cauchy noise removal using group based low rank prior abstract although the extensive research on gaussian noise removal few works consider the cauchy noise removal problem in this paper we propose a novel group based low rank method for cauchy noise removal by exploiting the nonlocal self similarity of natural images we consider a group of similar patches as an approximate low rank matrix and formulate the denoising of each group as a low rank matrix recovery problem meanwhile we develop the alternating direction method of multipliers algorithm to solve the proposed nonconvex model with guaranteed convergence experiments illustrate that our method has superior performance over the state of the art methods in terms of both visual and quantitative measures

bm3d frames and variational image deblurring a family of the block matching 3 d bm3d algorithms for various imaging problems has been recently proposed within the framework of nonlocal patchwise image modeling in this paper we construct analysis and synthesis frames formalizing bm3d image modeling and use these frames to develop novel iterative deblurring algorithms we consider two different formulations of the deblurring problem i e one given by the minimization of the single objective function and another based on the generalized nash equilibrium gne balance of two objective functions the latter results in the algorithm where deblurring and denoising operations are decoupled the convergence of the developed algorithms is proved simulation experiments show that the decoupled algorithm derived from the gne formulation demonstrates the best numerical and visual results and shows superiority with respect to the state of the art in the field confirming a valuable potential of bm3d frames as an advanced image modeling tool

a parallel proximal algorithm for anisotropic total variation minimization total variation tv is a one of the most popular regularizers for stabilizing the solution of ill posed inverse problems this paper proposes a novel proximal gradient algorithm for minimizing tv regularized least squares cost functionals unlike traditional methods that require nested iterations for computing the proximal step of tv our algorithm approximates the latter with several simple proximals that have closed form solutions we theoretically prove that the proposed parallel proximal method achieves the tv solution with arbitrarily high precision at a global rate of converge that is equivalent to the fast proximal gradient methods the results in this paper have the potential to enhance the applicability of tv for solving very large scale imaging inverse problems

improved robust h2 and h filtering for uncertain discrete time systems this paper is concerned with the robust h 2 and h filtering problems for linear discrete time systems with polytopic parameter uncertainty we aim to derive a less conservative design than existing linear matrix inequality lmi based sufficient conditions it is shown that a more efficient evaluation of robust h 2 or h performance can be obtained by a matrix inequality condition which contains additional free parameters as compared to existing characterizations when applying this new matrix inequality condition to the robust filter design these parameters provide extra degrees of freedom in optimizing the guaranteed h 2 or h performance and lead to a less conservative design

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

multi contrast multi scale surface registration for improved alignment of cortical areas the position of cortical areas can be approximately predicted from cortical surface folding patterns however there is extensive inter subject variability in cortical folding patterns prohibiting a one to one mapping of cortical folds in certain areas in addition the relationship between cortical area boundaries and the shape of the cortex is variable and weaker for higher order cortical areas current surface registration techniques align cortical folding patterns using sulcal landmarks or cortical curvature for instance the alignment of cortical areas by these techniques is thus inherently limited by the sole use of geometric similarity metrics magnetic resonance imaging t1 maps show intra cortical contrast that reflects myelin content and thus can be used to improve the alignment of cortical areas in this article we present a new symmetric diffeomorphic multi contrast multi scale surface registration mmsr technique that works with partially inflated surfaces in the level set framework mmsr generates a more precise alignment of cortical surface curvature in comparison to two widely recognized surface registration algorithms the resulting overlap in gyrus labels is comparable to freesurfer most importantly mmsr improves the alignment of cortical areas further by including t1 maps as a first application we present a group average t1 map at a uniquely high resolution and multiple cortical depths which reflects the myeloarchitecture of the cortex mmsr can also be applied to other mr contrasts such as functional and connectivity data

patch ordering based wavelet frame and its use in inverse problems in our previous work 1 we have introduced a redundant tree based wavelet transform rtbwt originally designed to represent functions defined on high dimensional data clouds and graphs we have further shown that rtbwt can be used as a highly effective image adaptive redundant transform that operates on an image using orderings of its overlapped patches the resulting transform is robust to corruptions in the image and thus able to efficiently represent the unknown target image even when it is calculated from its corrupted version in this paper we utilize this redundant transform as a powerful sparsity promoting regularizer in inverse problems in image processing we show that the image representation obtained with this transform is a frame expansion and derive the analysis and synthesis operators associated with it we explore the use of this frame operators to image denoising and deblurring and demonstrate in both these cases state of the art results

restoration by compression in this paper we study the topic of signal restoration using complexity regularization quantifying the compression bit cost of the signal estimate while complexity regularized restoration is an established concept solid practical methods were suggested only for the gaussian denoising task leaving more complicated restoration problems without a generally constructive approach here we present practical methods for complexity regularized restoration of signals accommodating deteriorations caused by a known linear degradation operator of an arbitrary form our iterative procedure obtained using the alternating direction method of multipliers admm approach addresses the restoration task as a sequence of simpler problems involving ell 2 regularized estimations and rate distortion optimizations considering the squared error criterion we replace the rate distortion optimizations with an arbitrary standardized compression technique and thereby restore the signal by leveraging underlying models designed for compression additionally we propose a shift invariant complexity regularizer measuring the bit cost of all the shifted forms of the estimate extending our method to use averaging of decompressed outputs gathered from compression of shifted signals on the theoretical side we present an analysis of complexity regularized restoration of a cyclo stationary gaussian signal from deterioration by a linear shift invariant operator and an additive white gaussian noise the theory shows that optimal complexity regularized restoration relies on an elementary restoration filter and compression spreading reconstruction quality unevenly based on the energy distribution of the degradation filter these ideas are realized also in the proposed practical methods finally we present experiments showing good results for image deblurring and inpainting using the jpeg2000 and hevc compression standards

variational bayesian image restoration with a product of spatially weighted total variation image priors in this paper a new image prior is introduced and used in image restoration this prior is based on products of spatially weighted total variations tv these spatial weights provide this prior with the flexibility to better capture local image features than previous tv based priors bayesian inference is used for image restoration with this prior via the variational approximation the proposed restoration algorithm is fully automatic in the sense that all necessary parameters are estimated from the data and is faster than previous similar algorithms numerical experiments are shown which demonstrate that image restoration based on this prior compares favorably with previous state of the art restoration algorithms

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

a parameter dependent approach to robust h_ infty filtering for time delay systems this paper is concerned with the problem of robust h infin filtering for linear continuous time systems with polytopic parameter uncertainties and time varying delay in the state we utilize the polynomially parameter dependent idea to solve the robust h infin filtering problem with new linear matrix inequality conditions obtained for the existence of admissible filters these conditions are developed based on homogeneous polynomially parameter dependent matrices of arbitrary degree the delay dependence and polynomial parameter dependence guarantee the proposed approach to be potentially less conservative which is shown via a numerical example

nonuniform fast fourier transforms using min max interpolation the fast fourier transform fft is used widely in signal processing for efficient computation of the ft of finite length signals over a set of uniformly spaced frequency locations however in many applications one requires nonuniform sampling in the frequency domain i e a nonuniform ft several papers have described fast approximations for the nonuniform ft based on interpolating an oversampled fft this paper presents an interpolation method for the nonuniform ft that is optimal in the min max sense of minimizing the worst case approximation error over all signals of unit norm the proposed method easily generalizes to multidimensional signals numerical results show that the min max approach provides substantially lower approximation errors than conventional interpolation methods the min max criterion is also useful for optimizing the parameters of interpolation kernels such as the kaiser bessel function

brief paper robust h filtering for a class of uncertain linear systems with time varying delay this paper deals with the problem of delay dependent robust h filtering for uncertain linear systems with time varying delay two cases of time varying delays are fully considered one is the time varying delay being continuous uniformly bounded while the other is the time varying delay being differentiable uniformly bounded with delay derivative bounded by a constant a stable linear filter is designed to ensure that the filtering error system is asymptotically stable with a prescribed level of h noise attenuation based on a new integral inequality delay dependent sufficient conditions for the existence of such a filter are established in terms of linear matrix inequalities lmis through deriving these conditions neither model transformation nor bounding technique for cross terms is employed moreover the relationship between the sufficient conditions for the two cases of time varying delay is disclosed finally two examples are also given to illustrate the effectiveness of the proposed methodology

image restoration using total variation with overlapping group sparsity image restoration is one of the most fundamental issues in imaging science total variation regularization is widely used in image restoration problems for its capability to preserve edges in the literature however it is also well known for producing staircase artifacts in this work we extend the total variation with overlapping group sparsity which we previously developed for one dimension signal processing to image restoration a convex cost function is given and an efficient algorithm is proposed for solving the corresponding minimization problem in the experiments we compare our method with several state of the art methods the results illustrate the efficiency and effectiveness of the proposed method in terms of psnr and computing time

h sub infinity minimum error state estimation of linear stationary processes a state estimator is derived which minimizes the h sub infinity norm of the estimation error power spectrum matrix two approaches are presented the first achieves the optimal estimator in the frequency domain by finding the filter transfer function matrix that leads to an equalizing solution the second approach establishes a duality between the problem of h sub infinity filtering and the problem of unconstrained input h sub infinity optimal regulation using this duality previously published results for the latter regulation problem are applied which lead to an optimal filter that possess the structure of the corresponding kalman filter the two approaches usually lead to different results they are compared by a simple example which also demonstrates a clear advantage of the h sub infinity estimate over the conventional l sub 2 estimate

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 averaging for denoising with overcomplete dictionaries we consider the scenario where additive independent and identically distributed i i d noise in an image is removed using an overcomplete set of linear transforms and thresholding rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates provided by denoising with each of the transforms we formulate the optimal combination as a conditional linear estimation problem and solve it for optimal estimates our approach is independent of the utilized transforms and the thresholding scheme and as we illustrate using oracle based denoisers it extends established work by exploiting a separate degree of freedom that is in general not reachable using previous techniques our derivation of the optimal estimates specifically relies on the assumption that the utilized transforms provide sparse decompositions at the same time our work is robust as it does not require any assumptions about image statistics beyond sparsity unlike existing work which tries to devise ever more sophisticated transforms and thresholding algorithms to deal with the myriad types of image singularities our work uses basic tools to obtain very high performance on singularities by taking better advantage of the sparsity that surrounds them with well established transforms we obtain results that are competitive with state of the art methods

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

brief paper robust stability of time varying polytopic systems via parameter dependent homogeneous lyapunov functions this paper deals with robust stability analysis of linear state space systems affected by time varying uncertainties with bounded variation rate a new class of parameter dependent lyapunov functions is introduced whose main feature is that the dependence on the uncertain parameters and the state variables are both expressed as polynomial homogeneous forms this class of lyapunov functions generalizes those successfully employed in the special cases of unbounded variation rates and time invariant perturbations the main result of the paper is a sufficient condition to determine the sought lyapunov function which amounts to solving an lmi feasibility problem derived via a suitable parameterization of polynomial homogeneous forms moreover lower bounds on the maximum variation rate for which robust stability of the system is preserved are shown to be computable in terms of generalized eigenvalue problems numerical examples are provided to illustrate how the proposed approach compares with other techniques available in the literature

a universal variational framework for sparsity based image inpainting in this paper we extend an existing universal variational framework for image inpainting with new numerical algorithms given certain regularization operator and denoting u the latent image the basic model is to minimize the l p p 0 1 norm of u preserving the pixel values outside the inpainting region utilizing the operator splitting technique the original problem can be approximated by a new problem with extra variable with the alternating minimization method the new problem can be decomposed as two subproblems with exact solutions there are many choices for in our approach such as gradient operator wavelet transform framelet transform or other tight frames moreover with slight modification we can decouple our framework into two relatively independent parts 1 denoising and 2 linear combination therefore we can take any denoising method including bm3d filter in the denoising step the numerical experiments on various image inpainting tasks such as scratch and text removal randomly missing pixel filling and block completion clearly demonstrate the super performance of the proposed methods furthermore the theoretical convergence of the proposed algorithms is proved

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

robust image restoration via adaptive low rank approximation and joint kernel regression in recent years image priors based on nonlocal self similarity and low rank approximation have been proven as powerful tools for image restoration many restoration methods group similar patches as a matrix and recover the underlying low rank structure from the corrupted matrix via rank minimization however both the nonlocally redundant and low rank properties are highly content dependent and whether they can faithfully characterize a wide range of natural images still remains unclear in this paper we analyze these two properties and provide quantifications of them in a data driven and parametric way respectively obtaining the new measures of regional redundancy and nonlocal patch rank leveraging these prior leads to an adaptive image restoration method with content awareness in particular our method iteratively removes outliers and recovers latent fine details to handle outliers we propose an adaptive low rank and sparse matrix approximation algorithm to encourage the estimated nonlocal rank in the patch matrix the guidance of regional redundancy further gives rise to the denoise quality in the detail recovery step we propose an adaptive joint kernel regression algorithm using the redundancy measure to determine the confidence of each regression group it also bridges the gap between our online and offline dictionary learning schemes experiments on synthetic and real world images show the efficacy of our method in image deblurring and super resolution tasks especially when subject to practical outliers such as rain drops

single image motion deblurring using an adaptive image prior blind deblurring is the restoration of a sharp image from a blurred image when the blur kernel is unknown most image deblurring algorithms impose a uniform sparse gradient prior on the whole image and reconstruct the image with piecewise smooth characteristics although the sparse gradient prior removes ringing and noise artifacts it inevitably removes mid frequency structures leading to poor visual quality the gradient profile of fractal like structures is close to a gaussian distribution and small gradients from such regions are severely penalized by the sparse gradient prior in this paper we introduce an image deblurring algorithm that adapts the image prior to the underlying detailed structures the statistics of a local detailed structure can be different from those of the global structure by identifying the correct image prior for each pixel in the image our approach models the spatially varying motion blur exhibited by camera motion more effectively than conventional methods based on space invariant blur kernels using different priors for the local region and the motion blur kernel we derive a minimization energy function that alternates between blur kernel estimation and deblurring image restoration until convergence experimental results demonstrate that the proposed approach is efficient and effective in reducing motion blur in an arbitrary direction in a single image

forward fourier wavelet regularized deconvolution for ill conditioned systems we propose an efficient hybrid fourier wavelet regularized deconvolution forward algorithm that performs noise regularization via scalar shrinkage in both the fourier and wavelet domains the fourier shrinkage exploits the fourier transform s economical representation of the colored noise inherent in deconvolution whereas the wavelet shrinkage exploits the wavelet domain s economical representation of piecewise smooth signals and images we derive the optimal balance between the amount of fourier and wavelet regularization by optimizing an approximate mean squared error mse metric and find that signals with more economical wavelet representations require less fourier shrinkage forward is applicable to all ill conditioned deconvolution problems unlike the purely wavelet based wavelet vaguelette deconvolution wvd moreover its estimate features minimal ringing unlike the purely fourier based wiener deconvolution even in problems for which the wvd was designed we prove that forward s mse decays with the optimal wvd rate as the number of samples increases further we demonstrate that over a wide range of practical sample lengths forward improves on wvd s performance

sharpness in motion corrected quantitative imaging at 7t sub millimeter imaging at 7t has opened new possibilities for qualitatively and quantitatively studying brain structure as it evolves throughout the life span however subject motion introduces image blurring on the order of magnitude of the spatial resolution and is thus detrimental to image quality such motion can be corrected for but widespread application has not yet been achieved and quantitative evaluation is lacking this raises a need to quantitatively measure image sharpness throughout the brain we propose a method to quantify sharpness of brain structures at sub voxel resolution and use it to assess to what extent limited motion is related to image sharpness the method was evaluated in a cohort of 24 healthy volunteers with a wide and uniform age range aiming to arrive at results that largely generalize to larger populations using 3d fat excited motion navigators quantitative r1 r2 and quantitative susceptibility maps and t1 weighted images were retrospectively corrected for motion sharpness was quantified in all modalities for selected regions of interest roi by fitting the sigmoidally shaped error function to data within locally homogeneous clusters a strong almost linear correlation between motion and sharpness improvement was observed and motion correction significantly improved sharpness overall the full width at half maximum reduced from 0 88 mm to 0 70 mm after motion correction equivalent to a 2 0 times smaller voxel volume motion and sharpness were not found to correlate with the age of study participants we conclude that in our data motion correction using fat navigators is overall able to restore the measured sharpness to the imaging resolution irrespective of the amount of motion observed during scanning

dct regularized extreme visual recovery here we study the extreme visual recovery problem in which over 90 of pixel values in a given image are missing existing low rank based algorithms are only effective for recovering data with at most 90 missing values thus we exploit visual data s smoothness property to help solve this challenging extreme visual recovery problem based on the discrete cosine transform dct we propose a novel dct regularizer that involves all pixels and produces smooth estimations in any view our theoretical analysis shows that the total variation regularizer which only achieves local smoothness is a special case of the proposed dct regularizer we also develop a new visual recovery algorithm by minimizing the dct regularizer and nuclear norm to achieve a more visually pleasing estimation experimental results on a benchmark image data set demonstrate that the proposed approach is superior to the state of the art methods in terms of peak signal to noise ratio and structural similarity

a general framework for regularized similarity based image restoration any image can be represented as a function defined on a weighted graph in which the underlying structure of the image is encoded in kernel similarity and associated laplacian matrices in this paper we develop an iterative graph based framework for image restoration based on a new definition of the normalized graph laplacian we propose a cost function which consists of a new data fidelity term and regularization term derived from the specific definition of the normalized graph laplacian the normalizing coefficients used in the definition of the laplacian and associated regularization term are obtained using fast symmetry preserving matrix balancing this results in some desired spectral properties for the normalized laplacian such as being symmetric positive semidefinite and returning zero vector when applied to a constant image our algorithm comprises of outer and inner iterations where in each outer iteration the similarity weights are recomputed using the previous estimate and the updated objective function is minimized using inner conjugate gradient iterations this procedure improves the performance of the algorithm for image deblurring where we do not have access to a good initial estimate of the underlying image in addition the specific form of the cost function allows us to render the spectral analysis for the solutions of the corresponding linear equations in addition the proposed approach is general in the sense that we have shown its effectiveness for different restoration problems including deblurring denoising and sharpening experimental results verify the effectiveness of the proposed algorithm on both synthetic and real examples

delay dependent robust h sub spl infin and l sub 2 l sub spl infin filtering for a class of uncertain nonlinear time delay systems this note presents delay dependent robust h sub spl infin and l sub 2 l sub spl infin filter designs for a class of nonlinear systems with multiple time varying delays in the state and parameter uncertainties residing in a polytope the nonlinearities are assumed to satisfy global lipschitz conditions attention is focused on the design of robust full order and reduced order filters guaranteeing a prescribed noise attenuation level in an h sub spl infin or l sub 2 l sub spl infin sense the admissible filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms

game theory approach to optimal linear state estimation and its relation to the minimum h sub infinity norm estimation a possible game theory approach to optimal state estimation is presented it is found that in a certain differential game the minimizer s policy is identical to the one obtained by optimal estimation in the minimum h sub infinity norm sense this interpretation of h sub infinity optimal state estimation provides better insight into the mechanism of h sub infinity optimal filtering especially in the case where the exogenous signals are not energy bounded

image restoration using space variant gaussian scale mixtures in overcomplete pyramids in recent years bayes least squares gaussian scale mixtures bls gsm has emerged as one of the most powerful methods for image restoration its strength relies on providing a simple and yet very effective local statistical description of oriented pyramid coefficient neighborhoods via a gsm vector this can be viewed as a fine adaptation of the model to the signal variance at each scale orientation and spatial location here we present an enhancement of the model by introducing a coarser adaptation level where a larger neighborhood is used to estimate the local signal covariance within every subband we formulate our model as a bls estimator using space variant gsm the model can be also applied to image deconvolution by first performing a global blur compensation and then doing local adaptive denoising we demonstrate through simulations that the proposed method besides being model based and noniterative it is also robust and efficient its performance measured visually and in l2 norm terms is significantly higher than the original bls gsm method both for denoising and deconvolution

a non local low rank approach to enforce integrability we propose a new approach to enforce integrability using recent advances in non local methods our formulation consists in a sparse gradient data fitting term to handle outliers together with a gradient domain non local low rank prior this regularization has two main advantages 1 the low rank prior ensures similarity between non local gradient patches which helps recovering high quality clean patches from severe outliers corruption and 2 the low rank prior efficiently reduces dense noise as it has been shown in recent image restoration works we propose an efficient solver for the resulting optimization formulation using alternate minimization experiments show that the new method leads to an important improvement compared with previous optimization methods and is able to efficiently handle both outliers and dense noise mixed together

image restoration via simultaneous sparse coding where structured sparsity meets gaussian scale mixture in image processing sparse coding has been known to be relevant to both variational and bayesian approaches the regularization parameter in variational image restoration is intrinsically connected with the shape parameter of sparse coefficients distribution in bayesian methods how to set those parameters in a principled yet spatially adaptive fashion turns out to be a challenging problem especially for the class of nonlocal image models in this work we propose a structured sparse coding framework to address this issue more specifically a nonlocal extension of gaussian scale mixture gsm model is developed using simultaneous sparse coding ssc and its applications into image restoration are explored it is shown that the variances of sparse coefficients the field of scalar multipliers of gaussians if treated as a latent variable can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization when applied to image restoration our experimental results have shown that the proposed ssc gsm technique can both preserve the sharpness of edges and suppress undesirable artifacts thanks to its capability of achieving a better spatial adaptation ssc gsm based image restoration often delivers reconstructed images with higher subjective objective qualities than other competing approaches

image deblurring with an inaccurate blur kernel using a group based low rank image prior abstract we address the problem of restoring an original image from its blurry and noisy observation together with inaccurate information of the blurring process for this purpose we propose an enhanced regularized structured total least squares rstls model that can estimate the latent image and blur kernel simultaneously in the proposed model both the image and the blur kernel are characterized by a group based low rank prior which assumes that a group of vectorized similar data patches can be well approximated by a low rank matrix we develop an alternating minimization algorithm to solve the proposed model efficiently numerical experiments demonstrate the effectiveness of our method in terms of both quantitative measures and visual quality

parameter estimation for blind and non blind deblurring using residual whiteness measures image deblurring id is an ill posed problem typically addressed by using regularization or prior knowledge on the unknown image and also on the blur operator in the blind case id is often formulated as an optimization problem where the objective function includes a data term encouraging the estimated image and blur in blind id to explain the observed data well typically the squared norm of a residual plus a regularizer that penalizes solutions deemed undesirable the performance of this approach depends critically among other things on the relative weight of the regularizer the regularization parameter and on the number of iterations of the algorithm used to address the optimization problem in this paper we propose new criteria for adjusting the regularization parameter and or the number of iterations of id algorithms the rationale is that if the recovered image and blur in blind id is well estimated the residual image is spectrally white contrarily a poorly deblurred image typically exhibits structured artifacts e g ringing oversmoothness yielding residuals that are not spectrally white the proposed criterion is particularly well suited to a recent blind id algorithm that uses continuation i e slowly decreases the regularization parameter along the iterations in this case choosing this parameter and deciding when to stop are one and the same thing our experiments show that the proposed whiteness based criteria yield improvements in snr on average only 0 15 db below those obtained by clairvoyantly stopping the algorithm at the best snr we also illustrate the proposed criteria on non blind id reporting results that are competitive with state of the art criteria such as monte carlo based gsure and projected sure which however are not applicable for blind id

filter design for lpv systems using quadratically parameter dependent lyapunov functions this paper considers design problems of robust gain scheduled h and h 2 filters for linear parameter varying lpv systems whose state space matrices are represented as parametrically affine matrices using quadratically parameter dependent lyapunov functions and proposes methods of filter design via parametrically affine linear matrix inequalities lmis for robust filters our design methods theoretically encompass those that use constant lyapunov functions several numerical examples are included that demonstrate the effectiveness of gain scheduled and robust filters using our proposed methods compared with robust filters using existing methods

iterative algorithms based on decoupling of deblurring and denoising for image restoration in this paper we propose iterative algorithms for solving image restoration problems the iterative algorithms are based on decoupling of deblurring and denoising steps in the restoration process in the deblurring step an efficient deblurring method using fast transforms can be employed in the denoising step effective methods such as the wavelet shrinkage denoising method or the total variation denoising method can be used the main advantage of this proposal is that the resulting algorithms can be very efficient and can produce better restored images in visual quality and signal to noise ratio than those by the restoration methods using the combination of a data fitting term and a regularization term the convergence of the proposed algorithms is shown in the paper numerical examples are also given to demonstrate the effectiveness of these algorithms

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

technical communique delay range dependent stability for systems with time varying delay this paper is concerned with the stability analysis for systems with time varying delay in a range an appropriate type of lyapunov functionals is proposed to investigate the delay range dependent stability problem the present results may improve the existing ones due to a method to estimate the upper bound of the derivative of lyapunov functional without ignoring some useful terms and the introduction of additional terms into the proposed lyapunov functional which take into account the range of delay numerical examples are given to demonstrate the effectiveness and the benefits of the proposed method

brief homogeneous lyapunov functions for systems with structured uncertainties the problem addressed in this paper is the construction of homogeneous polynomial lyapunov functions hplfs for linear systems with time varying structured uncertainties a sufficient condition for the existence of an hplf of given degree is formulated in terms of a linear matrix inequalities lmi feasibility problem this condition turns out to be also necessary in some cases depending on the dimension of the system and the degree of the lyapunov function the maximum norm of the parametric uncertainty for which there exists a homogeneous polynomial lyapunov function is computed by solving a generalized eigenvalue problem the construction of such lyapunov functions is efficiently performed by means of popular convex optimization tools for the solution of problems in lmi form comparisons with other classes of lyapunov functions through numerical examples taken from the literature show that hplfs are a powerful tool for robustness analysis

a delay dependent approach to robust h sub spl infin filtering for uncertain discrete time state delayed systems a delay dependent approach to robust h sub spl infin filtering is proposed for linear discrete time uncertain systems with multiple delays in the state the uncertain parameters are supposed to reside in a polytope and the attention is focused on the design of robust filters guaranteeing a prescribed h sub spl infin noise attenuation level the proposed filter design methodology incorporates some recently appeared results such as moon s new version of the upper bound for the inner product of two vectors and de oliveira s idea of parameter dependent stability which greatly reduce the overdesign introduced in the derivation process in addition to the full order filtering problem the challenging reduced order case is also addressed by using different linearization procedures both full and reduced order filters can be obtained from the solution of convex optimization problems in terms of linear matrix inequalities which can be solved via efficient interior point algorithms numerical examples have been presented to illustrate the feasibility and advantages of the proposed methodologies

motion adaptive patch based low rank approach for compressed sensing cardiac cine mri one of the technical challenges in cine magnetic resonance imaging mri is to reduce the acquisition time to enable the high spatio temporal resolution imaging of a cardiac volume within a short scan time recently compressed sensing approaches have been investigated extensively for highly accelerated cine mri by exploiting transform domain sparsity using linear transforms such as wavelets and fourier however in cardiac cine imaging the cardiac volume changes significantly between frames and there often exist abrupt pixel value changes along time in order to effectively sparsify such temporal variations it is necessary to exploit temporal redundancy along motion trajectories this paper introduces a novel patch based reconstruction method to exploit geometric similarities in the spatio temporal domain in particular we use a low rank constraint for similar patches along motion based on the observation that rank structures are relatively less sensitive to global intensity changes but make it easier to capture moving edges a nash equilibrium formulation with relaxation is employed to guarantee convergence experimental results show that the proposed algorithm clearly reconstructs important anatomical structures in cardiac cine image and provides improved image quality compared to existing state of the art methods such as k t focuss k t slr and master