supersymmetric transformations for coupled channels with threshold differences the asymptotic behaviour of the superpotential of general susy transformations for a coupled channel hamiltonian with different thresholds is analysed it is shown that asymptotically the superpotential can tend to a diagonal matrix with an arbitrary number of positive and negative entries depending on the choice of the factorization solution the transformation of the jost matrix is generalized to non conservative susy transformations introduced in sparenberg et al 2006 j phys a math gen 39 l639 applied to the zero initial potential the method permits the construction of superpartners with a nontrivially coupled jost matrix illustrations are given for two and three channel cases

microlocal analysis of some isospectral deformations we study the microlocal structure of the examples of isospectral deformations of riemannian manifolds given by d deturck and c gordon in det gi the schwartz kernel of the intertwining operators considered by them may be written as an oscillatory integral with a singular phase function and product type amplitude in certain instances we identify them as belonging to the space of fourier integral operators associated with various pairwise intersecting lagrangians after formulating a class of operators incorporating the most relevant features of the operators above we establish a composition calculus for this class and show that is not necessary to introduce new lagrangians in the composition

local tomography for the generalized radon transform let f be piecewise smooth with only jump discontinuities across s singsupp f the asymptotic behavior of cal b f near s is obtained here cal b is an elliptic pseudodifferential operator which satisfies certain not very restrictive assumptions an efficient numerical scheme for computing local tomography lt functions for the generalized radon transform grt is proposed the effect of mollification of the two lt functions is investigated an algorithm for finding values of jumps of f knowing local tomographic data corresponding to the grt is developed and tested on the simulated data

convergence of an iterative method for total variation denoising in total variation denoising one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion several approaches based on this idea have recently been shown to be very effective particularly for denoising functions with discontinuities this paper analyzes the convergence of an iterative method for solving such problems the iterative method involves a lagged diffusivity approach in which a sequence of linear diffusion problems are solved global convergence in a finite dimensional setting is established and local convergence properties including rates and their dependence on various parameters are examined

an explicit koppelman formula for ddc and green currents on mathbb p n we compute a quite explicit koppelman formula for dd c on projective space and obtain green currents for closed p p currents

on sobolev instability of the interior problem of tomography as is known solving the interior problem with prior data specified on a finite collection of intervals i i i i is equivalent to analytic continuation of a function from i i i i to an open set j in the paper we prove that this analytic continuation can be obtained with the help of a simple explicit formula which involves summation of a series our second result is that the operator of analytic continuation is not stable for any pair of sobolev spaces regardless of how close the set j is to i i i i our main tool is the singular value decomposition of the operator h e 1 that arises when the interior problem is reduced to a problem of inverting the hilbert transform from incomplete data the asymptotics of the singular values and singular functions of h e 1 the latter being valid uniformly on compact subsets of the interior of i i i i was obtained in 5 using these asymptotics we can accurately measure the degree of ill posedness of the analytic continuation as a function of the target interval j our last result is the convergence of the asymptotic approximation of the singular functions in the l 2 i i l 2 i i sense we also present a preliminary numerical experiment which illustrates how to use our results for reducing the instability of the analytic continuation by optimizing the position of the intervals with prior knowledge

permittivity recovery from multiple characteristic electric waves we use the calculus of fourier integral operators with singular symbols to reconstruct electrical permittivity singularities from remote measurements of scattered electric waves the reconstruction is microlocal and is uniformly valid in the neighborhood of conically refracted waves

local algorithms in exterior tomography exterior tomographic data are taken over lines outside a central region and such data occur in the industrial nondestructive evaluation of large objects such as rockets we explain using microlocal analysis which singularities are well reconstructed from exterior data and we explain how this phenomenon is reflected in the singular value decomposition for the exterior transform e t quinto singular value decompositions and inversion methods for the exterior radon transform and a spherical transform j math anal appl 95 1983 437 448 we extend lambda tomography to exterior data and to limited angle exterior data the algorithm is tested on industrial data from perceptics inc

eigenphase preserving two channel susy transformations we propose a new kind of supersymmetric susy transformation in the case of the two channel scattering problem with equal thresholds for partial waves of the same parity this two fold transformation is based on two imaginary factorization energies with opposite signs and with mutually conjugated factorization solutions we call it an eigenphase preserving susy transformation as it relates two hamiltonians the scattering matrices of which have identical eigenphase shifts in contrast to known phase equivalent transformations the mixing parameter is modified by the eigenphase preserving transformation

local tomography for the limited angle problem abstract we investigate local tomography in the case of limited angle data the main theoretical tool is analysis of the singularities of pseudodifferential operators pdo acting on piecewise smooth functions amplitudes of the pdo we consider are allowed to be nonsmooth in the dual variable across the boundary of a wedge results of numerical simulation of limited angle local tomography confirm basic theoretical conclusions

total variation projection with first order schemes this article proposes a new algorithm to compute the projection on the set of images whose total variation is bounded by a constant the projection is computed through a dual formulation that is solved by first order non smooth optimization methods this yields an iterative algorithm that applies iterative soft thresholding to the dual vector field and for which we establish convergence rate on the primal iterates this projection algorithm can then be used as a building block in a variety of applications such as solving inverse problems under a total variation constraint or for texture synthesis numerical results are reported to illustrate the usefulness and potential applicability of our tv projection algorithm on various examples including denoising texture synthesis inpainting deconvolution and tomography problems we also show that our projection algorithm competes favorably with state of the art tv projection methods in terms of convergence speed

singular matrix darboux transformations in the inverse scattering method singular darboux transformations in contrast to the conventional ones have a singular matrix as a coefficient before the derivative we incorporated such transformations into a chain of conventional transformations and presented determinant formulas for the resulting action of the chain a determinant representation of the kohlhoff von geramb solution to the marchenko equation is given

interpolation of missing data in image sequences this paper presents a number of model based interpolation schemes tailored to the problem of interpolating missing regions in image sequences these missing regions may be of arbitrary size and of random but known location this problem occurs regularly with archived film material the film is abraded or obscured in patches giving rise to bright and dark flashes known as dirt and sparkle in the motion picture industry both 3 d autoregressive models and 3 d markov random fields are considered in the formulation of the different reconstruction processes the models act along motion directions estimated using a multiresolution block matching scheme it is possible to address this sort of impulsive noise suppression problem with median filters and comparisons with earlier work using multilevel median filters are performed these comparisons demonstrate the higher reconstruction fidelity of the new interpolators

iterative deblurring for ct metal artifact reduction iterative deblurring methods using the expectation maximization em formulation and the algebraic reconstruction technique art respectively are adapted for metal artifact reduction in medical computed tomography ct in experiments with synthetic noise free and additive noisy projection data of dental phantoms it is found that both simultaneous iterative algorithms produce superior image quality as compared to filtered backprojection after linearly fitting projection gaps furthermore the em type algorithm converges faster than the art type algorithm in terms of either the i divergence or euclidean distance between ideal and reprojected data in the authors simulation also for a given iteration number the em type deblurring method produces better image clarity but stronger noise than the art type reconstruction the computational complexity of em and art based iterative deblurring is essentially the same dominated by reprojection and backprojection relevant practical and theoretical issues are discussed

an axiomatic approach to image interpolation we discuss possible algorithms for interpolating data given in a set of curves and or points in the plane we propose a set of basic assumptions to be satisfied by the interpolation algorithms which lead to a set of models in terms of possibly degenerate elliptic partial differential equations the absolute minimal lipschitz extension model amle is singled out and studied in more detail we show experiments suggesting a possible application the restoration of images with poor dynamic range

variational restoration of nonflat image features models and algorithms we develop both mathematical models and computational algorithms for variational denoising and restoration of nonflat image features nonflat image features are those that live on riemannian manifolds instead of on the euclidean spaces familiar examples include the orientation feature from optical flows or gradient flows that lives on the unit circle s1 the alignment feature from fingerprint waves or certain texture images that lives on the real projective line mathbb rp 1 and the chromaticity feature from color images that lives on the unit sphere s2 in this paper we apply the variational method to denoise and restore general nonflat image features mathematical models for both continuous image domains and discrete domains or graphs are constructed riemannian objects such as metric distance and levi civita connection play important roles in the models computational algorithms are also developed for the resulting nonlinear equations the mathematical framework can be applied to res

orientation diffusions diffusions are useful for image processing and computer vision because they provide a convenient way of smoothing noisy data analyzing images at multiple scales and enhancing discontinuities a number of diffusions of image brightness have been defined and studied so far they may be applied to scalar and vector valued quantities that are naturally associated with intervals of either the real line or other flat manifolds some quantities of interest in computer vision and other areas of engineering that deal with images are defined on curved manifolds typical examples are orientation and hue that are defined on the circle generalizing brightness diffusions to orientation is not straightforward especially in the case where a discrete implementation is sought an example of what may go wrong is presented a method is proposed to define diffusions of orientation like quantities first a definition in the continuum is discussed then a discrete orientation diffusion is proposed the behavior of such diffusions is explored both analytically and experimentally it is shown how such orientation diffusions contain a nonlinearity that is reminiscent of edge process and anisotropic diffusion a number of open questions are proposed

cone beam local tomography methods systems and processes for providing efficient image reconstruction using local cone beam tomography which provide a reduced level of artifacts without suppressing the strength of the useful features and in a dynamic case provide reconstruction of objects that are undergoing a change during the scan an embodiment provides a method of reconstructing an image from cone beam data provided by at least one detector the method includes collecting cb projection data of an object storing the cb projection data in a memory and reconstructing the image from the local cb projection data in the reconstructing step a combination of derivatives of the cb projection data that will result in suppressing the artifacts are found the combination of derivatives includes collecting cone beam data that represents a collection of integrals that represent the object

maximum likelihood reconstruction for emission tomography previous models for emission tomography et do not distinguish the physics of et from that of transmission tomography we give a more accurate general mathematical model for et where an unknown emission density x y z generates and is to be reconstructed from the number of counts n d in each of d detector units d within the model we give an algorithm for determining an estimate of which maximizes the probability p n of observing the actual detector count data n over all possible densities let independent poisson variables n b with unknown means b b 1 b represent the number of unobserved emissions in each of b boxes pixels partitioning an object containing an emitter suppose each emission in box b is detected in detector unit d with probability p b d d 1 d with p b d a one step transition matrix assumed known we observe the total number n n d of emissions in each detector unit d and want to estimate the unknown b b 1 b for each the observed data n has probability or likelihood p n the em algorithm of mathematical statistics starts with an initial estimate 0 and gives the following simple iterative procedure for obtaining a new estimate new from an old estimate old to obtain k k 1 2 new b old b dd 1 n d p b d old b p b d b 1 b

coupled channel scattering and separation of coupled differential equations by generalized darboux transformations general methods for separation of coupled differential equations are applied in coupled channel scattering theory with appropriate asymptotic conditions it is shown that the problems with thresholds cannot be separated finally it is pointed out that separation of the coupled channel s wave problem without thresholds can be realized by the use of generalized darboux transformations

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

characterization of metal artifacts in x ray computed tomography metal streak artifacts in x ray computerized tomography ct are characterized here using the notion of the wavefront set from microlocal analysis the metal artifacts are caused mainly from the mismatch of the forward model of the filtered back projection the presence of metallic subjects in an imaging subject violates the model s assumption of the ct sinogram data being the radon transform of an image the increasing use of metallic implants has increased demand for the reduction of metal artifacts in the field of dental and medical radiography however it is a challenging issue due to the serious difficulties in analyzing the x ray data which depends nonlinearly on the distribution of the metallic subject in this paper we for the first time provide a mathematical analysis to characterize the structure of metal streaking artifacts the metal streaking artifacts are produced along the line tangent to boundaries of the metal region touching at least two different boundaries we also found a sufficient condition for the nonexistence of the metal streaking artifacts 2016 wiley periodicals inc

hilbert integrals singular integrals and radon transforms i on introduit deux nouvelles classes d operateurs on etudie leur relation et on montre comment on peut les appliquer a l etude des problemes aux valeurs limites

lp harmonic analysis and radon transforms on the heisenberg group in this paper harmonic analysis in the heisenberg group heisn cn r with group law z t z t z z t t 12im z z is taken to mean the joint spectral theory of the operators l heisenberg laplacian and t t the spectral decomposition of e l2 is given explicitly as e 0 e d where e 1 k 0 1 2 and e z t n 2 n 1 n 2k n 1 exp ie tn 2k exp z 24 n 2k lkn 1 z 22 n 2k where lkn 1 denotes the laguerre polynomial the eigenvalues are it e e n 2k e and l k e k e this decomposition is essentially well known but has not previously been described in this light it is also the decomposition into irreducibles of the representation of the heisenberg motion group semi direct product of heisn and u n on l2 heisn the main result is a summability in lp of the decomposition for e lp 1 p limr 1 rk 0 ed for p 1 only a weaker substitute is available and for p the decomposition is false there is also a plancherel formula for l2 2 2 k e n 2k 0 k e z 0 2dzd a number of explicit examples of the decomposition are computed including part of the schrodinger propagator eisl the heisenberg radon transform is defined by r z t n z t w 0 dw this operator was studied by geller and stein it is shown to be bounded from lp to lq if and only if p 2n 2 2n 1 and q 2n 2 some generalizations of these results to the free step two nilpotent lie groups are given but the results are not as complete

the asymptotics of optimal equiripple filters for equiripple filters the relation among the filter length n 1 the transition bandwidth spl delta spl omega and the optimal passband and stopband errors spl delta sub p and spl delta sub s has been a secret for more than 20 years this paper is aimed at solving this mystery we derive the exact asymptotic results in the weight free case spl delta sub p spl delta sub s spl delta which enables us to interpret and improve the existing empirical formulas our main results are finally combined into a formula in the transition band the filter response is discovered to be asymptotically close to a scaled error function the main tools are potential theory in the complex plane and asymptotic analysis

color image enhancement via chromaticity diffusion a novel approach for color image denoising is proposed in this paper the algorithm is based on separating the color data into chromaticity and brightness and then processing each one of these components with partial differential equations or diffusion flows in the proposed algorithm each color pixel is considered as an n dimensional vector the vectors direction a unit vector gives the chromaticity while the magnitude represents the pixel brightness the chromaticity is processed with a system of coupled diffusion equations adapted from the theory of harmonic maps in liquid crystals this theory deals with the regularization of vectorial data while satisfying the intrinsic unit norm constraint of directional data such as chromaticity both isotropic and anisotropic diffusion flows are presented for this n dimensional chromaticity diffusion flow the brightness is processed by a scalar median filter or any of the popular and well established anisotropic diffusion flows for scalar image enhancement we present the underlying theory a number of examples and briefly compare with the current literature

on the equivalence of the integral and the differential exact solution generation methods for the one dimensional schrodinger equation it is demonstrated that the integral exact solution generation methods for the one dimensional schrodinger equation based on the gelfand levitan formalism are in some cases equivalent to the differential ones based on the n order darboux transformation some new exact solvable potentials are generated from the effective coulomb potential and the harmonic oscillator potential a new form of n soliton potential i e reflectionless potential with n discrete energy levels disposed in a desirable manner based on an explicit expression for an n order wronski determinant constructed from hyperbolic functions and its orthonormal discrete spectrum eigenfunctions are given

orientation matching minimization for image denoising and inpainting in this paper we propose an orientation matching functional minimization for image denoising and image inpainting following the two step tv stokes algorithm rahman et al in scale space and variational methods in computer vision pp 473 482 springer heidelberg 2007 tai et al in image processing based on partial differential equations pp 3 22 springer heidelberg 2006 bertalmio et al in proc conf comp vision pattern rec pp 355 362 2001 a regularized tangential vector field with zero divergence condition is first obtained then a novel approach to reconstruct the image is proposed instead of finding an image that fits the regularized normal direction from the first step we propose to minimize an orientation matching cost measuring the alignment between the image gradient and the regularized normal direction this functional yields a new nonlinear partial differential equation pde for reconstructing denoised and inpainted images the equation has an adaptive diffusivity depending on the orientation of the regularized normal vector field providing reconstructed images which have sharp edges and smooth regions the additive operator splitting aos scheme is used for discretizing euler lagrange equations we present the results of various numerical experiments that illustrate the improvements obtained with the new functional

the geodesic ray transform on riemannian surfaces with conjugate points we study the geodesic x ray transform x on compact riemannian surfaces with conjugate points regardless of the type of the conjugate points we show that we cannot recover the singularities and therefore this transform is always unstable ill posed we describe the microlocal kernel of x and relate it to the conjugate locus we present numerical examples illustrating the cancellation of singularities we also show that the attenuated x ray transform is well posed if the attenuation is positive and there are no more than two conjugate points along each geodesic but it is still ill posed if there are three or more conjugate points those results follow from our analysis of the weighted x ray transform

nonlocal inversion formulas for the x ray transform etude de la reconstruction d une fonction f x sur r n a partir de ses integrales sur des plans k dimensionnels cas de k 1

optimal approximations by piecewise smooth functions and associated variational problems abstract this reprint will introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision in computer vision a fundamental problem is to appropriately decompose the domain r of a function g x y of two variables this problem starts by describing the physical situation which produces images assume that a three dimensional world is observed by an eye or camera from some point p and that g1 rho represents the intensity of the light in this world approaching the point sub 1 from a direction rho if one has a lens at p focusing this light on a retina or a film in both cases a plane domain r in which we may introduce coordinates x y then let g x y be the strength of the light signal striking r at a point with coordinates x y g x y is essentially the same as sub 1 rho possibly after a simple transformation given by the geometry of the imaging syste the function g x y defined on the plane domain r will be called an image what sort of function is g the light reflected off the surfaces si of various solid objects o sub i visible from p will strike the domain r in various open subsets r sub i when one object o1 is partially in front of another object o2 as seen from p but some of object o2 appears as the background to the sides of o1 then the open sets r1 and r2 will have a common boundary the edge of object o1 in the image defined on r and one usually expects the image g x y to be discontinuous along this boundary jhd

near peak scattering and the corrected kirchhoff approximation for a convex obstacle abstract the uniform asympotic behavior of the scattering amplitude near the forward peak in the case of classical scattering of waves by a convex obstacle is derived a microlocal model is obtained for the scattering operator this is achieved by use of a parametrix for diffractive boundary problems and by a new study of a class of fourier integral operators those with folding canonical relations a crucial ingredient consists of putting a fourier integral operator with folding canonical relation into a normal form the analysis also gives the asymptotic behavior of the normal derivative of the scattered wave on a neighbourhood of the shadow boundary thus providing a corrected version of the kirchhoff approximation

support theorems for radon transforms on real analytic line complexes in three space in this article we prove support theorems for radon transforms with arbitrary nonzero real analytic measures on line complexes three dimensional sets of lines in r 3 let f be a distribution of compact support on r 3 assume y is a real analytic admissible line complex and y 0 is an open connected subset of y with one line in y 0 disjoint from supp f under weak geometric assumptions if the radon transform of f is zero for all lines in y 0 then supp f intersects no line in y 0 these theorems are more general than previous results even for the classical transform we also prove a support theorem for the radon transform on a nonadmissible line complex our proofs use analytic microlocal analysis and information about the analytic wave front set of a distribution at the boundary of its support

fourier integral operators with cusp singularities we study the boundedness properties on lebesgue and sobolev spaces of fourier integral operators associated with canonical relations such that at least one of the projections is a simple whitney cusp in the process we obtain decay estimates for oscillatory integral operators whose symplectic relations have the same singular structure such singularities occur generically for averages over lines and curves in inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 01i on l 2 we show that the operators lose 1 3 derivative to obtain sharp results off of l 2 we need to impose an additional transversality condition satisfied by many geometric averaging operators which leads to the notion of a strong cusp these estimates can be further improved if we impose curvature conditions on the cusp surface one application is the l 2 comp l 2 1 6 loc and l 12 7 comp l 2 loc boundedness of restrictions of the x ray transform on inline graphic xmlns xlink http www w3 org 1999 xlink xlink href 02i to four dimensional families of lines satisfying a natural curvature and torsion condition

single and coupled channel radial inverse scattering with supersymmetric transformations the present status of the three dimensional inverse scattering method with supersymmetric transformations is reviewed for the coupled channel case we first revisit in a pedagogical way the single channel case where the supersymmetric approach is shown to provide a complete efficient and elegant solution to the inverse scattering problem for the radial schrodinger equation with short range interactions a special emphasis is put on the differences between conservative and non conservative transformations i e transformations that do or do not conserve the behaviour of solutions of the radial schrodinger equation at the origin in particular we show that for the zero initial potential a non conservative transformation is always equivalent to a pair of conservative transformations these single channel results are illustrated on the inversion of the neutron proton triplet eigenphase shifts for the s and d waves we then summarize and extend our previous works on the coupled channel case i e on systems of coupled radial schrodinger equations and stress remaining difficulties and open questions of this problem by putting it in perspective with the single channel case we mostly concentrate on two channel examples to illustrate general principles while keeping mathematics as simple as possible in particular we discuss the important difference between the equal threshold and different threshold problems for equal thresholds conservative transformations can provide non diagonal jost and scattering matrices iterations of such transformations in the two channel case are studied and shown to lead to practical algorithms for inversion a convenient particular technique where the mixing parameter can be fitted without modifying the eigenphases is developed with iterations of pairs of conjugate transformations this technique is applied to the neutron proton triplet s d scattering matrix for which exactly solvable matrix potential models are constructed for different thresholds conservative transformations do not seem to be able to provide a non trivial coupling between channels in contrast a single non conservative transformation can generate coupled channel potentials starting from the zero potential and is a promising first step towards a full solution to the coupled channel inverse problem with threshold differences

super potentials of positive closed currents intersection theory and dynamics we introduce a notion of super potential for positive closed currents of bidegree p p on projective spaces this gives a calculus on positive closed currents of arbitrary bidegree we define in particular the intersection of such currents and the pull back operator by meromorphic maps one of the main tools is the introduction of structural discs in the space of positive closed currents which gives a geometry on that space we apply the theory of super potentials to construct green currents for rational maps and to study equidistribution problems for holomorphic endomorphisms and for polynomial automorphisms

a class of singular fourier integral operators in synthetic aperture radar imaging in this article we analyze the microlocal properties of the linearized forward scattering operator f and the normal operator f f where f is the l 2 adjoint of f which arises in synthetic aperture radar imaging for the common midpoint acquisition geometry when f is applied to the scattered data artifacts appear we show that f f can be decomposed as a sum of four operators each belonging to a class of distributions associated to two cleanly intersecting lagrangians i p l 0 1 thereby explaining the latter artifacts

local tomography in electron microscopy we present a new local tomographic algorithm applicable to electron microscope tomography our algorithm applies to the standard data acquisition method single axis tilting as well as to more arbitrary acquisition methods including double axis and conical tilt using microlocal analysis we put the reconstructions in a mathematical context explaining which singularities are stably visible from the limited data given by the data collection protocol in the electron microscope finally we provide reconstructions of real specimens from electron tomography data

on the convergence of the lagged diffusivity fixed point method in total variation image restoration in this paper we show that the lagged diffusivity fixed point algorithm introduced by vogel and oman in siam j sci comput 17 1996 pp 227 238 to solve the problem of total variation denoising proposed by rudin osher and fatemi in phys d 60 1992 pp 259 268 is a particular instance of a class of algorithms introduced by voss and eckhardt in computing 25 1980 pp 243 251 whose origins can be traced back to weiszfeld s original work for minimizing a sum of euclidean lengths tohoku math j 43 1937 pp 355 386 there have recently appeared several proofs for the convergence of this algorithm g aubert et al technical report 94 01 informatique signaux et systemes de sophia antipolis 1994 a chambolle and p l lions technical report 9509 ceremade 1995 and d c dobson and c r vogel siam j numer anal 34 1997 pp 1779 1791 here we present a proof of the global and linear convergence using the framework introduced in h voss and u eckhart computing 25 1980 pp 243 251 and give a bound for the convergence rate of the fixed point iteration that agrees with our experimental results these results are also valid for suitable generalizations of the fixed point algorithm

detection of missing data in image sequences bright and dark flashes are typical artifacts in degraded motion picture material the distortion is referred to as dirt and sparkle in the motion picture industry this is caused either by dirt becoming attached to the frames of the film or by the film material being abraded the visual result is random patches of the frames having grey level values totally unrelated to the initial information at those sites to restore the film without causing distortion to areas of the frames that are not affected the locations of the blotches must be identified heuristic and model based methods for the detection of these missing data regions are presented in this paper and their action on simulated and real sequences is compared

l p improving bounds for averages along curves we establish local l p l q mapping properties for averages on curves the exponents are sharp except for endpoints let n 2 and let m1 and m2 be two smooth n 1 dimensional manifolds 1 each containing a preferred origin 0m1 and 0m2 we shall abuse notation and write 0 for both 0m1 and 0m2 for the purposes of integration we shall place a smooth riemannian metric on m1 and m2 although the exact choice of this metric will not be relevant all our considerations shall be local to the origin 0 we are interested in the local l p improving properties of averaging operators on curves before we give the rigorous description of these operators let us first give an informal discussion informally we assume that we have a smooth assignment x2 7 x2 taking points in m2 to curves in m1 with a corresponding dual assignment x1 x1 taking points in m1 to curves in m2 such that x1 x2 x2 1 we then form the operator r taking functions 2 on m1 to functions on m2 defined

turning diffusion based image colorization into efficient color compression the work of levin et al 2004 popularized stroke based methods that add color to gray value images according to a small amount of user specified color samples even though such reconstructions from sparse data suggest a possible use in compression only few attempts were made so far in this direction diffusion based compression methods pursue a similar idea they store only few image pixels and inpaint the missing regions despite this close relation and a lack of diffusion based color codecs colorization ideas were so far only integrated into transform based approaches such as jpeg we address this missing link with two contributions first we show the relation between the discrete colorization of levin et al and continuous diffusion based inpainting in the ycbcr color space it decomposes the image into a luma brightness channel and two chroma color channels our luma guided diffusion framework steers the diffusion inpainting in the chroma channels according to the structure in the luma channel we show that making the luma guided colorization anisotropic outperforms the method of levin et al significantly second we propose a new luma preference codec that invests a large fraction of the bit budget into an accurate representation of the luma channel this allows a high quality reconstruction of color data with our colorization technique simultaneously we exploit the fact that the human visual system is more sensitive to structural than to color information our experiments demonstrate that our new codec outperforms the state of the art in diffusion based image compression and is competitive to transform based codecs

singular integrals related to the radon transform and boundary value problems abstract two classes of integral operators are introduced that combine features of calderon zygmund singular integrals the hilbert integral and the radon transform examples and applications arising from integral geometry and several complex variables are discussed

mathematical models for local nontexture inpaintings dedicated to stanley osher on the occasion of his 60th birthday abstract inspired by the recent work of bertalmio et al on digital inpaintings siggraph 2000 we develop general mathematical models for local inpaintings of nontexture images on smooth regions inpaintings are connected to the harmonic and biharmonic extensions and inpainting orders are analyzed for inpaintings involving the recovery of edges we study a variational model that is closely connected to the classical total variation tv denoising model of rudin osher and fatemi phys d 60 1992 pp 259 268 other models are also discussed based on the mumford shah regularity comm pure appl math xlii 1989 pp 577 685 and curvature driven diffusions cdd of chan and shen j visual comm image rep 12 2001 the broad applications of the inpainting models are demonstrated through restoring scratched old photos disocclusion in vision analysis text removal digital zooming and edge based image coding

a primal dual active set method for non negativity constrained total variation deblurring problems this paper studies image deblurring problems using a total variation based model with a non negativity constraint the addition of the non negativity constraint improves the quality of the solutions but makes the solution process a difficult one the contribution of our work is a fast and robust numerical algorithm to solve the non negatively constrained problem to overcome the nondifferentiability of the total variation norm we formulate the constrained deblurring problem as a primal dual program which is a variant of the formulation proposed by chan golub and mulet for unconstrained problems here dual refers to a combination of the lagrangian and fenchel duals to solve the constrained primal dual program we use a semi smooth newton s method we exploit the relationship between the semi smooth newton s method and the primal dual active set method to achieve considerable simplification of the computations the main advantages of our proposed scheme are no parameters need significant adjustment a standard inverse preconditioner works very well quadratic rate of local convergence theoretical and numerical numerical evidence of global convergence and high accuracy of solving the optimality system the scheme shows robustness of performance over a wide range of parameters a comprehensive set of numerical comparisons are provided against other methods to solve the same problem which show the speed and accuracy advantages of our scheme