coulomb plus power law potentials in quantum mechanics we study the discrete spectrum of the hamiltonian h v r for the coulomb plus power law potential v r 1 r sgn q rq where 0 q 2 and q 0 we show by envelope theory that the discrete eigenvalues enl of h may be approximated by the semiclassical expression enl q minr 0 1 r2 1 r sgn q r q values of and are prescribed which yield upper and lower bounds accurate upper bounds are also obtained by use of a trial function of the form r rl 1 e xr d we give detailed results for v r 1 r rq q 0 5 1 2 for n 1 l 0 1 2 along with comparison eigenvalues found by direct numerical methods

noise estimation and filtering using block based singular value decomposition preprocessing of image and video sequences with spatial filtering techniques usually improves the image quality and compressibility we present a block based nonlinear filtering algorithm based on singular value decomposition and compression based filtering experiments show that the proposed filter preserves edge details and can significantly improve the compression performance

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

image quality assessment by discrete orthogonal moments this paper proposes a novel full reference quality assessment qa metric that automatically assesses the quality of an image in the discrete orthogonal moments domain this metric is constructed by representing the spatial information of an image using low order moments the computation up to fourth order moments is performed on each individual 8x8 non overlapping block for both the test and reference images then the computed moments of both the test and reference images are combined in order to determine the moment correlation index of each block in each order the number of moment correlation indices used in this study is nine next the mean of each moment correlation index is computed and thereafter the single quality interpretation of the test image with respect to its reference is determined by taking the mean value of the computed means of all the moment correlation indices the proposed objective metrics based on two discrete orthogonal moments tchebichef and krawtchouk moments are developed and their performances are evaluated by comparing them with subjective ratings on several publicly available databases the proposed discrete orthogonal moments based metric performs competitively well with the state of the art models in terms of quality prediction while outperforms them in terms of computational speed

sparse feature fidelity for perceptual image quality assessment the prediction of an image quality metric iqm should be consistent with subjective human evaluation as the human visual system hvs is critical to visual perception modeling of the hvs is regarded as the most suitable way to achieve perceptual quality predictions sparse coding that is equivalent to independent component analysis ica can provide a very good description of the receptive fields of simple cells in the primary visual cortex which is the most important part of the hvs with this inspiration a quality metric called sparse feature fidelity sff is proposed for full reference image quality assessment iqa on the basis of transformation of images into sparse representations in the primary visual cortex the proposed method is based on the sparse features that are acquired by a feature detector which is trained on samples of natural images by an ica algorithm in addition two strategies are designed to simulate the properties of the visual perception 1 visual attention and 2 visual threshold the computation of sff has two stages training and fidelity computation in addition the fidelity computation consists of two components feature similarity and luminance correlation the feature similarity measures the structure differences between the two images whereas the luminance correlation evaluates brightness distortions sff also reflects the chromatic properties of the hvs and it is very effective for color iqa the experimental results on five image databases show that sff has a better performance in matching subjective ratings compared with the leading iqms

convergence of the nelder mead simplex method to a nonstationary point this paper analyzes the behavior of the nelder mead simplex method for a family of examples which cause the method to converge to a nonstationary point all the examples use continuous functions of two variables the family of functions contains strictly convex functions with up to three continuous derivatives in all the examples the method repeatedly applies the inside contraction step with the best vertex remaining fixed the simplices tend to a straight line which is orthogonal to the steepest descent direction it is shown that this behavior cannot occur for functions with more than three continuous derivatives the stability of the examples is analyzed

fortified descent simplicial search method a general approach we propose a new simplex based direct search method for unconstrained minimization of a real valued function f of n variables as in other methods of this kind the intent is to iteratively improve an n dimensional simplex through certain reflection expansion contraction steps the method has three novel features first a user chosen integer bar m k specifies the number of good vertices to be retained in constructing the initial trial simplices reflected then either expanded or contracted at iteration k second a trial simplex is accepted only when it satisfies the criteria of fortified descent which are stronger than the criterion of strict descent used in most direct search methods third the number of additional function evaluations needed to check a trial reflected expanded simplex for fortified descent can be controlled if one of the initial trial simplices satisfies the fortified descent criteria it is accepted as the new simplex otherwise the simplex is shrunk a fraction of the way toward a best vertex and the process is restarted etc until either a trial simplex is accepted or the simplex effectively has shrunk to a single point we prove several theoretical properties of the new method if f is continuously differentiable bounded below and uniformly continuous on its lower level set and we choose bar m k with the same value at all iterations k then every cluster point of the generated sequence of iterates is a stationary point the same conclusion holds if the function is continuously differentiable bounded below and we choose bar m k 1 at all iterations k

on the roots of certain polynomials arising from the analysis of the nelder mead simplex method abstract the study of the effect of dimensionality on the nelder mead simplex method for unconstrained optimization leads us to the study of a two parameter family of polynomials of the form p n z b az az n 1 z n we show that provided that a a b is real it is possible to use primarily the schur cohn criterion in order to determine the configuration of the roots of p n z with respect to the unit circle

wave atoms based compression method for fingerprint images this paper proposes a new fingerprint image compression approach where the quality of the decoded image is perceptually controlled using wave atom transform a comparative study of different transforms shows that wave atom transform is more appropriate than wavelets for fingerprint image compression a new image quality metric based on the same transform is proposed to control the compression performance some properties of the human visual system are exploited in the design of the proposed image quality metric simulations show that this metric correlates well with the subjective human judgment based on these interesting results a compression method with a perceptual distortion control mechanism specific to fingerprint images is developed finally the performance of the proposed compression scheme is evaluated in terms of fingerprint recognition rate the experimental results clearly show that the proposed strategy offers better results than some traditional compression methods

rate bounds on ssim index of quantized images in this paper we derive bounds on the structural similarity ssim index as a function of quantization rate for fixed rate uniform quantization of image discrete cosine transform dct coefficients under the high rate assumption the space domain ssim index is first expressed in terms of the dct coefficients of the space domain vectors the transform domain ssim index is then used to derive bounds on the average ssim index as a function of quantization rate for uniform gaussian and laplacian sources as an illustrative example uniform quantization of the dct coefficients of natural images is considered we show that the ssim index between the reference and quantized images fall within the bounds for a large set of natural images further we show using a simple example that the proposed bounds could be very useful for rate allocation problems in practical image and video coding applications

on the convergence of pattern search algorithms we introduce an abstract definition of pattern search methods for solving nonlinear unconstrained optimization problems our definition unifies an important collection of optimization methods that neither compute nor explicitly approximate derivatives we exploit our characterization of pattern search methods to establish a global convergence theory that does not enforce a notion of sufficient decrease our analysis is possible because the iterates of a pattern search method lie on a scaled translated integer lattice this allows us to relax the classical requirements on the acceptance of the step at the expense of stronger conditions on the form of the step and still guarantee global convergence

bounds on schrodinger eigenvalues for polynomial potentials in n dimensions if a single particle obeys nonrelativistic qm in rn and has the hamiltonian h q 0 a q rq a q 0 then the lowest eigenvalue e is given approximately by the semiclassical expression e minr 0 1 r2 q 0 a q p q n r q it is proved that this formula yields a lower bound when p q n ne 2 1 2 n qe 1 q 1 n 2 1 n q 1 n and an upper bound when p q n n 2 1 2 n q 2 n 2 1 q an extension is made to allow for a coulomb term when n 1 the general formula is applied to the examples v r r r2 r3 and v r r2 r4 r6 in dimensions 1 to 10 and the results are compared to accurate eigenvalues obtained numerically

dct qm a dct based quality degradation metric for image quality optimization problems recent development of computational image quality assessment methods has shown to give very promising results in measuring perceptual visual quality for distorted images however most of them are difficult to be applied for optimization problems due to the lack of desirable mathematical properties such as differentiability convexity and valid distance metricability this paper proposes a novel discrete cosine transform dct based quality degradation metric called dct qm which is based on the probability summation theory with a psychometric function for neural responses in the receptive fields of visual cortex in psychophysics consequently the dct qm is formulated as a weighted mean text l 2 norm in the dct domain which is very easy to implement and inherits the three desirable mathematical properties that is differentiability convexity and valid distance metricability for image quality optimization problems the extensive experimental results show that the proposed dct qm has promising results for many practical distortion types in image processing problems by showing high consistency with perceived visual quality

contrast sensitivity of the wavelet dual tree complex wavelet curvelet and steerable pyramid transforms accurate estimation of the contrast sensitivity of the human visual system is crucial for perceptually based image processing in applications such as compression fusion and denoising conventional contrast sensitivity functions csfs have been obtained using fixed sized gabor functions however the basis functions of multiresolution decompositions such as wavelets often resemble gabor functions but are of variable size and shape therefore to use the conventional csfs in such cases is not appropriate we have therefore conducted a set of psychophysical tests in order to obtain the csf for a range of multiresolution transforms the discrete wavelet transform the steerable pyramid the dual tree complex wavelet transform and the curvelet transform these measures were obtained using contrast variation of each transforms basis functions in a 2afc experiment combined with an adapted version of the quest psychometric function method the results enable future image processing applications that exploit these transforms such as signal fusion superresolution processing denoising and motion estimation to be perceptually optimized in a principled fashion the results are compared with an existing vision model hdr vdp2 and are used to show quantitative improvements within a denoising application compared with using conventional csf values

multivariable control design for stochastic systems with saturated driving lqg optimal approach a stability criterion for stochastic multivariable feedback systems with saturated actuators is derived an algorithm is proposed to choose an appropriate linear quadratic gaussian lqg performance index scalar to satisfy the stability criterion and then a robust lqg optimal controller is obtained to override the limit cycle or instability incurred by saturated actuators employed in control systems finally a simulation is given to support the results

blur identification using the bispectrum the authors propose inspecting the zero crossings in the central slice of the bispectrum of the observed image for blur identification this method is an extension of the classical methods for blur identification in which the power spectrum or the power cepstrum of the blurred image is applied to the bispectrum domain the proposed bispectrum based approach utilizes the ability of the bispectrum to suppress additive signal independent gaussian observation noise simulation results indicate that the method performs significantly better than the classical power spectrum based approach at low signal to noise ratios

dynamic contrast based quantization for lossy wavelet image compression this paper presents a contrast based quantization strategy for use in lossy wavelet image compression that attempts to preserve visual quality at any bit rate based on the results of recent psychophysical experiments using near threshold and suprathreshold wavelet subband quantization distortions presented against natural image backgrounds subbands are quantized such that the distortions in the reconstructed image exhibit root mean squared contrasts selected based on image subband and display characteristics and on a measure of total visual distortion so as to preserve the visual system s ability to integrate edge structure across scale space within a single unified framework the proposed contrast based strategy yields images which are competitive in visual quality with results from current visually lossless approaches at high bit rates and which demonstrate improved visual quality over current visually lossy approaches at low bit rates this strategy operates in the context of both nonembedded and embedded quantization the latter of which yields a highly scalable codestream which attempts to maintain visual quality at all bit rates a specific application of the proposed algorithm to jpeg 2000 is presented

vsnr a wavelet based visual signal to noise ratio for natural images this paper presents an efficient metric for quantifying the visual fidelity of natural images based on near threshold and suprathreshold properties of human vision the proposed metric the visual signal to noise ratio vsnr operates via a two stage approach in the first stage contrast thresholds for detection of distortions in the presence of natural images are computed via wavelet based models of visual masking and visual summation in order to determine whether the distortions in the distorted image are visible if the distortions are below the threshold of detection the distorted image is deemed to be of perfect visual fidelity vsnr infin and no further analysis is required if the distortions are suprathreshold a second stage is applied which operates based on the low level visual property of perceived contrast and the mid level visual property of global precedence these two properties are modeled as euclidean distances in distortion contrast space of a multiscale wavelet decomposition and vsnr is computed based on a simple linear sum of these distances the proposed vsnr metric is generally competitive with current metrics of visual fidelity it is efficient both in terms of its low computational complexity and in terms of its low memory requirements and it operates based on physical luminances and visual angle rather than on digital pixel values and pixel based dimensions to accommodate different viewing conditions

numerical study of blow up and dispersive shocks in solutions to generalized korteweg de vries equations abstract we present a detailed numerical study of solutions to general korteweg de vries equations with critical and supercritical nonlinearity both in the context of dispersive shocks and blow up we study the stability of solitons and show that they are unstable against being radiated away and blow up in the l 2 critical case the blow up mechanism by martel merle and raphael can be numerically identified in the limit of small dispersion it is shown that a dispersive shock always appears before an eventual blow up in the latter case always the first soliton to appear will blow up it is shown that the same type of blow up as for the perturbations of the soliton can be observed which indicates that the theory by martel merle and raphael is also applicable to initial data with a mass much larger than the soliton mass we study the scaling of the blow up time t in dependence of the small dispersion parameter and find an exponential dependence t and that there is a minimal blow up time t 0 greater than the critical time of the corresponding hopf solution for 0 to study the cases with blow up in detail we apply the first dynamic rescaling for generalized korteweg de vries equations this allows to identify the type of the singularity

image multidistortion estimation we present a method for estimating the amount of noise and blur in a distorted image our method is based on the multiscale structural similarity ms ssim framework that although designed to measure image quality is used to estimate the amount of blur and noise in a degraded image given a reference image we show that there exists a bijective mapping between the 2 d noise blur space and the 3 d ms ssim space which allows to recover distortion parameters that mapping allows to formulate the multidistortion estimation problem as a classical optimization problem various search strategies such as newton simplex newuoa and brute force search are presented and compared we also show that a bicubic patch can be used to approximate the bijective mapping between the noise blur space and the 3 d ms ssim space interestingly the use of such a patch reduces the processing time by a factor of 40 without significantly reducing precision based on quantitative results we show that the amount of different types of blur and noise in a distorted image can be recovered with accuracy of roughly 2 and 8 respectively our methods are compared with four state of the art noise and blur estimation techniques

color image quality assessment from prediction to optimization while image difference metrics show good prediction performance on visual data they often yield artifact contaminated results if used as objective functions for optimizing complex image processing tasks we investigate in this regard the recently proposed color image difference cid metric particularly developed for predicting gamut mapping distortions we present an algorithm for optimizing gamut mapping employing the cid metric as the objective function resulting images contain various visual artifacts which are addressed by multiple modifications yielding the improved color image difference icid metric the icid based optimizations are free from artifacts and retain contrast structure and color of the original image to a great extent furthermore the prediction performance on visual data is improved by the modifications

direct search methods on parallel machines direct search methods are methods designed to solve unconstrained minimization problems of the form mathop min limits x in mathbb r n f x where f n these methods are distinguished by the fact that they neither use nor require explicit derivative information the search for a local minimizer is driven solely by function information popular methods in this class include the factorial design algorithm of box 1 the pattern search algorithm of hooke and jeeves 4 and the simplex method of neider and mead 5

design of linear equalizers optimized for the structural similarity index we propose an algorithm for designing linear equalizers that maximize the structural similarity ssim index between the reference and restored signals the ssim index has enjoyed considerable application in the evaluation of image processing algorithms algorithms however have not been designed yet to explicitly optimize for this measure the design of such an algorithm is nontrivial due to the nonconvex nature of the distortion measure in this paper we reformulate the nonconvex problem as a quasi convex optimization problem which admits a tractable solution we compute the optimal solution in near closed form with complexity of the resulting algorithm comparable to complexity of the linear minimum mean squared error mmse solution independent of the number of filter taps to demonstrate the usefulness of the proposed algorithm it is applied to restore images that have been blurred and corrupted with additive white gaussian noise as a special case we consider blur free image denoising in each case its performance is compared to a locally adaptive linear mse optimal filter we show that the images denoised and restored using the ssim optimal filter have higher ssim index and superior perceptual quality than those restored using the mse optimal adaptive linear filter through these results we demonstrate that a designing image processing algorithms and in particular denoising and restoration type algorithms can yield significant gains over existing in particular linear mmse based algorithms by optimizing them for perceptual distortion measures and b these gains may be obtained without significant increase in the computational complexity of the algorithm

picture quality prediction based on a visual model distortion measures are developed for the purpose of predicting the subjective quality of moving monochrome television pictures the need for such measures is particularly recognized in the area of digital picture coding subjectively relevant distortion measures that mirror viewers assessments of picture quality would make the task of designing and optimizing coding schemes considerably easier the distortion measures are based on a spatiotemporal model of threshold vision that incorporates the filtering and masking processes the visual filtering is carried out by parallel excitation and inhibition paths each of which is separately linear but which combine in a nonlinear way to take account of the adaptation with background luminance the masking is in the form of a point by point weighting of the filtered error based on the amount of spatial and temporal activity in the immediate surround the processed error averaged over the picture is then used as a prediction of picture quality three classes of distortion measure are considered 1 the raw error measures that have been used in the past 2 the filtered error measures where the filtering properties of vision are taken into account and 3 the masked error measures where the masking processes are also included it is shown that the filtered error measures are better predictors of picture quality than the raw error measures the masked error measures lead to further improvements but only if local rather than global averaging procedures are used it is postulated that this is because viewers tend to base their quality ratings on critical areas rather than on the whole picture

a distortion measure for blocking artifacts in images based on human visual sensitivity a visual model that gives a distortion measure for blocking artifacts in images is presented given the original and reproduced image as inputs the model output is a numerical value that quantifies the visibility of blocking error in the reproduced image the model is derived based on the human visual sensitivity to horizontal and vertical edge artifacts that result from blocking psychovisual experiments have been carried out to measure the visual sensitivity to these artifacts in the experiments typical edge artifacts are shown to subjects and the sensitivity to them is measured with the variation of background luminance background activity edge length and edge amplitude synthetic test patterns are used as background images in the experiments the sensitivity measures thus obtained are used to estimate the model parameters the final model is tested on real images and the results show that the error visibility predicted by the model correlates well with the subjective ranking

on the mathematical properties of the structural similarity index since its introduction in 2004 the structural similarity ssim index has gained widespread popularity as a tool to assess the quality of images and to evaluate the performance of image processing algorithms and systems there has been also a growing interest of using ssim as an objective function in optimization problems in a variety of image processing applications one major issue that could strongly impede the progress of such efforts is the lack of understanding of the mathematical properties of the ssim measure for example some highly desirable properties such as convexity and triangular inequality that are possessed by the mean squared error may not hold in this paper we first construct a series of normalized and generalized vector valued metrics based on the important ingredients of ssim we then show that such modified measures are valid distance metrics and have many useful properties among which the most significant ones include quasi convexity a region of convexity around the minimizer and distance preservation under orthogonal or unitary transformations the groundwork laid here extends the potentials of ssim in both theoretical development and practical applications

image quality assessment based on matching pursuit abstract the objective assessment of image quality is an essential part of many visual processing systems the challenge lies in evaluating the image quality consistently under subjective perceptions in this paper we propose a novel image quality metric based on the matching pursuit algorithm under the principle of structural information distortion we assume that various structure data contributes differently to the single image quality score specifically we decompose the reference image using matching pursuit with a separable 2d gabor dictionary thus obtaining structural information and develop a characterization for this information and its importance we then discuss the relationship between the structural distortion intensity and the subjective quality measurement on the energy scale in experiments we compare the performance of our algorithm with both subjective ratings and state of the art objective methods on image datasets with multi type distortions the experimental results validate our proposed method

convergence properties of the nelder mead simplex method in low dimensions the nelder mead simplex algorithm first published in 1965 is an enormously popular direct search method for multidimensional unconstrained minimization despite its widespread use essentially no theoretical results have been proved explicitly for the nelder mead algorithm this paper presents convergence properties of the nelder mead algorithm applied to strictly convex functions in dimensions 1 and 2 we prove convergence to a minimizer for dimension 1 and various limited convergence results for dimension 2 a counterexample of mckinnon gives a family of strictly convex functions in two dimensions and a set of initial conditions for which the nelder mead algorithm converges to a nonminimizer it is not yet known whether the nelder mead method can be proved to converge to a minimizer for a more specialized class of convex functions in two dimensions

compressed image quality metric based on perceptually weighted distortion objective quality assessment for compressed images is critical to various image compression systems that are essential in image delivery and storage although the mean squared error mse is computationally simple it may not be accurate to reflect the perceptual quality of compressed images which is also affected dramatically by the characteristics of human visual system hvs such as masking effect in this paper an image quality metric iqm is proposed based on perceptually weighted distortion in terms of the mse to capture the characteristics of hvs a randomness map is proposed to measure the masking effect and a preprocessing scheme is proposed to simulate the processing that occurs in the initial part of hvs since the masking effect highly depends on the structural randomness the prediction error from neighborhood with a statistical model is used to measure the significance of masking meanwhile the imperceptible signal with high frequency could be removed by preprocessing with low pass filters the relation is investigated between the distortions before and after masking effect and a masking modulation model is proposed to simulate the masking effect after preprocessing the performance of the proposed iqm is validated on six image databases with various compression distortions the experimental results show that the proposed algorithm outperforms other benchmark iqms

detection and remediation of stagnation in the nelder mead algorithm using a sufficient decrease condition the nelder mead algorithm can stagnate and converge to a nonoptimal point even for very simple problems in this note we propose a test for sufficient decrease which if passed for all iterations will guarantee convergence of the nelder mead iteration to a stationary point if the objective function is smooth and the diameters of the nelder mead simplices converge to zero failure of this condition is an indicator of potential stagnation as a remedy we propose a new step which we call an oriented restart that reinitializes the simplex to a smaller one with orthogonal edges whose orientation is determined by an approximate descent direction from the current best point we also give results that apply when the objective function is a low amplitude perturbation of a smooth function we illustrate our results with some numerical examples

generalized comparison theorems in quantum mechanics this paper is concerned with the discrete spectra of schrodinger operators h v where v r is an attractive potential in n spatial dimensions two principal results are reported for the bottom of the spectrum of h in each angular momentum subspace l i an optimized lower bound when the potential is a sum of terms v r v 1 r v 2 r and the bottoms of the spectra of v 1 r and v 2 r in l are known and ii a generalized comparison theorem which predicts spectral ordering when the graphs of the comparison potentials v 1 r and v 2 r intersect in a controlled way pure power law potentials are studied and an application of the results to the coulomb plus linear potential v r a r br is presented in detail for this problem an earlier formula for energy bounds is sharpened and generalized to n dimensions

a global multilevel coordinate search procedure for estimating the unsaturated soil hydraulic properties we present a new inverse modeling procedure to characterize the hydraulic properties of partially saturated soils from soil moisture measurements during a natural transient flow experiment the inversion of the governing one dimensional richards equation is carried out using the global multilevel coordinate search optimization algorithm in sequential combination with the local nelder mead simplex algorithm gmcs nms we introduce this optimization method in the area of unsaturated zone hydrology since it is adapted for solving accurately and efficiently complex nonlinear problems several numerical experiments have been conducted to evaluate the proposed inversion method using synthetic error free and error contaminated data for different textured soils inversion of the simulated error free data and examination of the related response surfaces demonstrated the uniqueness of the inverse solution and the suitability of the gmcs nms strategy when identifying four key parameters of the hydraulic functions described by the mualem van genuchten model inversion of the error contaminated data proved further the good stability of the inverse solution that is consistent with the needs required by real experiments

robustness results in linear quadratic gaussian based multivariable control designs the robustness of control systems with respect to model uncertainty is considered using simple frequency domain criteria available and new results are derived under a common framework in which the minimum singular value of the return differences transfer matrix is the key quantity in particular robustness results associated with multivariable control systems designed on the basis of linear quadratic lq and the linear quadratic gaussian lqg design methodologies are presented

reduced reference image quality assessment by structural similarity estimation reduced reference image quality assessment rr iqa provides a practical solution for automatic image quality evaluations in various applications where only partial information about the original reference image is accessible in this paper we propose an rr iqa method by estimating the structural similarity index ssim which is a widely used full reference fr image quality measure shown to be a good indicator of perceptual image quality specifically we extract statistical features from a multiscale multiorientation divisive normalization transform and develop a distortion measure by following the philosophy in the construction of ssim we find an interesting linear relationship between the fr ssim measure and our rr estimate when the image distortion type is fixed a regression by discretization method is then applied to normalize our measure across image distortion types we use six publicly available subject rated databases to test the proposed rr ssim method which shows strong correlations with both ssim and subjective quality evaluations finally we introduce the novel idea of partially repairing an image using rr features and use deblurring as an example to demonstrate its application

reduced reference quality assessment based on the entropy of dwt coefficients of locally weighted gradient magnitudes perceptual image quality assessment iqa attempts to use computational models to estimate the image quality in accordance with subjective evaluations reduced reference iqa rriqa methods make use of partial information or features extracted from the reference image for estimating the quality of distorted images finding a balance between the number of rr features and accuracy of the estimated image quality is essential and important in iqa in this paper we propose a training free low cost rriqa method that requires a very small number of rr features six rr features the proposed rriqa algorithm is based on the discrete wavelet transform dwt of locally weighted gradient magnitudes we apply human visual system s contrast sensitivity and neighborhood gradient information to weight the gradient magnitudes in a locally adaptive manner the rr features are computed by measuring the entropy of each dwt subband for each scale and pooling the subband entropies along all orientations resulting in l rr features one average entropy per scale for an l level dwt extensive experiments performed on seven large scale benchmark databases demonstrate that the proposed rriqa method delivers highly competitive performance as compared with the state of the art rriqa models as well as full reference ones for both natural and texture images the matlab source code of redlog and the evaluation results are publicly available online at https http lab engineering asu edu ivulab software redlog

a novel image quality assessment with globally and locally consilient visual quality perception computational models for image quality assessment iqa have been developed by exploring effective features that are consistent with the characteristics of a human visual system hvs for visual quality perception in this paper we first reveal that many existing features used in computational iqa methods can hardly characterize visual quality perception for local image characteristics and various distortion types to solve this problem we propose a new iqa method called the structural contrast quality index sc qi by adopting a structural contrast index sci which can well characterize local and global visual quality perceptions for various image characteristics with structural distortion types in addition to sci we devise some other perceptually important features for our sc qi that can effectively reflect the characteristics of hvs for contrast sensitivity and chrominance component variation furthermore we develop a modified sc qi called structural contrast distortion metric sc dm which inherits desirable mathematical properties of valid distance metricability and quasi convexity so it can effectively be used as a distance metric for image quality optimization problems extensive experimental results show that both sc qi and sc dm can very well characterize the hvs s properties of visual quality perception for local image characteristics and various distortion types which is a distinctive merit of our methods compared with other iqa methods as a result both sc qi and sc dm have better performances with a strong consilience of global and local visual quality perception as well as with much lower computation complexity compared with the state of the art iqa methods the matlab source codes of the proposed sc qi and sc dm are publicly available online at https sites google com site sunghobaecv iqa

visibility of wavelet quantization noise the discrete wavelet transform dwt decomposes an image into bands that vary in spatial frequency and orientation it is widely used for image compression measures of the visibility of dwt quantization errors are required to achieve optimal compression uniform quantization of a single band of coefficients results in an artifact that we call dwt uniform quantization noise it is the sum of a lattice of random amplitude basis functions of the corresponding dwt synthesis filter we measured visual detection thresholds for samples of dwt uniform quantization noise in y cb and cr color channels the spatial frequency of a wavelet is r2 sup spl lambda where r is the display visual resolution in pixels degree and spl lambda is the wavelet level thresholds increase rapidly with wavelet spatial frequency thresholds also increase from y to cr to cb and with orientation from lowpass to horizontal vertical to diagonal we construct a mathematical model for dwt noise detection thresholds that is a function of level orientation and display visual resolution this allows calculation of a perceptually lossless quantization matrix for which all errors are in theory below the visual threshold the model may also be used as the basis for adaptive quantization schemes

a visual model weighted cosine transform for image compression and quality assessment utilizing a cosine transform in image compression has several recognized performance benefits resulting in the ability to attain large compression ratios with small quality loss also incorporation of a model of the human visual system into an image compression or quality assessment technique intuitively should and has often proven to improve performance clearly then it should prove highly beneficial to combine the image cosine transform with a visual model in the past combining these two has been hindered by a fundamental problem resulting from the scene alteration that is necessary for proper cosine transform utilization a new analytical solution to this problem taking the form of a straightforward multiplicative weighting function is developed in this paper this solution is readily applicable to image compression and quality assessment in conjunction with a visual model and the image cosine transform in the development relevant aspects of a human visual system model are discussed and a refined version of the mean square error quality assessment measure is given which should increase this measure s utility

an efficient temporal distortion measure of videos based on spacetime texture abstract objective video quality assessment vqa plays an important role in controlling video quality most of the existing vqa methods measure motion related temporal distortion based on optical flow methods which are not consistently reliable in modeling general visual dynamics this paper presents a full reference temporal distortion measure based on spacetime texture a uniform and distributive descriptor of a broad set of spacetime structures our method measures the distortion of spacetime texture in video with a motion tuning strategy which effectively captures temporal distortion along the motion trajectories then it estimates self information based visual saliency for spatial pooling by reusing the motion descriptors we evaluated our method on two public vqa databases with a wide variety of distortion types in which the videos were viewed on a large screen or mobile devices the results show that our method correlates highly with the subjective quality and has high computational efficiency

shape from defocus via diffusion defocus can be modeled as a diffusion process and represented mathematically using the heat equation where image blur corresponds to the diffusion of heat this analogy can be extended to nonplanar scenes by allowing a space varying diffusion coefficient the inverse problem of reconstructing 3d structure from blurred images corresponds to an inverse diffusion that is notoriously ill posed we show how to bypass this problem by using the notion of relative blur given two images within each neighborhood the amount of diffusion necessary to transform the sharper image into the blurrier one depends on the depth of the scene this can be used to devise a global algorithm to estimate the depth profile of the scene without recovering the deblurred image using only forward diffusion

a geometrical theory of energy trajectories in quantum mechanics suppose f r is an attractive central potential of the form f r ki 1 g i f i r where f i is a set of basis potentials powers log hulthen sech2 and g i is a set of smooth increasing transformations which for a given f are either all convex or all concave formulas are derived for bounds on the energy trajectories enl fnl v of the hamiltonian h vf r where v is a coupling constant the transform f f is carried out in two steps f f f where f s is called the kinetic potential of f and is defined by f s inf f subject to d l2 r3 where d is the domain of h 1 and s a table is presented of the basis kinetic potentials f i s the general trajectory bounds f v are then shown to be given by a legendre transformation of the form s f s v f v where f s ki 1g i f i s and f v mins 0 s v f s with the aid of this potential construction set a kind of schrodinger lego ground state trajectory bounds are derived for a vari

square well representations for potentials in quantum mechanics a single particle moves in one dimension and obeys nonrelativistic quantum mechanics if the potential shape f x is symmetric and vanishes at infinity then without loss of generality it can be represented in the form of a mixture f x 0 a t w x t dt of square wells w x it is shown that a t f t and that the discrete eigenvalues of the schrodinger operator h d2 vf x are given approximately by the general formula en ean mins 0 s v 0 f t wn st2 dt where wn s n 0 are the known kinetic potentials associated with the simple square well problem for n 0 or 1 the approximations ena are lower bounds to the corresponding exact energies en the general formula is applied to the sech squared potential and to the truncated quartic oscillator

kinetic potentials in quantum mechanics suppose that the hamiltonian h vf r represents the energy of a particle which moves in an attractive central potential and obeys nonrelativistic quantum mechanics the discrete eigenvalues enl fnl v of h may be expressed as a legendre transformation fnl v mins 0 s vfnl s n 1 2 3 l 0 1 2 where the kinetic potentials fnl s associated with f r are defined by fnl s infdnl sup dnl 1 r f s 1 2r r d3r and dnl is an n dimensional subspace of l2 r3 labeled by ylm m 0 and contained in the domain d h of h if the potential has the form f r ni 1 g i f i r then in many interesting cases it turns out that the corresponding kinetic potentials can be closely approximated by ni 1 g i fnl i s this nice behavior of the kinetic potentials leads to a constructive global approximation theory for schrodinger eigenvalues as an illustration detailed recipes are provided for arbitrary linear combinations of power law potentials and the log potential fo

wavelet filter evaluation for image compression choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design although regularity is sometimes used in filter evaluation its success at predicting compression performance is only partial a more reliable evaluation can be obtained by considering an l level synthesis analysis system as a single input single output linear shift variant system with a response that varies according to the input location module 2 sup l 2 sup l by characterizing a filter bank according to its impulse response and step response in addition to regularity we obtain reliable and relevant for image coding filter evaluation metrics using this approach we have evaluated all possible reasonably short less than 36 taps in the synthesis analysis pair minimum order biorthogonal wavelet filter banks of this group of over 4300 candidate filter banks we have selected and present here the filters best suited to image compression while some of these filters have been published previously others are new and have properties that make them attractive in system design

wiener system modelling by exponentially weighted aggregation abstractin the paper the aggregation algorithm for wiener system modelling is proposed the method uses exponential weights to combine aggregate models from a given collection of d linear dynamic and dm nonlinear static models of the genuine system blocks that can be a priori hypotheses other system identification outcomes etc the resulting model has a noteworthy property it is almost as accurate as the best hypothetical wiener model built from a given collection this is caused by the fact that the error introduced by the aggregation routine decreases in the mean squared sense with growing number of measurements n as fast as cqn 1ln dmd where c and q are known constants simulations confirm theoretical findings and demonstrate applicability of the algorithm in engineering problems for small and moderate measurement data sets

asymptotic properties of eigenvalues in variational calculations for double well oscillators simple and accurate formulae for the eigenvalues of the hamiltonian with an anharmonic double well potential are presented special attention is paid to the following three regions of coupling parameters where difficulties arise i in the weak coupling limit the eigenvalues depend on the coupling parameter nonanalytically to obtain accurate explicit expressions in this limit a composite asymptotic expansion is applied ii in the strong coupling limit the derivation of asymptotic expansions is obstructed by the nonuniqueness of solutions to variational equations to overcome this obstacle a restricted variational procedure is suggested iii there exist also critical values of the coupling parameter at which eigenvalues cross zero in the regions around these critical values a dramatic increase of the percentage error occurs a remedy against this critical behaviour is the positive definite shift removing the critical regions the formulae obtained for the eigenvalues provide an accuracy within the errors not exceeding 3 for all values of the coupling parameter from zero to infinity

computation of matrix fraction descriptions of linear time invariant systems in this paper algorithms are presented for obtaining relatively prime matrix fraction descriptions mfd s of linear time invariant systems orthogonal coordinate transformations are used to reduce a given state space model to one whose state matrix is in block hessenberg form the observability controllability indexes of the system are also obtained in the process a recursive algorithm is then described for obtaining a relatively prime mfd from the block hessenberg representation it is then shown that some simplification can be made in the recursive algorithm by first reducing the block hessenberg form by means of a nonsingular triangular coordinate transformation to a more compact form such as the block frobenius form a permutation of the state variables of the block frobenius form yields a canonical representation similar to the luenberger canonical form some numerical and other properties of the algorithms are discussed and the use of the algorithms is illustrated by numerical examples the numerical performance of the algorithms is also compared with that of the structure algorithm of wolovich and falb

image quality assessment based on a degradation model we model a degraded image as an original image that has been subject to linear frequency distortion and additive noise injection since the psychovisual effects of frequency distortion and noise injection are independent we decouple these two sources of degradation and measure their effect on the human visual system we develop a distortion measure dm of the effect of frequency distortion and a noise quality measure nqm of the effect of additive noise the nqm which is based on peli s 1990 contrast pyramid takes into account the following 1 variation in contrast sensitivity with distance image dimensions and spatial frequency 2 variation in the local luminance mean 3 contrast interaction between spatial frequencies 4 contrast masking effects for additive noise we demonstrate that the nonlinear nqm is a better measure of visual quality than peak signal to noise ratio psnr and linear quality measures we compute the dm in three steps first we find the frequency distortion in the degraded image second we compute the deviation of this frequency distortion from an allpass response of unity gain no distortion finally we weight the deviation by a model of the frequency response of the human visual system and integrate over the visible frequencies we demonstrate how to decouple distortion and additive noise degradation in a practical image restoration system

objective picture quality scale pqs for image coding a new methodology for the determination of an objective metric for still image coding is reported this methodology is applied to obtain a picture quality scale pqs for the coding of achromatic images over the full range of image quality defined by the subjective mean opinion score mos this pqs takes into account the properties of visual perception for both global features and localized disturbances the pqs closely approximates the mos with a correlation coefficient of more than 0 92 as compared to 0 57 obtained using the conventional weighted mean square error wmse extensions and applications of the methodology and of the resulting metric are discussed

monotonic regression a new way for correlating subjective and objective ratings in image quality research to assess the performance of image quality metrics iqms some regressions such as logistic regression and polynomial regression are used to correlate objective ratings with subjective scores however some defects in optimality are shown in these regressions in this correspondence monotonic regression mr is found to be an effective correlation method in the performance assessment of iqms both theoretical analysis and experimental results have proven that mr performs better than any other regression we believe that mr could be an effective tool for performance assessment in the iqm research

image deconvolution with multi stage convex relaxation and its perceptual evaluation this paper proposes a new image deconvolution method using multi stage convex relaxation and presents a metric for perceptual evaluation of deconvolution results recent work in image deconvolution addresses the deconvolution problem via minimization with non convex regularization since all regularization terms in the objective function are non convex this problem can be well modeled and solved by multi stage convex relaxation this method adopted from machine learning iteratively refines the convex relaxation formulation using concave duality the newly proposed deconvolution method has outstanding performance in noise removal and artifact control a new metric transduced contrast to distortion ratio tcdr is proposed based on a human vision system hvs model that simulates human responses to visual contrasts it is sensitive to ringing and boundary artifacts and very efficient to compute we conduct comprehensive perceptual evaluation of image deconvolution using visual signal to noise ratio vsnr and tcdr experimental results of both synthetic and real data demonstrate that our method indeed improves the visual quality of deconvolution results with low distortions and artifacts

a detail based method for linear full reference image quality prediction in this paper a novel full reference method is proposed for image quality assessment using the combination of two separate metrics to measure the perceptually distinct impact of detail losses and of spurious details to this purpose the gradient of the impaired image is locally decomposed as a predicted version of the original gradient plus a gradient residual it is assumed that the detail attenuation identifies the detail loss whereas the gradient residuals describe the spurious details it turns out that the perceptual impact of detail losses is roughly linear with the loss of the positional fisher information while the perceptual impact of the spurious details is roughly proportional to a logarithmic measure of the signal to residual ratio the affine combination of these two metrics forms a new index strongly correlated with the empirical differential mean opinion score dmos for a significant class of image impairments as verified for three independent popular databases the method allowed alignment and merging of dmos data coming from these different databases to a common dmos scale by affine transformations unexpectedly the dmos scale setting is possible by the analysis of a single image affected by additive noise

two dimensional approach to full reference image quality assessment based on positional structural information a method for full reference visual quality assessment based on the 2 d combination of two diverse metrics is described the first metric is a measure of structural information loss based on the fisher information about the position of the structures in the observed images the second metric acts as a categorical indicator of the type of distortion that images underwent these two metrics constitute the inner state of a virtual cognitive model viewed as a system whose output is the automatic visual quality estimate the use of a 2 d metric fills the intrinsic incompleteness of methods based on a single metric while providing consistent response across different image impairment factors and blind distortion classification capability with a modest computational overhead the high accuracy and robustness of the method are demonstrated through cross validation experiments

depth from defocus a spatial domain approach a new method named stm is described for determining distance of objects and rapid autofocusing of camera systems stm uses image defocus information and is based on a new spatial domain convolution deconvolution transform the method requires only two images taken with different camera parameters such as lens position focal length and aperture diameter both images can be arbitrarily blurred and neither of them needs to be a focused image therefore stm is very fast in comparison with depth from focus methods which search for the lens position or focal length of best focus the method involves simple local operations and can be easily implemented in parallel to obtain the depth map of a scene stm has been implemented on an actual camera system named sparcs experiments on the performance of stm and their results on real world planar objects are presented the results indicate that the accuracy of stm compares well with depth from focus methods and is useful in practical applications the utility of the method is demonstrated for rapid autofocusing of electronic cameras

mixtures of potentials in quantum mechanics a global geometrical approximation theory for the spectra of schrodinger operators h d2 vf x is discussed the potential f x is composed either of sums or of continuous mixtures of soluble potentials in both cases it is proved that the kinetic potential formalism j math phys 24 324 1983 25 2078 1984 automatically yields optimal energy lower bounds the examples f x x x2 and f x basech2 tx dt are treated in detail

an svd based grayscale image quality measure for local and global assessment the important criteria used in subjective evaluation of distorted images include the amount of distortion the type of distortion and the distribution of error an ideal image quality measure should therefore be able to mimic the human observer we present a new grayscale image quality measure that can be used as a graphical or a scalar measure to predict the distortion introduced by a wide range of noise sources based on singular value decomposition it reliably measures the distortion not only within a distortion type at different distortion levels but also across different distortion types the measure was applied to five test images airplane boat goldhill lena and peppers using six types of distortion jpeg jpeg 2000 gaussian blur gaussian noise sharpening and dc shifting each with five distortion levels its performance is compared with psnr and two recent measures

an efficient technique to find semi analytical solutions for higher order multi point boundary value problems abstract a new semi analytical algorithm is presented to solve general multi point boundary value problems this method can be applied on nth order linear nonlinear singular and nonsingular multi point boundary value problems mathematical base of the method is presented convergence of the method is proved also the algorithm is applied to solve multi point boundary value problems including nonlinear sixth order nonlinear singular second order five point boundary value problems and a singularly perturbed boundary value problem comparison results show that the new method works more accurate than the other methods