a specific class of two dimensional curves which are defined implicitly as the zeros of a mask function here the mask function has a parametric representation as a weighted summation of a finite number of complex exponentials and therefore has finite rate of innovation an associated edge image which is discontinuous on the predefined parametric curve is proved to satisfy a set of linear annihilation equations we show that it is possible to reconstruct the parameters of the curve i e to detect the exact edge positions in the continuous domain based on the annihilation equations robust reconstruction algorithms are also developed to cope with scenarios with model mismatch moreover the annihilation equations that characterize the curve are linear constraints that can be easily exploited in optimization problems for further image processing e g image up sampling we demonstrate one potential application of the annihilation algorithm with examples in edge preserving interpolation experimental results with both synthetic curves as well as edges of natural images clearly show the effectiveness of the annihilation constraint in preserving sharp edges and improving snrs

kernel collaborative face recognition recent research has demonstrated the effectiveness of linear representation i e sparse representation group sparse representation and collaborative representation for face recognition and other vision problems however this linear representation assumption does not consider the non linear relationship of samples and limits the usage of different features with non linear metrics in this paper we present some insights of linear and non linear representation based classifiers first we present a general formulation known as kernel collaborative representation to encompass several effective representation based classifiers within a unified framework based on this framework different algorithms can be developed by choosing proper kernel functions regularization terms and additional constraints second within the proposed framework we develop a simple yet effective algorithm with squared 2 regularization and apply it to face recognition with local binary patterns as well as the hamming kernel we conduct numerous experiments on the extended yale b ar multi pie ployu nir ployu hs eurecom kinect and feret face databases experimental results demonstrate that our algorithm achieves favorable performance in terms of accuracy and speed especially for the face recognition problems with small training datasets and heavy occlusion in addition we attempt to combine different kernel functions by using different weights in an additive manner the experimental results show that the proposed combination scheme provides some additional improvement in terms of accuracy highlightswe present a general formulation known as kernel collaborative representation we develop an effective algorithm with squared l2 regularization we combine different kernels by using different weights in an additive manner our algorithm can achieve favorable performance in terms of accuracy and speed

responses of the complex ginzburg landau equation under harmonic forcing abstract we study the effect of external harmonic forcing on a one dimensional complex ginzburg landau equation cgle for a sufficiently large forcing amplitude a homogeneous state with no spatial structure is observed as the forcing amplitude decreases the state becomes unstable forming a spatially periodic stripe state via a supercritical bifurcation an approximate phase equation is derived and an analytic solution for the stripe state is obtained as the forcing amplitude decreases even further the system undergoes a depinning transition into the state where the average phase has a non zero velocity

blind facial image quality enhancement using non rigid semantic patches we propose a new way to solve a very general blind inverse problem of multiple simultaneous degradations such as blur resolution reduction noise and contrast changes without explicitly estimating the degradation the proposed concept is based on combining semantic non rigid patches problem specific high quality prior data and non rigid registration tools we show how a significant quality enhancement can be achieved both visually and quantitatively in the case of facial images the method is demonstrated on the problem of cellular photography quality enhancement of dark facial images for different identities expressions and poses and is compared with the state of the art denoising deblurring super resolution and color correction methods

novel example based method for super resolution and denoising of medical images in this paper we propose a novel example based method for denoising and super resolution of medical images the objective is to estimate a high resolution image from a single noisy low resolution image with the help of a given database of high and low resolution image patch pairs denoising and super resolution in this paper is performed on each image patch for each given input low resolution patch its high resolution version is estimated based on finding a nonnegative sparse linear representation of the input patch over the low resolution patches from the database where the coefficients of the representation strongly depend on the similarity between the input patch and the sample patches in the database the problem of finding the nonnegative sparse linear representation is modeled as a nonnegative quadratic programming problem the proposed method is especially useful for the case of noise corrupted and low resolution image experimental results show that the proposed method outperforms other state of the art super resolution methods while effectively removing noise

dual sparsity regularized sparse representation for single image super resolution row nonlocal similarity regularization term with l1 norm constraint is explored dual sparsity regularized sparse representation model is presented for sisr iterative shrinkage algorithm is extended to solve dual l1 norm constraints model recently by exploring the column nonlocal similarity prior among the sparse representation coefficients the column nonlocal similarity sparse representation models for solving the ill posed single image super resolution sisr problem are attracting more and more attention however these conventional models consider only the prior among nonlocal similar sparse representation coefficients and fail to consider the prior among all entries or rows of the sparse representation coefficient hence the modeling capability may be limited in fact if a cluster of similar representation coefficients is rearranged into a matrix in the sparse representation coefficient space the nonlocal similarity priors exist both among columns and rows using the row nonlocal similarity prior a row nonlocal similarity regularization term with l1 norm constraint is explored by introducing it to the conventional column nonlocal similarity sparse representation model we present a dual sparsity regularized sparse representation dsrsr model a surrogate function based iterative shrinkage algorithm is introduced to effectively solve the proposed model extensive experiments on sisr demonstrate that the presented model can effectively reconstruct the edge structures and suppress the noise achieving convincing improvement over many state of the art example based methods in terms of psnr ssim and visual quality

discriminative metric preservation for tracking low resolution targets tracking low resolution lr targets is a practical yet quite challenging problem in real video analysis applications lack of discriminative details in the visual appearance of the lr target leads to the matching ambiguity which confronts most existing tracking methods although artificially enhancing the video resolution by superresolution sr techniques before analyzing might be an option the high demand of computational cost can hardly meet the requirements of the tracking scenario this paper presents a novel solution to track lr targets without explicitly performing sr this new approach is based on discriminative metric preservation that preserves the data affinity structure in the high resolution hr feature space for effective and efficient matching of lr images in addition we substantialize this new approach in a solid case study of differential tracking under metric preservation and derive a closed form solution to motion estimation for lr video in addition this paper extends the basic linear metric preservation method to a more powerful nonlinear kernel metric preservation method such a solution to lr target tracking is discriminative robust and efficient extensive experiments validate the entrustments and effectiveness of the proposed approach and demonstrate the improved performance of the proposed method in tracking lr targets

two phase resonant patterns in forced oscillatory systems boundaries mechanisms and forms we use the forced complex ginzburg landau cgl equation to study resonance in oscillatory systems periodically forced at approximately twice the natural oscillation frequency the cgl equation has both resonant spatially uniform solutions and resonant two phase standing wave pattern solutions such as stripes or labyrinths the spatially uniform solutions form a tongueshaped region in the parameter plane of the forcing amplitude and frequency but the parameter range of resonant standing wave patterns does not coincide with the tongue of spatially uniform oscillations on one side of the tongue the boundary of resonant patterns is inside the tongue and is formed by the nonequilibrium ising bloch bifurcation and the instability to traveling waves on the other side of the tongue the resonant patterns extend outside the tongue forming a parameter region in which standing wave patterns are resonant but uniform oscillations are not the standing wave patterns in that region appear similar to those inside the tongue but the mechanism of their formation is different the formation mechanism is studied using a weakly nonlinear analysis near a hopf turing bifurcation the analysis also gives the existence and stability regions of the standing wave patterns outside the resonant tongue the analysis is supported by numerical solutions of the forced complex ginzburg landau equation 2004 elsevier b v all rights reserved

multiphase patterns in periodically forced oscillatory systems periodic forcing of an oscillatory system produces frequency locking bands within which the system frequency is rationally related to the forcing frequency we study extended oscillatory systems that respond to uniform periodic forcing at one quarter of the forcing frequency the 4 1 resonance these systems possess four coexisting stable states corresponding to uniform oscillations with successive phase shifts of pi 2 using an amplitude equation approach near a hopf bifurcation to uniform oscillations we study front solutions connecting different phase states these solutions divide into two groups pi fronts separating states with a phase shift of pi and pi 2 fronts separating states with a phase shift of pi 2 we find a type of front instability where a stationary pi front open quotes decomposes close quotes into a pair of traveling pi 2 fronts as the forcing strength is decreased the instability is degenerate for an amplitude equation with cubic nonlinearities at the instability point a continuous family of pair solutions exists consisting of pi 2 fronts separated by distances ranging from zero to infinity quintic nonlinearities lift the degeneracy at the instability point but do not change the basic nature of the instability we conjecture the existence of similar instabilities in higher 2n 1 resonances n 3 4 hor ellipsis where stationarymore pi fronts decompose into ital n traveling pi n fronts the instabilities designate transitions from stationary two phase patterns to traveling 2n phase patterns as an example we demonstrate with a numerical solution the collapse of a four phase spiral wave into a stationary two phase pattern as the forcing strength within the 4 1 resonance is increased copyright ital 1999 ital the american physical society less

wavenumber locking and pattern formation in spatially forced systems we study wavenumber locking and pattern formation resulting from weak spatially periodic one dimensional forcing of two dimensional systems we consider systems that produce stationary or traveling stripe patterns when unforced and apply forcing aligned with the stripes forcing at close to twice the pattern wavenumber selects stabilizes or creates resonant stripes locked at half the forcing wavenumber if the mismatch between the forcing and pattern wavenumber is high we find that the pattern still locks but develops a wave vector component perpendicular to the forcing direction and forms rectangular and oblique patterns when the unforced system supports traveling waves resonant rectangular patterns remain stationary but oblique patterns travel in a direction orthogonal to the traveling waves

fast acquisition and reconstruction of optical coherence tomography images via sparse representation in this paper we present a novel technique based on compressive sensing principles for reconstruction and enhancement of multi dimensional image data our method is a major improvement and generalization of the multi scale sparsity based tomographic denoising msbtd algorithm we recently introduced for reducing speckle noise our new technique exhibits several advantages over msbtd including its capability to simultaneously reduce noise and interpolate missing data unlike msbtd our new method does not require an a priori high quality image from the target imaging subject and thus offers the potential to shorten clinical imaging sessions this novel image restoration method which we termed sparsity based simultaneous denoising and interpolation sbsdi utilizes sparse representation dictionaries constructed from previously collected datasets we tested the sbsdi algorithm on retinal spectral domain optical coherence tomography images captured in the clinic experiments showed that the sbsdi algorithm qualitatively and quantitatively outperforms other state of the art methods

geometry consistent light field super resolution via graph based regularization light field cameras capture the 3d information in a scene with a single exposure this special feature makes light field cameras very appealing for a variety of applications from post capture refocus to depth estimation and image based rendering however light field cameras suffer by design from strong limitations in their spatial resolution off the shelf super resolution algorithms are not ideal for light field data as they do not consider its structure on the other hand the few super resolution algorithms explicitly tailored for light field data exhibit significant limitations such as the need to carry out a costly disparity estimation procedure with sub pixel precision we propose a new light field super resolution algorithm meant to address these limitations we use the complementary information in the different light field views to augment the spatial resolution of the whole light field at once in particular we show that coupling the multi view approach with a graph based regularizer which enforces the light field geometric structure permits to avoid the need of a precise and costly disparity estimation step extensive experiments show that the new algorithm compares favorably to the state of the art methods for light field super resolution both in terms of visual quality and in terms of reconstruction error

lorentzian type soliton solutions of ac driven complex ginzburg landau equation abstract fractional transform solutions of modified complex ginzburg landau equation phase locked to a time dependent force have been found the reported solutions are necessarily of the lorentzian type containing trigonometric hyperbolic and pure cnoidal functions numerical simulations indicated that the periodic solutions and soliton solutions are quite stable against finite perturbations

image super resolution via sparse representation this paper presents a new approach to single image superresolution based upon sparse signal representation research on image statistics suggests that image patches can be well represented as a sparse linear combination of elements from an appropriately chosen over complete dictionary inspired by this observation we seek a sparse representation for each patch of the low resolution input and then use the coefficients of this representation to generate the high resolution output theoretical results from compressed sensing suggest that under mild conditions the sparse representation can be correctly recovered from the downsampled signals by jointly training two dictionaries for the low and high resolution image patches we can enforce the similarity of sparse representations between the low resolution and high resolution image patch pair with respect to their own dictionaries therefore the sparse representation of a low resolution image patch can be applied with the high resolution image patch dictionary to generate a high resolution image patch the learned dictionary pair is a more compact representation of the patch pairs compared to previous approaches which simply sample a large amount of image patch pairs reducing the computational cost substantially the effectiveness of such a sparsity prior is demonstrated for both general image super resolution sr and the special case of face hallucination in both cases our algorithm generates high resolution images that are competitive or even superior in quality to images produced by other similar sr methods in addition the local sparse modeling of our approach is naturally robust to noise and therefore the proposed algorithm can handle sr with noisy inputs in a more unified framework

compressive sampling based image coding for resource deficient visual communication in this paper a new compressive sampling based image coding scheme is developed to achieve competitive coding efficiency at lower encoder computational complexity while supporting error resilience this technique is particularly suitable for visual communication with resource deficient devices at the encoder compact image representation is produced which is a polyphase down sampled version of the input image but the conventional low pass filter prior to down sampling is replaced by a local random binary convolution kernel the pixels of the resulting down sampled pre filtered image are local random measurements and placed in the original spatial configuration the advantages of the local random measurements are two folds 1 preserve high frequency image features that are otherwise discarded by low pass filtering and 2 remain a conventional image and can therefore be coded by any standardized codec to remove the statistical redundancy of larger scales moreover measurements generated by different kernels can be considered as the multiple descriptions of the original image and therefore the proposed scheme has the advantage of multiple description coding at the decoder a unified sparsity based soft decoding technique is developed to recover the original image from received measurements in a framework of compressive sensing experimental results demonstrate that the proposed scheme is competitive compared with existing methods with a unique strength of recovering fine details and sharp edges at low bit rates

defect structures in sine gordon like models abstract we investigate several models described by real scalar fields searching for topological defects some models are described by a single field and support one or two topological sectors and others are two field models which support several topological sectors almost all the defect structures that we find are stable and finite energy solutions of first order differential equations that solve the corresponding equations of motion in particular for the double sine gordon model we show how to find small and large bps solutions as deformations of the bps solution of the 4 model and also for most of the two field models we find the corresponding integrating factors which lead to the complete set of bps solutions nicely unveiling how they bifurcate among the several topological sectors

hyperbolic partial differential difference equation in the mathematical modeling of neuronal firing and its numerical solution abstract first we assume a simple neuronal model based on stein s model richard b stein a theoretical analysis of neuronal variability biophys j 5 1965 173 194 in which after a refractory period excitatory and inhibitory exponentially decaying inputs of constant size occur at random intervals and sum until a threshold is reached we briefly discuss the distribution of time intervals between successive neuronal firings the firing rate as a function of input frequency the strength duration curve and the role of inhibition then a first order partial differential difference equation for the distribution of neuronal firing intervals is derived and a numerical scheme based on finite difference is constructed for solving such type of initial and boundary value problems the proposed method is analyzed for stability and convergence finally some test examples are given to validate convergence and the computational efficiency of the present scheme

coupled kernel embedding for low resolution face image recognition practical video scene and face recognition systems are sometimes confronted with low resolution lr images the faces may be very small even if the video is clear thus it is difficult to directly measure the similarity between the faces and the high resolution hr training samples face recognition based on traditional super resolution sr methods usually have limited performance because the target of sr may not be consistent with that of classification and time consuming sr algorithms are not suitable for real time applications in this paper a new feature extraction method called coupled kernel embedding cke is proposed for lr face recognition without any sr preprocessing in this method the final kernel matrix is constructed by concatenating two individual kernel matrices in the diagonal direction and the semi positively definite properties are preserved for optimization cke addresses the problem of comparing multimodal data that are difficult for conventional methods in practice due to the lack of an efficient similarity measure particularly different kernel types e g linear gaussian polynomial can be integrated into a uniform optimization objective which cannot be achieved by simple linear methods cke solves this problem by minimizing the dissimilarities captured by their kernel gram matrices in the lr and hr spaces in the implementation the nonlinear objective function is minimized by a generalized eigenvalue decomposition experiments on benchmark and real databases show that our cke method indeed improves the recognition performance

a stable noniterative prediction correction domain decomposition method for hyperbolic problems in this paper a noniterative domain decomposition algorithm for solving hyperbolic partial differential equations is presented the algorithm includes a prediction to estimate the values at the interface and these values are corrected by a scheme that improves the accuracy it has been shown that the algorithm is unconditionally stable efficiency is analyzed in terms of speedup and operation ratio numerical experiments illustrate that the method is stable and efficient