high quality image resizing using oblique projection operators the standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate however one can obtain more accurate results if one applies a filter prior to sampling a fact well known from sampling theory the optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space unfortunately the optimal projection prefilter is difficult to implement when sine or high order spline functions are used we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster simpler and more general algorithms we show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space the main advantage is that it becomes perfectly feasible to use higher order models e g splines of degree n spl ges 3 we develop the theoretical background and present a simple and practical implementation procedure using b splines our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure least squares solution with considerably fewer computations the method works for arbitrary scaling factors and is applicable to both image enlargement and reduction

wavelets and filter banks theory and design the wavelet transform is compared with the more classical short time fourier transform approach to signal analysis then the relations between wavelets filter banks and multiresolution signal processing are explored a brief review is given of perfect reconstruction filter banks which can be used both for computing the discrete wavelet transform and for deriving continuous wavelet bases provided that the filters meet a constraint known as regularity given a low pass filter necessary and sufficient conditions for the existence of a complementary high pass filter that will permit perfect reconstruction are derived the perfect reconstruction condition is posed as a bezout identity and it is shown how it is possible to find all higher degree complementary filters based on an analogy with the theory of diophantine equations an alternative approach based on the theory of continued fractions is also given these results are used to design highly regular filter banks which generate biorthogonal continuous wavelet bases with symmetries

e isometries in euclidean spaces abstract let 0 r r and a be a subset of the n dimensional euclidean space e n which is contained in b x 0 r and contains points x 0 x 0 re 1 x 0 re n where the vectors e i i 1 n are orthonormal we show that if f a e n is an e isometry then there is an affine isometry u such that f x u x n e r r for all x in a where n cn moreover if a is star shaped with respect to x 0 and contains b x 0 r then n c log n 1 both results are sharp

a matrix stability analysis of the carbuncle phenomenon the carbuncle phenomenon is a shock instability mechanism which ruins all efforts to compute grid aligned shock waves using low dissipative upwind schemes the present study develops a stability analysis for two dimensional steady shocks on structured meshes based on the matrix method the numerical resolution of the corresponding eigenvalue problem confirms the typical odd even form of the unstable mode and displays a mach number threshold effect currently observed in computations furthermore the present method indicates that the instability of steady shocks is not only governed by the upstream mach number but also by the numerical shock structure finally the source of the instability is localized in the upstream region providing some clues to better understand and control the onset of the carbuncle

on the approximation power of convolution based least squares versus interpolation there are many signal processing tasks for which convolution based continuous signal representations such as splines and wavelets provide an interesting and practical alternative to the more traditional sine based methods the coefficients of the corresponding signal approximations are typically obtained by direct sampling interpolation or quasi interpolation or by using least squares techniques that apply a prefilter prior to sampling we compare the performance of these approaches and provide quantitative error estimates that can be used for the appropriate selection of the sampling step h specifically we review several results in approximation theory with a special emphasis on the strang fix 1971 conditions which relate the general o h sup l behavior of the error to the ability of the representation to reproduce polynomials of degree n l 1 we use this theory to derive pointwise error estimates for the various algorithms and to obtain the asymptotic limit of the l sub 2 error as h tends to zero we also propose a new improved l sub 2 error bound for the least squares case in the process we provide all the relevant bound constants for polynomial splines some of our results suggest the existence of an intermediate range of sampling steps where the least squares method is roughly equivalent to an interpolator with twice the order we present experimental examples that illustrate the theory and confirm the adequacy of our various bound and limit determinations

stability of banach spaces via nonlinear e isometries abstract in this paper we prove that the existence of an e isometry from a separable banach space x into y the james space or a reflexive space implies the existence of a linear isometry from x into y then we present a set valued mapping version lemma on non surjective e isometries of banach spaces using the above results we also discuss the rotundity and smoothness of banach spaces under the perturbation by e isometries

on an n dimensional mixed type additive and quadratic functional equation in this paper we investigate the generalized hyers ulam stability of the functional email protected k 2 k n 01fx email protected i 2n 1 k ix i 2 n 1f x 1 2 n email protected i 2nf x i f x i 0for integer values of n such that n 2 where f is a function from a normed space x to a banach space y the solutions of the equation are called additive quadratic mappings

a fixed point theorem and the hyers ulam stability in non archimedean spaces abstract we prove a fixed point theorem in complete non archimedean normed spaces and show its applications in the hyers ulam stability of some functional equations

generalized sampling stability and performance analysis generalized sampling provides a general mechanism for recovering an unknown input function f x spl epsiv spl hscr from the samples of the responses of m linear shift invariant systems sampled at 1 mth the reconstruction rate the system can be designed to perform a projection of f x onto the reconstruction subspace v spl phi span spl phi x k sub k spl epsiv z for example the family of bandlimited signals with spl phi x sinc x this implies that the reconstruction will be perfect when the input signal is included in v spl phi the traditional framework of papoulis 1977 generalized sampling theory otherwise one recovers a signal approximation f x spl epsiv v spl phi that is consistent with f x in the sense that it produces the same measurements to characterize the stability of the algorithm we prove that the dual synthesis functions that appear in the generalized sampling reconstruction formula constitute a riesz basis of v spl phi and we use the corresponding riesz bounds to define the condition number of the system we then use these results to analyze the stability of various instances of interlaced and derivative sampling next we consider the issue of performance which becomes pertinent once we have extended the applicability of the method to arbitrary input functions that is when spl hscr is considerably larger than v spl phi and the reconstruction is no longer exact we show that the generalized sampling solution is essentially equivalent to the optimal minimum error approximation we then perform a detailed analysis for the case in which the analysis filters are in l sub 2 and determine all relevant bound constants explicitly finally we use an interlaced sampling example to illustrate these various calculations

an evaluation of roe s scheme generalizations for equilibrium real gas flows the extension of roe s approximate riemann solver to equilibrium real gas is analyzed by means of a general formulation allowing us to clarify the inherent nonuniqueness of the average state and the influence of the functional form of the equation of state several generalizations of roe s scheme are then reviewed and their numerical performances are discussed by computing some 2d steady hypersonic flows the flow solvers are coupled with a newly developed efficient and robust procedure for thermochemical air properties evaluation all of the tested equilibrium solvers achieve very similar results they are found of comparable numerical efficiency the higher performances being associated with vinokur s and liou s solvers it is concluded that equilibrium simulations in 2d are by no means less robust than the perfect gas ones when coupled with the proposed procedure for properties evaluation

curvature interpolation method for image zooming we introduce a novel image zooming algorithm called the curvature interpolation method cim which is partial differential equation pde based and easy to implement in order to minimize artifacts arising in image interpolation such as image blur and the checkerboard effect the cim first evaluates the curvature of the low resolution image after interpolating the curvature to the high resolution image domain the cim constructs the high resolution image by solving a linearized curvature equation incorporating the interpolated curvature as an explicit driving force it has been numerically verified that the new zooming method can produce clear images of sharp edges which are already denoised and superior to those obtained from linear methods and pde based methods of no curvature information various results are given to prove effectiveness and reliability of the new method

asymptotic error expansion of wavelet approximations of smooth functions ii we generalize earlier results concerning an asymptotic error expansion of wavelet approximations the properties of the monowavelets which are the building blocks for the error expansion are studied in more detail and connections between spline wavelets and euler and bernoulli polynomials are pointed out the expansion is used to compare the error for different wavelet families we prove that the leading terms of the expansion only depend on the multiresolution subspaces v j and not on how the complementary subspaces w j are chosen consequently for a fixed set of subspaces v j the leading terms do not depend on the fact whether the wavelets are orthogonal or not we also show that daubechies orthogonal wavelets need in general one level more than spline wavelets to obtain an approximation with a prescribed accuracy these results are illustrated with numerical examples

color image resolution conversion in this paper we look at the problem of spatially scaling color images we focus on an approach that takes advantage of the human visual system s color spatial frequency sensitivity the algorithm performs an efficient least squares ls resolution conversion for the luminance channel and a low complexity pixel replication reduction in the chrominance channels the performance of the algorithm is compared to a ls method in srgb and cielab color spaces as well as standard bilinear interpolation in srgb space the comparisons are made in terms of computational cost and color error in scielab

on the optimality of ideal filters for pyramid and wavelet signal approximation the reconstructed lowpass component in a quadrature mirror filter qmf bank provides a coarser resolution approximation of the input signal since the outputs of the two qmf branches are orthogonal the transformation that provides the maximum energy compaction in the lowpass channel is also the one that results in the minimum approximation error this property is used as a common strategy for the optimization of qmf banks orthogonal wavelet transforms and least squares pyramids a general solution is derived for the qmf bank that provides the optimal decomposition of an arbitrary wide sense stationary process this approach is extended to the continuous case to obtain the minimum error approximation of a signal at a given sampling rate in particular it is shown that the sine wavelet transform is optimal for the representation at all scales of signals with non increasing spectral density

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

optimized least square nonuniform fast fourier transform the main focus of this paper is to derive a memory efficient approximation to the nonuniform fourier transform of a support limited sequence we show that the standard nonuniform fast fourier transform nufft scheme is a shift invariant approximation of the exact fourier transform based on the theory of shift invariant representations we derive an exact expression for the worst case mean square approximation error using this metric we evaluate the optimal scale factors and the interpolator that provides the least approximation error we also derive the upper bound for the error component due to the lookup tablebased evaluation of the interpolator we use this metric to ensure that this component is not the dominant one theoretical and experimental comparisons with standard nufft schemes clearly demonstrate the significant improvement in accuracy over conventional schemes especially when the size of the uniform fast fourier transform fft is small since the memory requirement of the algorithm is dependent on the size of the uniform fft the proposed developments can lead to iterative signal reconstruction algorithms with significantly lower memory demands

least squares image resizing using finite differences we present an optimal spline based algorithm for the enlargement or reduction of digital images with arbitrary noninteger scaling factors this projection based approach can be realized thanks to a new finite difference method that allows the computation of inner products with analysis functions that are b splines of any degree n a noteworthy property of the algorithm is that the computational complexity per pixel does not depend on the scaling factor a for a given choice of basis functions the results of our method are consistently better than those of the standard interpolation procedure the present scheme achieves a reduction of artifacts such as aliasing and blocking and a significant improvement of the signal to noise ratio the method can be generalized to include other classes of piecewise polynomial functions expressed as linear combinations of b splines and their derivatives

on the stability of functional equations in banach spaces the paper is devoted to some results on the problem of s m ulam for the stability of functional equations in banach spaces the problem was posed by ulam 60 years ago

b spline signal processing ii efficiency design and applications for pt i see ibid vol 41 no 2 p 821 33 1993 a class of recursive filtering algorithms for the efficient implementation of b spline interpolation and approximation techniques is described in terms of simplicity of realization and reduction of computational complexity these algorithms compare favorably with conventional matrix approaches a filtering interpretation low pass filter followed by an exact polynomial spline interpolator of smoothing spline and least squares approximation methods is proposed these techniques are applied to the design of digital filters for cubic spline signal processing an efficient implementation of a smoothing spline edge detector is proposed it is also shown how to construct a cubic spline image pyramid that minimizes the loss of information in passage from one resolution level to the next in terms of common measures of fidelity this data structure appears to be superior to the gaussian laplacian pyramid

recursive regularization filters design properties and applications least squares approximation problems that are regularized with specified highpass stabilizing kernels are discussed for each problem there is a family of discrete regularization filters r filters which allow an efficient determination of the solutions these operators are stable symmetric lowpass filters with an adjustable scale factor two decomposition theorems for the z transform of such systems are presented one facilitates the determination of their impulse response while the other allows an efficient implementation through successive causal and anticausal recursive filtering a case of special interest is the design of r filters for the first and second order difference operators these results are extended for two dimensional signals and for illustration purposes are applied to the problem of edge detection this leads to a very efficient implementation 8 multiplies 10 adds per pixel of the optimal canny edge detector based on the use of a separable second order r filter

self adjusting grid methods for one dimensional hyperbolic conservation laws it is shown how to automatically adjust the grid to follow the dynamics of the numerical solution of hyperbolic conservation laws the grid motion is determined by averaging the local characteristic velocities of the equations with respect to the amplitudes of the signals the resulting algorithm is a simple extension of many currently popular godunov type methods computer codes using one of these methods can be easily modified to add the moving mesh as an option numerical examples are given that illustrate the improved accuracy of godunov s and roe s methods on a self adjusting mesh

viewing distance aware super resolution for high definition display in this paper we propose a novel algorithm for high definition displays to enlarge low resolution images while maintaining perceptual constancy i e the same field of view perceptual blur radius and the retinal image size in viewer s eyes we model the relationship between a viewer and a display by considering two main aspects of visual perception i e scaling factor and perceptual blur radius as long as we enlarge an image while adjust its image blur levels on the display we can maintain viewer s perceptual constancy we show that the scaling factor should be set in proportion to the viewing distance and the blur levels on the display should be adjusted according to the focal length of a viewer toward this we first refer to edge directions to interpolate a low resolution image with the increasing of viewing distance and the scaling factor after images are interpolated we utilize a local contrast to estimate the spatially varying image blur levels of the interpolated image we then further adjust the image blur levels using a parametric deblurring method which combines l1 as well as l2 reconstruction errors and tikhonov with total variation regularization terms by taking these factors into account high resolution images adaptive to viewing distance on a display can be generated experimental results on both natural image metric and user subjective studies across image scales demonstrate that the proposed super resolution algorithm for high definition displays performs favorably against the state of the art methods

on stability of nonlinear non surjective e isometries of banach spaces abstract let x y be two banach spaces e 0 and let f x y be an e isometry with f 0 0 in this paper we show first that for every x x there exists y with x r such that f x x x 4 e r for all x x making use of it we prove that if y is reflexive and if e y the annihilator of the subspace f y consisting of all functionals bounded on co f x f x is complemented in y then there is a bounded linear operator t y x with t such that t f x x 4 e for all x x if in addition y is gateaux smooth strictly convex and admitting the kadec klee property in particular locally uniformly convex then we have the following sharp estimate t f x x 2 e for all x x

fixed point theorems and the ulam hyers stability in non archimedean cone metric spaces abstract let x p be a metric space with a k valued non archimedean metric p in this paper we prove the existence and approximation of a fixed point for operators f x x satisfying the contractive condition in the form p f x f y q p x y where q k k is an increasing operator then we study the generalized ulam hyers stability of fixed point equations we next obtain an extension of the krasnoselskii fixed point theorem for the sum of two operators finally an application to functional equations is given

comparative study of high resolution shock capturing schemes for a real gas recently developed second order explicit shock capturing methods in conjunction with generalized flux vector splittings and a generalized approximate riemann solver for a real gas are studied the comparisons are made on different one dimensional riemann shock tube problems for equilibrium air with various ranges of mach numbers densities and pressures six different riemann problems are considered these tests provide a check on the validity of the generalized formulas since theoretical prediction of their properties appears to be difficult because of the non analytical form of the state equation the numerical results in the supersonic and low hypersonic regimes indicate that these produce good shock capturing capability and that the shock resolution is only slightly affected by the state equation of equilibrium air the difference in shock resolution between the various methods varies slightly from one riemann problem to the other but the overall accuracy is very similar for the one dimensional case the relative efficiency in terms of operation count for the different methods is within 30 percent the main difference between the methods lies in their versatility in being extended to multidimensional problems with efficient implicit solution procedures

an efficient method for fitting large data sets using t splines data fitting is a fundamental tool in scientific research and engineering applications generally there are two ingredients in solving data fitting problems one is the fitting representation and the other is the fitting method nowadays the fitting of larger and larger quantities of data sets requires more compact fitting representation and faster fitting methods the t spline is a recently invented spline representation whose control mesh t mesh allows a row of control points to terminate thus reducing the number of superfluous control points in the b spline representation significantly this property makes t splines more compact than b splines in fitting large data sets however the adaptivity of the t spline causes the coefficient matrix of a least squares fitting linear system to lose its block structure thus when fitting large data sets with t splines by iterative methods only point iterative methods can be used and the iteration speeds of typically employed point iterative methods are r

stability of the preservation of the equality of distance abstract we study the stability problem for mappings satisfying the equation f x y f x f y as a result we obtain the stability of functions preserving the equality of distance that is satisfying for all x y u v the condition x y u v f x f y f u f v

dissipation additions to flux difference splitting abstract although the flux difference splitting methods for solving the euler equations are generally very robust and no explicit dissipation is required there are situations where explicit dissipation is needed two cases a slowly moving shock problem and a blunt body calculation are discussed in this paper the slowly moving shock problem is tested extensively by roe s riemann solver and a cure for roe s riemann solver is proposed for the second order scheme it is found necessary to reduce the second order accuracy to first order accuracy inside the shock layer for the supersonic blunt body calculation adding dissipation in the linear waves in roe s riemann solver can prevent numerical instability in the subsonic pocket the drawback of yee s formula to cure the instability when used on viscous flow calculation is demonstrated a better solution based on the pressure gradient is proposed

shifting interpolation kernel toward orthogonal projection orthogonal projection offers the optimal solution for many sampling reconstruction problems in terms of the least square error in the standard interpolation setting where the sampling is assumed to be ideal however the projection is impossible unless the interpolation kernel is related to the sinc function and the input is bandlimited in this paper we propose a notion of shifting kernel toward the orthogonal projection for a given interpolation kernel we formulate optimization problems whose solutions lead to shifted interpolations that while still being interpolatory are closest to the orthogonal projection in the sense of the minimax regret the quality of interpolation is evaluated in terms of the average approximation error over input shift for the standard linear interpolation we obtain several values of optimal shift dependent on a priori information on input signals for evaluation we apply the new shifted linear interpolations to a gaussian signal an ecg signal a speech signal a two dimensional signal and three natural images significant improvements are observed over the standard and the 0 21 shifted linear interpolation proposed early

nonsurjective nearisometries of banach spaces abstract we obtain sharp approximation results for into nearisometries between l p spaces and nearisometries into a hilbert space our main theorem is the optimal approximation result for nearsurjective nearisometries between general banach spaces

fast b spline transforms for continuous image representation and interpolation efficient algorithms for the continuous representation of a discrete signal in terms of b splines direct b spline transform and for interpolative signal reconstruction indirect b spline transform with an expansion factor m are described expressions for the z transforms of the sampled b spline functions are determined and a convolution property of these kernels is established it is shown that both the direct and indirect spline transforms involve linear operators that are space invariant and are implemented efficiently by linear filtering fast computational algorithms based on the recursive implementations of these filters are proposed a b spline interpolator can also be characterized in terms of its transfer function and its global impulse response cardinal spline of order n the case of the cubic spline is treated in greater detail the present approach is compared with previous methods that are reexamined from a critical point of view it is concluded that b spline interpolation correctly applied does not result in a loss of image resolution and that this type of interpolation can be performed in a very efficient manner

enlargement or reduction of digital images with minimum loss of information the purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary noninteger scaling factors in our formulation the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and spl delta respectively the change of scale is achieved by determining the spline with step size spl delta that provides the closest approximation of the original signal in the l sub 2 norm we show that this approximation can be computed in three steps i a digital prefilter that provides the b spline coefficients of the input signal ii a resampling using an expansion formula with a modified sampling kernel that depends explicitly on spl delta and iii a digital postfilter that maps the result back into the signal domain we provide explicit formulas for n 0 1 and 3 and propose solutions for the efficient implementation of these algorithms we consider image processing examples and show that the present method compares favorably with standard interpolation techniques finally we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity

b spline signal processing i theory the use of continuous b spline representations for signal processing applications such as interpolation differentiation filtering noise reduction and data compressions is considered the b spline coefficients are obtained through a linear transformation which unlike other commonly used transforms is space invariant and can be implemented efficiently by linear filtering the same property also applies for the indirect b spline transform as well as for the evaluation of approximating representations using smoothing or least squares splines the filters associated with these operations are fully characterized by explicitly evaluating their transfer functions for b splines of any order applications to differentiation filtering smoothing and least squares approximation are examined the extension of such operators for higher dimensional signals such as digital images is considered

on approximate solutions of the linear functional equation of higher order abstract we show that under some assumptions every approximate solution of the linear functional equation of higher order in single variable generates a solution of the equation that is close to it we also give a description of a procedure that yields such a solution estimate the distance between those approximate and exact solutions to the equation and discuss the problem of uniqueness moreover as a consequence we obtain some results concerning the hyers ulam stability of the equation

orthonormal bases of compactly supported wavelets we construct orthonormal bases of compactly supported wavelets with arbitrarily high regularity the order of regularity increases linearly with the support width we start by reviewing the concept of multiresolution analysis as well as several algorithms in vision decomposition and reconstruction the construction then follows from a synthesis of these different approaches

approximation power of biorthogonal wavelet expansions this paper looks at the effect of the number of vanishing moments on the approximation power of wavelet expansions the strang fix conditions imply that the error for an orthogonal wavelet approximation at scale a 2 sup i globally decays as a sup n where n is the order of the transform this is why for a given number of scales higher order wavelet transforms usually result in better signal approximations we prove that this result carries over for the general biorthogonal case and that the rate of decay of the error is determined by the order properties of the synthesis scaling function alone we also derive asymptotic error formulas and show that biorthogonal wavelet transforms are equivalent to their corresponding orthogonal projector as the scale goes to zero these results strengthen sweldens earlier analysis and confirm that the approximation power of biorthogonal and semi orthogonal wavelet expansions is essentially the same finally we compare the asymptotic performance of various wavelet transforms and briefly discuss the advantages of splines we also indicate how the smoothness of the basis functions is beneficial in reducing the approximation error

fixed points of a mapping and hyers ulam stability abstract we show that many general results on hyers ulam stability of some functional equations in a single variable follow immediately from a simple fixed point theorem the theorem is formulated for self maps of some subsets of the space of functions from a nonempty set into the set of reals we also give some applications of that theorem e g in investigations of solutions of some difference equations and functional inequalities

survey interpolation methods in medical image processing image interpolation techniques often are required in medical imaging for image generation e g discrete back projection for inverse radon transform and processing such as compression or resampling since the ideal interpolation function spatially is unlimited several interpolation kernels of finite size have been introduced this paper compares 1 truncated and windowed sine 2 nearest neighbor 3 linear 4 quadratic 5 cubic b spline 6 cubic g lagrange and 7 gaussian interpolation and approximation techniques with kernel sizes from 1 spl times 1 up to 8 spl times 8 the comparison is done by 1 spatial and fourier analyses 2 computational complexity as well as runtime evaluations and 3 qualitative and quantitative interpolation error determinations for particular interpolation tasks which were taken from common situations in medical image processing for local and fourier analyses a standardized notation is introduced and fundamental properties of interpolators are derived successful methods should be direct current dc constant and interpolators rather than dc inconstant or approximators each method s parameters are tuned with respect to those properties this results in three novel kernels which are introduced in this paper and proven to be within the best choices for medical image interpolation the 6 spl times 6 blackman harris windowed sinc interpolator and the c2 continuous cubic kernels with n 6 and n 8 supporting points for quantitative error evaluations a set of 50 direct digital x rays was used they have been selected arbitrarily from clinical routine in general large kernel sizes were found to be superior to small interpolation masks except for truncated sine interpolators all kernels with n 6 or larger sizes perform significantly better than n 2 or n 3 point methods p spl lt 0 005 however the differences within the group of large sized kernels were not significant summarizing the results the cubic 6 spl times 6 interpolator with continuous second derivatives as defined in 24 can be recommended for most common interpolation tasks it appears to be the fastest six point kernel to implement computationally it provides eminent local and fourier properties is easy to implement and has only small errors the same characteristics apply to b spline interpolation but the 6 spl times 6 cubic avoids the intrinsic border effects produced by the b spline technique however the goal of this study was not to determine an overall best method but to present a comprehensive catalogue of methods in a uniform terminology to define general properties and requirements of local techniques and to enable the reader to select that method which is optimal for his specific application in medical imaging

on approximate isometries and application to stability of a functional equation abstract in this paper we show a generalized stability of isometries between banach spaces making use of this result we prove the corresponding stability of the functional equation f x y f x f y

a new flux splitting scheme a new flux splitting scheme is proposed the scheme is remarkably simple and yet its accuracy rivals and in some cases surpasses that of roe s solver in the euler and navier stokes solutions carried out in this study the scheme is robust and converges as fast as the roe splitting we propose an appropriately defined cell face advection mach number using values from the two straddling cells via associated characteristic speeds this interface mach number is then used to determine the upwind extrapolation for the convective quantities accordingly the name of the scheme is coined as the advection upstream splitting method ausm we also introduce a new pressure splitting which is shown to behave successfully yielding much smoother results than other existing pressure splittings of particular interest is the supersonic blunt body problem in which the roe scheme gives anomalous solutions the ausm produces correct solutions without difficulty for a wide range of flow conditions as well as grids

a robust low diffusive kinetic scheme for the navier stokes euler equations a new kinetic scheme based on the equilibrium flux method efm and modified using osher intermediate states is proposed this new scheme called efmo combines the robustness of the equilibrium flux method and the accuracy of flux difference splitting schemes the original efm scheme is expressed in terms of simple wave decomposition in which only the linearly degenerate subpath is calculated from osher numerical flux while nonlinear waves are still evaluated from the regular efm splitting owing to its capability of withstanding intense nonlinear waves and yet exactly resolving contact discontinuities efmo is particularly well suited for the resolution of the navier stokes equations as demonstrated by a series of severe test cases including the high speed viscous flow around a cone a shock boundary layer interaction problem a vacuum apparition problem the hypersonic flow around a circular cylinder at mach 100 and the forward facing step at mach 3

generalized stability of isometries abstract let x and y be real banach spaces and let e p 0 a mapping f x y is called an e p isometry if f x f y x y e x y p holds for all x y x a pair x y is p stable with respect to isometries if there exists a function 0 0 with lime 0 e 0 such that for every surjective e p isometry f x y there is a surjective isometry u x y satisfying the estimate f x u x e x p x x we show that every pair of banach spaces x y is p stable for 0 p r 2 r 2 is not 1 stable when p 1 a superstability phenomenon occurs for finite dimensional banach spaces

a general sampling theory for nonideal acquisition devices the authors first describe the general class of approximation spaces generated by translation of a function spl psi x and provide a full characterization of their basis functions they then present a general sampling theorem for computing the approximation of signals in these subspaces based on a simple consistency principle the theory puts no restrictions on the system input which can be an arbitrary finite energy signal bandlimitedness is not required in contrast to previous approaches this formulation allows for an independent specification of the sampling analysis and approximation synthesis spaces in particular when both spaces are identical the theorem provides a simple procedure for obtaining the least squares approximation of a signal they discuss the properties of this new sampling procedure and present some examples of applications involving bandlimited and polynomial spline signal representations they also define a spectral coherence function that measures the similarity between the sampling and approximation spaces and derive a relative performance bound for the comparison with the least squares solution

high quality parallel ray x ray ct back projection using optimized interpolation we propose a new cost efficient method for computing back projections in parallel ray x ray ct forward and back projections are the basis of almost all x ray ct reconstruction methods but computing these accurately is costly in the special case of parallel ray geometry it turns out that reconstruction requires back projection only one approach to accelerate the back projection is through interpolation fit a continuous representation to samples of the desired signal then sample it at the required locations instead we propose applying a prefilter that has the effect of orthogonally projecting the underlying signal onto the space spanned by the interpolator which can significantly improve the quality of the interpolation we then build on this idea by using oblique projection which simplifies the computation while giving effectively the same improvement in quality our experiments on analytical phantoms show that this refinement can improve the reconstruction quality for both filtered back projection and iterative reconstruction in the high quality regime i e with low noise and many measurements

shock stable roe scheme combining entropy fix and rotated riemann solver the roe scheme is an important shock capturing scheme that is known for its good performance however the classical roe scheme suffers from disastrous problems such as shock instability for hyper

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed