radial and non radial solutions to an elliptic problem on annular domains in riemannian manifolds with radial symmetry abstract we show existence and uniqueness of positive radial solutions to g u u u p 0 in a u 0 on a with 0 a being an annular domain in a riemannian manifold m of dimension n endowed with the metric d r 2 s 2 r g s n 1 secondly we show that there exist positive non radial solutions arising by bifurcation from the radial solution p and are the bifurcation parameters

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

efficient representation of induced currents on large scatterers using the generalized pencil of function method it is shown that the currents induced over large and smooth scatterers can often be represented by a series of complex exponentials with only a few terms the generalized pencil of function method is employed to extract these exponentials from the numerical solution of the scattering problem derived by using the method of moments illustrative examples include a partially coated two dimensional scatterer modeling a helicopter blade and the three dimensional problem of scattering by a thin plate the ultimate objective of this effort is to solve a class of large body scattering problems for arbitrary angles of incidence including the grazing angle by utilizing the numerically derived complex exponential type of basis functions extrapolated to higher frequencies it is well known that the physical optics approximation for the induced current becomes inaccurate when the angle of incidence is close to grazing and the asymptotic methods e g the gtd can become unwieldy for scatterers with edge treatments and those with complex geometrical shapes the approach based upon the use of numerically derived entire domain basis functions on a portion of the body is proposed as a means to circumventing this difficulty

scale space and edge detection using anisotropic diffusion a new definition of scale space is suggested and a class of algorithms used to realize a diffusion process is introduced the diffusion coefficient is chosen to vary spatially in such a way as to encourage intraregion smoothing rather than interregion smoothing it is shown that the no new maxima should be generated at coarse scales property of conventional scale space is preserved as the region boundaries in the approach remain sharp a high quality edge detector which successfully exploits global information is obtained experimental results are shown on a number of images parallel hardware implementations are made feasible because the algorithm involves elementary local operations replicated over the image

separation of branches of o n 1 invariant solutions for a semilinear elliptic equation abstract we consider the problem u u u p in a u 0 in a u 0 on a where a is an annulus in r n n 2 p 1 and 0 recent results ensure that there exists a sequence p k of exponents p k at which a nonradial bifurcation from the radial solution occurs exploiting the properties of o n 1 invariant spherical harmonics we introduce two suitable cones k 1 and k 2 of o n 1 invariant functions that allow to separate the branches of bifurcating solutions getting their unboundedness

unbiased risk estimates for singular value thresholding and spectral estimators in an increasing number of applications it is of interest to recover an approximately low rank data matrix from noisy observations this paper develops an unbiased risk estimate holding in a gaussian model for any spectral estimator obeying some mild regularity assumptions in particular we give an unbiased risk estimate formula for singular value thresholding svt a popular estimation strategy that applies a soft thresholding rule to the singular values of the noisy observations among other things our formulas offer a principled and automated way of selecting regularization parameters in a variety of problems in particular we demonstrate the utility of the unbiased risk estimation for svt based denoising of real clinical cardiac mri series data we also give new results concerning the differentiability of certain matrix valued functions

grouped coordinate ascent algorithms for penalized likelihood transmission image reconstruction presents a new class of algorithms for penalized likelihood reconstruction of attenuation maps from low count transmission scans we derive the algorithms by applying to the transmission log likelihood a version of the convexity technique developed by de pierro for emission tomography the new class includes the single coordinate ascent sca algorithm and lange s convex algorithm for transmission tomography as special cases the new grouped coordinate ascent gca algorithms in the class overcome several limitations associated with previous algorithms 1 fewer exponentiations are required than in the transmission maximum likelihood expectation maximization ml em algorithm or in the sca algorithm 2 the algorithms intrinsically accommodate nonnegativity constraints unlike many gradient based methods 3 the algorithms are easily parallelizable unlike the sca algorithm and perhaps line search algorithms we show that the gca algorithms converge faster than the sca algorithm even on conventional workstations an example from a low count positron emission tomography pet transmission scan illustrates the method

on the computation of the gram matrix in time domain and its application the gram matrix of the system involves evaluation of the scalar product of repeated integrals and has formerly been computed in frequency domain a time domain method for evaluation of the gram matrix is presented it is based on new properties of the gram matrix derived here a model reduction algorithm based on these properties is presented the method is illustrated by a numerical example

reduction of noise induced streak artifacts in x ray computed tomography through spline based penalized likelihood sinogram smoothing we present a statistically principled sinogram smoothing approach for x ray computed tomography ct with the intent of reducing noise induced streak artifacts these artifacts arise in ct when some subset of the transmission measurements capture relatively few photons because of high attenuation along the measurement lines attempts to reduce these artifacts have focused on the use of adaptive filters that strive to tailor the degree of smoothing to the local noise levels in the measurements while these approaches involve loose consideration of the measurement statistics to determine smoothing levels they do not explicitly model the statistical distributions of the measurement data we present an explicitly statistical approach to sinogram smoothing in the presence of photon starved measurements it is an extension of a nonparametric sinogram smoothing approach using penalized poisson likelihood functions that we have previously developed for emission tomography because the approach explicitly models the data statistics it is naturally adaptive it will smooth more variable measurements more heavily than it does less variable measurements we find that it significantly reduces streak artifacts and noise levels without comprising image resolution

susan a new approach to low level image processing this paper describes a new approach to low level image processing in particular edge and corner detection and structure preserving noise reduction non linear filtering is used to define which parts of the image are closely related to each individual pixel each pixel has associated with it a local image region which is of similar brightness to that pixel the new feature detectors are based on the minimization of this local image region and the noise reduction method uses this region as the smoothing neighbourhood the resulting methods are accurate noise resistant and fast details of the new feature detectors and of the new noise reduction method are described along with test results

uniqueness of positive radial solutions of a semilinear dirichlet problem in an annulus we establish the uniqueness of positive radial solutions of u u p u in b r 1 r 2 u 0 on b r 1 r 2 where b r 1 r 2 is an annulus and 0 r 1 r 2 in the following cases a n 3 4 and 1 p n n 2 b n 5 6 7 8 and 1 p p 0 n for some p 0 n n n 2 earlier to this result the uniqueness has been obtained by coffman for n 3 and 1 p 3 and by yadava for p n 2 n 2 and n 3

radiation dose reduction in ct myocardial perfusion imaging using smart recon in this paper a newly developed statistical model based image reconstruction referred to as simultaneous multiple artifacts reduction in tomographic reconstruction smart recon is applied to low dose computer tomography ct myocardial perfusion imaging ct mpi this method uses the nuclear norm of the spatial temporal image matrix of the ct mpi images as a regularizer rather than a conventional spatial regularizer that incorporates image smoothness edge preservation or spatial sparsity into the reconstruction in addition to providing the needed noise reduction for low dose ct mpi smart recon provides images with spatial resolution and noise power spectrum nps properties which are independent of contrast and dose levels both numerical simulations and in vivo animal studies were performed to validate the proposed method in these studies it was found that 1 quantitative accuracy of perfusion maps in ct mpi was well maintained for radiation dose level as low as 10 mas per image frame compared with the reference standard of 200 mas for conventional filtered backprojection 2 flow occluded myocardium in the porcine heart was well delineated by smart recon at 10 mas per frame when compared with model based image reconstruction using spatial total variation tv as the regularizer referred to as tv sir or spatial temporal tv st tv sir the ct mpi results were confirmed with positron emission tomography imaging 3 image sharpness in smart recon images was nearly independent of image contrast level and radiation dose level in stark contrast to tv sir and st tv sir which displayed a strong dependence on both image contrast and radiation dose levels and 4 the structure of the dose normalized nps for the smart recon method did not depend on dose while the tv sir and st tv sir nps structure was dose dependent

nonlinear multiscale analysis of three dimensional echocardiographic sequences introduces a new model for multiscale analysis of space time echocardiographic sequences the proposed nonlinear partial differential equation representing the multiscale analysis filters the sequence while keeping the space time coherent structures it combines the ideas of regularized perona malik anisotropic diffusion and the galilean invariant movie multiscale analysis of alvarez et al arch rat mech anal vol 123 p 200 57 1993 a numerical method for solving the proposed partial differential equation is suggested and its stability is shown computational results on synthesized and real sequences are provided a qualitative and quantitative evaluation of the accuracy of the method is presented

uniqueness of positive radial solutions for δu u up 0 on an annulus abstract we prove uniqueness of positive radial solutions to the semilinear elliptic equation u u u p 0 p 1 subject to the dirichlet boundary condition on an annulus in r n n 3 as a by product our argument also provides a much simpler if not the simplest new proof for the uniqueness of positive solutions to the same problem in a finite ball or in the whole space r n

uniqueness of radially symmetric positive solutions for delta u u u p in an annulus in this article we prove that the semi linear elliptic partial differential equation u u upin u 0in u 0on possesses a unique positive radially symmetric solution here p 1 and is the annulus x rn a x b with n 2 0 a b we also show the positive solution is non degenerate

adaptive two pass rank order filter to remove impulse noise in highly corrupted images in this paper we present an adaptive two pass rank order filter to remove impulse noise in highly corrupted images when the noise ratio is high rank order filters such as the median filter for example can produce unsatisfactory results better results can be obtained by applying the filter twice which we call two pass filtering to further improve the performance we develop an adaptive two pass rank order filter between the passes of filtering an adaptive process is used to detect irregularities in the spatial distribution of the estimated impulse noise the adaptive process then selectively replaces some pixels changed by the first pass of filtering with their original observed pixel values these pixels are then kept unchanged during the second filtering in combination the adaptive process and the second filter eliminate more impulse noise and restore some pixels that are mistakenly altered by the first filtering as a final result the reconstructed image maintains a higher degree of fidelity and has a smaller amount of noise the idea of adaptive two pass processing can be applied to many rank order filters such as a center weighted median filter cwmf adaptive cwmf lower upper middle filter and soft decision rank order mean filter results from computer simulations are used to demonstrate the performance of this type of adaptation using a number of basic rank order filters

wavelet transform domain filters a spatially selective noise filtration technique wavelet transforms are multiresolution decompositions that can be used to analyze signals and images they describe a signal by the power at each scale and position edges can be located very effectively in the wavelet transform domain a spatially selective noise filtration technique based on the direct spatial correlation of the wavelet transform at several adjacent scales is introduced a high correlation is used to infer that there is a significant feature at the position that should be passed through the filter the authors have tested the technique on simulated signals phantom images and real mr images it is found that the technique can reduce noise contents in signals and images by more than 80 while maintaining at least 80 of the value of the gradient at most edges the authors did not observe any gibbs ringing or significant resolution loss on the filtered images artifacts that arose from the filtration are very small and local the noise filtration technique is quite robust there are many possible extensions of the technique the authors see its applications in spatially dependent noise filtration edge detection and enhancement image restoration and motion artifact removal they have compared the performance of the technique to that of the weiner filter and found it to be superior

rational modeling by pencil of functions method pole zero modeling of signals such as an electromagnetic scatterer response is considered in this paper it is shown by use of the pencil of functions theorem that a the true parameters can be recovered in the ideal case where the signal is the impulse reponse of a rational function h z and b the parameters are optimal in the functional dependence sense when the observed data are corrupted by additive noise or by systematic error although the computations are more involved than in all pole modeling they are considerably less than those required in iterative schemes of pole zero modeling the advantages of the method are demonstrated by a simulation example and through application to the electromagnetic response of a scatterer the paper also includes very recent and promising results on a new approach to noise correction in contradistinction with spectral subtraction techniques where only amplitude information is emphasized and phase is ignored we propose a method that a estimates the noise spectral density for the data frame and then b performs the subtraction of the noise correlation matrix from the gram matrix of the signal

a global bifurcation result for a semilinear elliptic equation abstract we consider the problem u u p u in a u 0 in a u 0 on a where a is an annulus of r n n 2 p 1 and 0 recent results gladiali et al 2009 5 ensure that there exists a sequence of values of the exponent p k at which nonradial bifurcation from the radial solution occurs we prove the existence of global branches of nonradial solutions bifurcating from the curve of radial ones

clarification of issues on the closed form green s functions in stratified media the closed form green s functions cfgf derived for the vector and scalar potentials in planar multilayer media have been revisited to clarify some issues and misunderstandings on the derivation of these green s functions in addition the range of validity of these green s functions is assessed with and without explicit evaluation of the surface wave contributions as it is well known the derivation of the cfgf begins with the approximation of the spectral domain green s functions by complex exponentials and continues with applying the sommerfeld identity to cast these approximated spectral domain green s functions into the space domain in closed forms questions and misunderstandings of this derivation which have mainly originated from the approximation process of the spectral domain green s functions in terms of complex exponentials can be categorized and discussed under the topics of 1 branch point contributions 2 surface wave pole contributions and 3 the accuracy of the obtained cfgf when these issues are clarified the region of validity of the cfgf so obtained may be defined better therefore in this paper these issues will be addressed first and then their origins and possible remedies will be provided with solid analysis and numerical demonstrations

generalized pencil of function method for extracting poles of an em system from its transient response a generalized pencil of function gpof method is developed for extracting the poles of an electromagnetic system from its transient response the gpof method needs the solution of a generalized eigenvalue problem to find the poles subspace decomposition is also used to optimize the performance of the gpof method the gpof method has advantages over the prony method in both computation and noise sensitivity and approaches the cramer rao bound when the signal to noise ratio snr is above threshold an application of the gpof method to a thin wire target is presented

an improved pencil of functions method and comparisons with traditional methods of pole extraction prony s method is usually used for the determination of poles from experimental data in the singularity expansion method sem literature it is the aim here to show that this is not the best method and that jain s pencil of functions pof method can be generalized to provide a better method an example of such a method is given

arma based time signature estimator for analyzing resonant structures by the fdtd method we propose an algorithm for estimation of the optimal system parameters of time sequences tss computed by the finite difference time domain fdtd method with the goal of accurate representation of the time signature using low order models the fdtd method requires computation of very long time sequences to accurately characterize the slowly decaying transient behavior of resonant structures therefore it becomes critical to investigate methods of reducing the computational time for such objects several researchers have argued that the fdtd ts can be modeled as the impulse response ir of an autoregressive moving average arma transfer function however it is known that determination of arma parameters by ir matching is a complex nonlinear optimization problem hence many existing methods in em literature tend to use prony based linear predictor type spectrum estimation algorithms which minimize a linearized equation error criterion that approximates the true nonlinear model fitting error criterion as a result significantly high model orders are needed by these methods to achieve good corroboration in the frequency domain especially when a magnitude spectrum has deep nulls or notches we propose to use a deterministic arma approach which minimizes the true nonlinear criterion iteratively and attains significantly improved ir fit over prony s 1795 method using fewer arma model parameters for a given time sequence of an analyzed circuit the issues of model order selection and choice of decimation factor are also addressed systematically the improved performance of the proposed algorithm is demonstrated with transient simulation and signal analysis of microstrip structures which manifest deep nulls in the frequency domain

construction of a solution for the two component radial gross pitaevskii system with a large coupling parameter abstract we consider strongly coupled competitive elliptic systems that arise in the study of two component bose einstein condensates as the coupling parameter tends to infinity solutions that remain uniformly bounded are known to converge to a segregated limiting profile with the difference of its components satisfying a limit scalar pde in the case of radial symmetry under natural non degeneracy assumptions on a solution of the limit problem we establish by a perturbation argument its persistence as a solution to the elliptic system

ray contribution masks for structure adaptive sinogram filtering the patient dose in computed tomography ct imaging is linked to measurement noise various noise reduction techniques have been developed that adapt structure preserving filters like anisotropic diffusion or bilateral filters to ct noise properties we introduce a structure adaptive sinogram sas filter that incorporates the specific properties of the ct measurement process it uses a point based forward projector to generate a local structure representation called ray contribution mask rcm the similarities between neighboring rcms are used in an enhanced variant of the bilateral filtering concept where the photometric similarity is replaced with the structural similarity we evaluate the performance in four different scenarios the robustness against reconstruction artifacts is demonstrated by a scan of a high resolution phantom without changing the modulation transfer function mtf nor introducing artifacts the sas filter reduces the noise level by 13 6 the image sharpness and noise reduction capabilities are visually assessed on in vivo patient scans and quantitatively evaluated on a simulated phantom unlike a standard bilateral filter the sas filter preserves edge information and high frequency components of organ textures well it shows a homogeneous noise reduction behavior throughout the whole frequency range the last scenario uses a simulated edge phantom to estimate the filter mtf for various contrasts the noise reduction for the simple edge phantom exceeds 80 for low contrasts at 55 hounsfield units hu the mid frequency range is slightly attenuated at higher contrasts of approximately 100 hu and above the mtf is fully preserved

automatic lung segmentation for accurate quantitation of volumetric x ray ct images segmentation of pulmonary x ray computed tomography ct images is a precursor to most pulmonary image analysis applications this paper presents a fully automatic method for identifying the lungs in three dimensional 3 d pulmonary x ray ct images the method has three main steps first the lung region is extracted from the ct images by gray level thresholding then the left and right lungs are separated by identifying the anterior and posterior junctions by dynamic programming finally a sequence of morphological operations is used to smooth the irregular boundary along the mediastinum in order to obtain results consistent with these obtained by manual analysis in which only the most central pulmonary arteries are excluded from the lung region the method has been tested by processing 3 d ct data sets from eight normal subjects each imaged three times at biweekly intervals with lungs at 90 vital capacity the authors present results by comparing their automatic method to manually traced borders from two image analysts averaged over all volumes the root mean square difference between the computer and human analysis is 0 8 pixels 0 54 mm the mean intrasubject change in tissue content over the three scans was 2 75 spl plusmn 2 29 mean spl plusmn standard deviation

combining spatial and scale space techniques for edge detection to provide a spatially adaptive wavelet based noise filtering algorithm new methods for detecting edges in an image using spatial and scale space domains are proposed a priori knowledge about geometrical characteristics of edges is used to assign a probability factor to the chance of any pixel being on an edge an improved double thresholding technique is introduced for spatial domain filtering probabilities that pixels belong to a given edge are assigned based on pixel similarity across gradient amplitudes gradient phases and edge connectivity the scale space approach uses dynamic range compression to allow wavelet correlation over a wider range of scales a probabilistic formulation is used to combine the results obtained from filtering in each domain to provide a final edge probability image which has the advantages of both spatial and scale space domain methods decomposing this edge probability image with the same wavelet as the original image permits the generation of adaptive filters that can recognize the characteristics of the edges in all wavelet detail and approximation images regardless of scale these matched filters permit significant reduction in image noise without contributing to edge distortion the spatially adaptive wavelet noise filtering algorithm is qualitatively and quantitatively compared to a frequency domain and two wavelet based noise suppression algorithms using both natural and computer generated noisy images

uniqueness of sign changing radial solutions for δu u u p 1u 0 in some ball and annulus abstract the following dirichlet problem u u u p 1 u 0 in u 0 on is considered where is either an annulus or a ball in r n and p 1 the uniqueness of radial solutions having exactly k 1 nodes is shown for the following cases is a sufficiently thin annulus is a certain small ball n 4 and 1 p n n 2 is the unit ball n 3 and 1 p 3 is any annulus or any ball but p 1 is sufficiently close to 1 and n 3 5 or 7

tensor based dictionary learning for spectral ct reconstruction spectral computed tomography ct produces an energy discriminative attenuation map of an object extending a conventional image volume with a spectral dimension in spectral ct an image can be sparsely represented in each of multiple energy channels and are highly correlated among energy channels according to this characteristics we propose a tensor based dictionary learning method for spectral ct reconstruction in our method tensor patches are extracted from an image tensor which is reconstructed using the filtered backprojection fbp to form a training dataset with the candecomp parafac decomposition a tensor based dictionary is trained in which each atom is a rank one tensor then the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process and the alternating minimization scheme is adapted for optimization the effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets the results demonstrate that the proposed tensor based method generally produces superior image quality and leads to more accurate material decomposition than the currently popular popular methods

penalized likelihood sinogram restoration for computed tomography we formulate computed tomography ct sinogram preprocessing as a statistical restoration problem in which the goal is to obtain the best estimate of the line integrals needed for reconstruction from the set of noisy degraded measurements ct measurement data are degraded by a number of factors including beam hardening and off focal radiation that produce artifacts in reconstructed images unless properly corrected currently such effects are addressed by a sequence of sinogram preprocessing steps including deconvolution corrections for off focal radiation that have the potential to amplify noise noise itself is generally mitigated through apodization of the reconstruction kernel which effectively ignores the measurement statistics although in high noise situations adaptive filtering methods that loosely model data statistics are sometimes applied as an alternative we present a general imaging model relating the degraded measurements to the sinogram of ideal line integrals and propose to estimate these line integrals by iteratively optimizing a statistically based objective function we consider three different strategies for estimating the set of ideal line integrals one based on direct estimation of ideal monochromatic line integrals that have been corrected for single material beam hardening one based on estimation of ideal polychromatic line integrals that can be readily mapped to monochromatic line integrals and one based on estimation of ideal transmitted intensities from which ideal monochromatic line integrals can be readily estimated the first two approaches involve maximization of a penalized poisson likelihood objective function while the third involves minimization of a quadratic penalized weighted least squares pwls objective applied in the transmitted intensity domain we find that at low exposure levels typical of those being considered for screening ct the poisson likelihood based approaches outperform the pwls objective as well as a standard approach based on adaptive filtering followed by deconvolution at higher exposure levels the approaches all perform similarly

wavelet based noise reduction in ct images using correlation analysis the projection data measured in computed tomography ct and consequently the slices reconstructed from these data are noisy we present a new wavelet based structure preserving method for noise reduction in ct images that can be used in combination with different reconstruction methods the approach is based on the assumption that data can be decomposed into information and temporally uncorrelated noise in ct two spatially identical images can be generated by reconstructions from disjoint subsets of projections using the latest generation dual source ct scanners one image can be reconstructed from the projections acquired at the first the other image from the projections acquired at the second detector for standard ct scanners the two images can be generated by splitting up the set of projections into even and odd numbered projections the resulting images show the same information but differ with respect to image noise the analysis of correlations between the wavelet representations of the input images allows separating information from noise down to a certain signal to noise level wavelet coefficients with small correlation are suppressed while those with high correlations are assumed to represent structures and are preserved the final noise suppressed image is reconstructed from the averaged and weighted wavelet coefficients of the input images the proposed method is robust of low complexity and adapts itself to the noise in the images the quantitative and qualitative evaluation based on phantom as well as real clinical data showed that high noise reduction rates of around 40 can be achieved without noticeable loss of image resolution

local noise weighted filtering for emphysema scoring of low dose ct images computed tomography ct has become the new reference standard for quantification of emphysema the most popular measure of emphysema derived from ct is the pixel index pi which expresses the fraction of the lung volume with abnormally low intensity values as pi is calculated from a single fixed threshold on intensity this measure is strongly influenced by noise this effect shows up clearly when comparing the pi score of a high dose scan to the pi score of a low dose i e noisy scan of the same subject in this paper the noise variance nova filter is presented a general framework for iterative nonlinear filtering which uses an estimate of the spatially dependent noise variance in an image the nova filter iteratively estimates the local image noise and filters the image for the specific purpose of emphysema quantification of low dose ct images a dedicated noniterative nova filter is constructed by using prior knowledge of the data to obtain a good estimate of the spatially dependent noise in an image the performance of the nova filter is assessed by comparing characteristics of pairs of high dose and low dose scans the compared characteristics are the pi scores for different thresholds and the size distributions of emphysema bullae after filtering the pi scores of high dose and low dose images agree to within 2 3 points the reproducibility of the high dose bullae size distribution is also strongly improved nova filtering of a ct image of typically 400 spl times 512 spl times 512 voxels takes only a couple of minutes which makes it suitable for routine use in clinical practice

graph spectral image smoothing using the heat kernel a new method for smoothing both gray scale and color images is presented that relies on the heat diffusion equation on a graph we represent the image pixel lattice using a weighted undirected graph the edge weights of the graph are determined by the gaussian weighted distances between local neighboring windows we then compute the associated laplacian matrix the degree matrix minus the adjacency matrix anisotropic diffusion across this weighted graph structure with time is captured by the heat equation and the solution i e the heat kernel is found by exponentiating the laplacian eigensystem with time image smoothing is accomplished by convolving the heat kernel with the image and its numerical implementation is realized by using the krylov subspace technique the method has the effect of smoothing within regions but does not blur region boundaries we also demonstrate the relationship between our method standard diffusion based pdes fourier domain signal processing and spectral clustering experiments and comparisons on standard images illustrate the effectiveness of the method

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