the magnetic weyl calculus in the presence of a variable magnetic field the weyl pseudodifferential calculus must be modified the usual modification based on the minimal coupling principle at the level of the classical symbols does not lead to gauge invariant formulas if the magnetic field is not constant we present a gauge covariant quantization relying on the magnetic canonical commutation relations the underlying symbolic calculus is a deformation defined in terms of the magnetic flux through triangles of the classical moyal product

comparison theorems for the gap of schrodinger operators on cherche des bornes inferieures aux decompositions de valeur propre en fonction des proprietes geometriques de l ensemble avec v x e ainsi que sur la taille de v sur cet ensemble

on the continuity of spectra for families of magnetic pseudodifferential operators for families of magnetic pseudodifierential operators deflned by symbols and magnetic flelds depending continuously on a real parameter we show that the corresponding family of spectra also varies continuously with 1

experimental resuls of an evolution based adaptation strategy for vq image filtering abstract in this paper we propose the filtering of images based on the codebooks obtained from an evolution based adaptation strategy for vector quantization vq this evolution based vq bayesian filter vqbf is applied to noise removal and segmentation of a high resolution magnetic resonance image we compare our approach with other more conventional smoothing filters the results show that vqbf performs a smoothing that preserves region boundaries and small details it does not show the strong boundary diffusion and displacement that are common to smoothing filters border detection on the filtered images is also presented

lipshitz continuity of gap boundaries for hofstadter like spectra we consider an effective hamiltonianh representing the motion of a single band two dimensional electron in a uniform magnetic field thenh belongs to the rotation algebra namely the algebra of continuous functions over a non commutative 2 torus we define a non commutative analog of smooth functions by mean of elements of classc l n wherel andn characterize respectively the degree of differentiability with respect to the magnetic field and the torus variables we show that ifh is of classc 1 3 e the gap boundaries of the spectrum ofh are lipshitz continuous functions of the magnetic field at each point for which the gap is open

kronecker product approximations for image restoration with whole sample symmetric boundary conditions reflexive boundary conditions bcs assume that the array values outside the viewable region are given by a symmetry of the array values inside the reflection guarantees the continuity of the image in fact there are usually two choices for the symmetry symmetry around the meshpoint and symmetry around the midpoint the first is called whole sample symmetry in signal and image processing the second is half sample many researchers have developed some fast algorithms for the problems of image restoration with the half sample symmetric bcs over the years however little attention has been given to the whole sample symmetric bcs in this paper we consider the use of the whole sample symmetric boundary conditions in image restoration the blurring matrices constructed from the point spread functions psfs for the bcs have block toeplitz plus pseudohankel with toeplitz plus pseudohankel blocks structures recently regardless of symmetric properties of the psfs a technique of kronecker product approximations was successfully applied to restore images with the zero bcs half sample symmetric bcs and anti reflexive bcs respectively all these results extend quite naturally to the whole sample symmetric bcs since the resulting matrices have similar structures it is interesting to note that when the size of the true psf is small the computational complexity of the algorithm obtained for the kronecker product approximation of the resulting matrix in this paper is very small it is clear that in this case all calculations in the algorithm are implemented only at the upper left corner submatrices of the big matrices finally detailed experimental results reporting the performance of the proposed algorithm are presented

a new adaptive center weighted median filter for suppressing impulsive noise in images in this work a new adaptive center weighted median acwm filter is proposed for improving the performance of median based filters preserving image details while effectively suppressing impulsive noise the proposed filter is an adaptive cwm filter with an adjustable central weight obtained by partitioning the observation vector space to obtain the optimal weight for each block the efficient scalar quantization sq method is used to partition the observation vector space the center weight within each block is obtained by using a learning approach based on the least mean square lms algorithm the noise filtering procedure is progressively applied through several iterations so that the mean square error of the output can be minimized experimental results have demonstrated that the proposed filter outperforms many well accepted median based filters in terms of both noise suppression and detail preservation the proposed new filter also provides excellent robustness at various percentages of impulsive noise

quasi newton approach to nonnegative image restorations abstract image restoration or deblurring is the process of attempting to correct for degradation in a recorded image typically the blurring system is assumed to be linear and spatially invariant and fast fourier transform fft based schemes result in efficient computational image restoration methods however real images have properties that cannot always be handled by linear methods in particular an image consists of positive light intensities and thus a nonnegativity constraint should be enforced this constraint and other ways of incorporating a priori information have been suggested in various applications and can lead to substantial improvements in the reconstructions nevertheless such constraints are rarely implemented because they lead to nonlinear problems which require demanding computations we suggest efficient implementations for three nonnegatively constrained restorations schemes constrained least squares maximum likelihood and maximum entropy we show that with a certain parameterization and using a quasi newton scheme these methods are very similar in addition our formulation reveals a connection between our approach for maximum likelihood and the expectation maximization em method used extensively by astronomers numerical experiments illustrate that our approach is superior to em both in terms of accuracy and efficiency

an efficient iterative approach for large scale separable nonlinear inverse problems we present an efficient iterative approach to solving separable nonlinear least squares problems that arise in large scale inverse problems a variable projection gauss newton method is used to solve the nonlinear least squares problem and tikhonov regularization is incorporated using an iterative hybrid scheme regularization parameters are chosen automatically using a weighted generalized cross validation method thus providing a nonlinear solver that requires very little input from the user applications from image deblurring and digital tomosynthesis illustrate the effectiveness of the resulting numerical scheme

weighted and extended total variation for image restoration and decomposition in various information processing tasks obtaining regularized versions of a noisy or corrupted image data is often a prerequisite for successful use of classical image analysis algorithms image restoration and decomposition methods need to be robust if they are to be useful in practice in particular this property has to be verified in engineering and scientific applications by robustness we mean that the performance of an algorithm should not be affected significantly by small deviations from the assumed model in image processing total variation tv is a powerful tool to increase robustness in this paper we define several concepts that are useful in robust restoration and robust decomposition we propose two extended total variation models weighted total variation wtv and extended total variation etv we state generic approaches the idea is to replace the tv penalty term with more general terms the motivation is to increase the robustness of rof rudin osher fatemi model and to prevent the staircasing effect due to this method moreover rewriting the non convex sublinear regularizing terms as wtv we provide a new approach to perform minimization via the well known chambolle s algorithm the implementation is then more straightforward than the half quadratic algorithm the behavior of image decomposition methods is also a challenging problem which is closely related to anisotropic diffusion etv leads to an anisotropic decomposition close to edges improving the robustness it allows to respect desired geometric properties during the restoration and to control more precisely the regularization process we also discuss why compression algorithms can be an objective method to evaluate the image decomposition quality

fine granularity and spatially adaptive regularization for projection based image deblurring this paper studies two classes of regularization strategies to achieve an improved tradeoff between image recovery and noise suppression in projection based image deblurring the first is based on a simple fact that r times landweber iteration leads to a fixed level of regularization which allows us to achieve fine granularity control of projection based iterative deblurring by varying the value r the regularization behavior is explained by using the theory of lagrangian multiplier for variational schemes the second class of regularization strategy is based on the observation that various regularized filters can be viewed as nonexpansive mappings in the metric space a deeper understanding about different regularization filters can be gained by probing into their asymptotic behavior the fixed point of nonexpansive mappings by making an analogy to the states of matter in statistical physics we can observe that different image structures smooth regions regular edges and textures correspond to different fixed points of nonexpansive mappings when the temperature regularization parameter varies such an analogy motivates us to propose a deterministic annealing based approach toward spatial adaptation in projection based image deblurring significant performance improvements over the current state of the art schemes have been observed in our experiments which substantiates the effectiveness of the proposed regularization strategies

designing of a type 2 fuzzy logic filter for improving edge preserving restoration of interlaced to progressive conversion this paper focuses on recently advanced fuzzy models and the application of type 2 fuzzy sets in video deinterlacing the final goal of the proposed deinterlacing algorithm is to exactly determine an unknown pixel value while preserving the edges and details of the image to begin we will discuss some artefacts of spatial temporal and spatio temporal domain deinterlacing methods in order to address the aforementioned issues we adopted type 2 fuzzy sets concepts to design a weight evaluating approach in the proposed method the upper and lower fuzzy membership functions of the type 2 fuzzy logic filters are derived from the type 1 or primary fuzzy membership function the weights from upper and lower membership functions are considered to be multiplied with the candidate deinterlaced pixels experimental results proved that the performance of the proposed method was superior both objectively and subjectively to other different conventional deinterlacing methods moreover the proposed method preserved the smoothness of the original image edges and produced a high quality progressive image

low lying spectral gaps induced by slowly varying magnetic fields abstract we consider a periodic schrodinger operator in two dimensions perturbed by a weak magnetic field whose intensity slowly varies around a positive mean we show in great generality that the bottom of the spectrum of the corresponding magnetic schrodinger operator develops spectral islands separated by gaps reminding of a landau level structure first we construct an effective hofstadter like magnetic matrix which accurately describes the low lying spectrum of the full operator the construction of this effective magnetic matrix does not require a gap in the spectrum of the non magnetic operator only that the first and the second bloch eigenvalues do not cross but their ranges might overlap the crossing case is more difficult and will be considered elsewhere second we perform a detailed spectral analysis of the effective matrix using a gauge covariant magnetic pseudo differential calculus adapted to slowly varying magnetic fields as an application we prove in the overlapping case the appearance of spectral islands separated by gaps

on asymptotic perturbation theory for quantum mechanics almost invariant subspaces and gauge invariant magnetic perturbation theory singular perturbation theory for quantum mechanics is considered in a framework generalizing the spectral concentration theory under very general conditions asymptotic estimations on the rayleigh schrodinger expansions of the perturbed spectral projections are obtained as a consequence almost invariant subspaces of exponential order are constructed the results cover practically all singular perturbations considered in nonrelativistic quantum mechanics in the magnetic field case under the condition that the magnetic field does not increase at infinity a gauge invariant perturbation theory leading to convergent series with field dependent coefficients is developed

fast computation of exact zernike moments using cascaded digital filters zernike moments have been extensively used and have received much research attention in a number of fields object recognition image reconstruction image segmentation edge detection and biomedical imaging however computation of these moments is time consuming thus we present a fast computation technique to calculate exact zernike moments by using cascaded digital filters the novelty of the method proposed in this paper lies in the computation of exact geometric moments directly from digital filter outputs without the need to first compute geometric moments the mathematical relationship between digital filter outputs and exact geometric moments is derived and then they are used in the formulation of exact zernike moments a comparison of the speed of performance of the proposed algorithm with other state of the art alternatives shows that the proposed algorithm betters current computation time and uses less memory

spectral and propagation results for magnetic schrodinger operators a c algebraic framework abstract we study generalized magnetic schrodinger operators of the form h h a v h a v where h is an elliptic symbol a i a with a a vector potential defining a variable magnetic field b and v is a scalar potential we are mainly interested in anisotropic functions b and v the first step is to show that these operators are affiliated to suitable c algebras of magnetic pseudodifferential operators a study of the quotient of these c algebras by the ideal of compact operators leads to formulae for the essential spectrum of h h a v expressed as a union of spectra of some asymptotic operators supported by the quasi orbits of a suitable dynamical system the quotient of the same c algebras by other ideals give localization results on the functional calculus of the operators h h a v which can be interpreted as non propagation properties of their unitary groups

suppression of salt and pepper noise based on youden designs abstract this paper presents a new class of algorithms based on youden designs to detect and restore edges present in an image imbedded by mixture or salt and pepper noise the mixture noise consists of a uncorrelated or correlated noisy background plus uncorrelated impulsive noise the objective is to restore pixels affected by the impulsive part of the mixture noise the approach is to consider that these pixels have lost their true value and their estimate is obtained via the normal equation that yields the least sum of square error lsse this procedure is known in the literature as the missing value approach problem the estimates are introduced into the image data and an anova technique based on youden design is carried out we introduce youden designs which are special symmetric balanced incomplete block sbib designs the pertinent statistical tests and estimates of the factor effects we derive the estimate of the missing value for the uncorrelated noise environment as well as for the correlated one the high level of performance of these algorithms can be evaluated visually via the input output images and objectively via the input output signal to noise ratio snr

switching based filter based on dempster s combination rule for image processing in this work a two pass switching rank ordered arithmetic mean tsram filter that preserves image details while effectively suppressing impulse noise is proposed to improve the performance of switching based median filters the proposed filter mechanism includes an efficient impulse detector based on the dempster shafer d s evidence theory and a rank ordered arithmetic mean filter that works by estimating the noise free ordered mean values excluding the current pixel a modified dempster s combination rule is applied to the impulse detector to improve filtering performance a simple switching median filter is included to perform second pass filtering experimental results show that the proposed filter outperforms many well accepted switching based median filters in terms of both noise suppression and detail preservation providing excellent robustness at various percentages of impulse noise

universal lower bounds on eigenvalue splittings for one dimensional schrodinger operators we provide lower bounds on the eigenvalue splitting for d2 dx2 v x depending only on qualitative properties ofv for example ifv is c on a b ande n en 1 are two successive eigenvalues of d2 dx2 v withu a u b 0 boundary conditions and if lambda mathop max limits e in e n 1 e n x in a b e v x 1 2 then e n e n 1 geqq pi lambda 2 exp left lambda b a right the exponential factor in such bounds are saturated precisely in tunneling examples our results arenot restricted tov s of compact support but only require e n mathop lim limits overline x to infty v x

non relativistic coulomb problem in a one dimensional quantum mechanics it is shown that unlike the model based only on the potential singularity u x mod x mod 1 the group of hidden symmetry explains not only the double degeneration of the energy spectrum but also the explicit form of the spectrum wavefunctions and an extra constant of motion analogous to the runge lenz vector

effective dynamics for bloch electrons peierls substitution and beyond we consider an electron moving in a periodic potential and subject to an additional slowly varying external electrostatic potential x and vector potential a x with x d and 1 we prove that associated to an isolated family of bloch bands there exists an almost invariant subspace of l 2 d and an effective hamiltonian governing the evolution inside this subspace to all orders in to leading order the effective hamiltonian is given through the peierls substitution we explicitly compute the first order correction from a semiclassical analysis of this effective quantum hamiltonian we establish the first order correction to the standard semiclassical model of solid state physics

the discrete cosine transform each discrete cosine transform dct uses n real basis vectors whose components are cosines in the dct 4 for example the j th component of boldv k is cos j frac 1 2 k frac 1 2 frac pi n these basis vectors are orthogonal and the transform is extremely useful in image processing if the vector boldx gives the intensities along a row of pixels its cosine series sum c k boldv k has the coefficients c k boldx boldv k n they are quickly computed from a fast fourier transform but a direct proof of orthogonality by calculating inner products does not reveal how natural these cosine vectors are we prove orthogonality in a different way each dct basis contains the eigenvectors of a symmetric second difference matrix by varying the boundary conditions we get the established transforms dct 1 through dct 4 other combinations lead to four additional cosine transforms the type of boundary condition dirichlet or neumann centered at a meshpoint or a midpoint determines the applications that are appropriate for each transform the centering also determines the period n 1 or n in the established transforms n frac 1 2 or n frac 1 2 in the other four the key point is that all these eigenvectors of cosines come from simple and familiar matrices