A generalized eigensystem approach to the inverse problem ofelectrocardiography

The authors develop a new approach to the ill-conditioned inverse problem of electrocardiography which employs finite element techniques to generate a truncated eigenvector expansion to stabilize the inversion. Ordinary three-dimensional isoparametric finite elements are used to generate the conductivity matrix for the body. The authors introduce a related eigenproblem, for which a special two-dimensional isoparametric area matrix is used, and solve for the lowest eigenvalues and eigenvectors. The body surface potentials are expanded in terms, of the eigenvectors, and a least squares fit to the measured body surface potentials is used to determine the coefficients of the expansion. This expansion is then used directly to determine the potentials on the surface of the heart. The number of measurement points on the surface of the body can be less than the number of finite element nodes on the body surface, and the number of modes employed in the expansion can be adjusted to reduce errors due to noise     

A moment-based approach to registration of images with affinegeometric distortion

A new method is described for automatic control point selection and matching. First, reference and sensed images are segmented and closed-boundary regions are extracted. Each region is represented by a set of affine-invariant moment-based features. Correspondence between the regions is then established by a two-stage matching algorithm that works both in the feature space and in the image space. Centers of gravity of corresponding regions are used as control points. A practical use of the proposed method is demonstrated by registration of SPOT and Landsat TM images. It is shown that the authors' method can produce subpixel registration accuracy     

Simultaneous correction of ghost and geometric distortion artifactsin EPI using a multiecho reference scan

A computationally efficient technique is described for the simultaneous removal of ghosting and geometrical distortion artifacts in echo-planar imaging (EPI) utilizing a multiecho, gradient-echo reference scan. Nyquist ghosts occur in EPI reconstructions because odd and even lines of k-space are acquired with opposite polarity, and experimental imperfections such as gradient eddy currents, imperfect pulse sequence timing, B0 field inhomogeneity, susceptibility, and chemical shift result in the even and odd lines of k-space being offset by different amounts relative to the true center of the acquisition window. Geometrical distortion occurs due to the limited bandwidth of the EPI images in the phase-encode direction. This distortion can be problematic when attempting to overlay an activation map from a functional magnetic resonance imaging experiment generated from EPI data on a high-resolution anatomical image. The method described here corrects for geometrical distortion related to B0 inhomogeneity, gradient eddy currents, radio-frequency pulse frequency offset, and chemical shift effect. The algorithm for removing ghost artifacts utilizes phase information in two dimensions and is, thus, more robust than conventional one-dimensional methods. An additional reference scan is required which takes approximately 2 min for a matrix size of 64 X 64 and a repetition time of 2 s. Results from a water phantom and a human brain at 3 T demonstrate the effectiveness of the method for removing ghosts and geometric distortion artifacts.     

A new method for distortion correction of electronic endoscope images

A new method to correct the barrel distortion of an electronic endoscope image is presented. A correction model assuming circularly symmetric distortion is introduced with the following model parameters: the center of distortion and the coefficients of polynomials representing the distortion correction in the radial direction. If the imaging system is distortion-free, straight lines in the object space should be imaged as straight lines. Based on this criterion, a distorted image of a standard pattern consisting of a grid of several straight lines is recorded, and the model parameters are then estimated as a basis for straightening distorted lines. This method has the advantage of not needing a careful placement of the standard pattern for calibration. Correction results are presented for the grid pattern chart to verify a sufficient degree of correction. Examples of distortion correction of real intestinal images and physicians' comments are also presented.     

An application of Marquardt's procedure to the seismic inverse problem

The seismic inverse problem is to infer characteristics of the subsurface from measurements of the wave field at the surface. The Marquardt procedure offers one approach to this problem. In applying this procedure, a linear relationship is developed between the wave field and some parameter which describes a physical property of the subsurface. Then a selection criterion is designed to choose the subsurface parameter which provides the best match for the observed seismic data.     

Unwarping of unidirectionally distorted EPI images

Echo-planar imaging (EPI) is a fast nuclear magnetic resonance imaging (MRI) method. Unfortunately, local magnetic field inhomogeneities induced mainly by the subject's presence cause significant geometrical distortion, predominantly along the phase-encoding direction, which must be undone to allow for meaningful further processing. So far, this aspect has been too often neglected. In this paper, we suggest a new approach using an algorithm specifically developed for the automatic registration of distorted EPI images with corresponding anatomically correct MRI images. We model the deformation field with splines, which gives us a great deal of flexibility, while comprising the affine transform as a special case. The registration criterion is least squares. Interestingly, the complexity of its evaluation does not depend on the resolution of the control grid. The spline model gives us good accuracy thanks to its high approximation order. The short support of splines leads to a fast algorithm. A multiresolution approach yields robustness and additional speedup. The algorithm was tested on real as well as synthetic data, and the results were compared with a manual method. A wavelet-based Sobolev-type random deformation generator was developed for testing purposes. A blind test indicates that the proposed automatic method is faster, more reliable, and more precise than the manual one.     

An analytical approach to the dynamic topology problem

Currently, it is possible to modify (say, hourly) the topology of a data communications network by adding or deleting network links and/or by increasing or decreasing bandwidth on existing links in response to changing traffic loads and/or projected network conditions. The intent of this paper is to study a Markov decision process (MDP) model of the dynamic topology problem (DTP), the problem of activating and/or deleting links, as a function of the current traffic in the network and of the most recent network topology design. We present a decomposition of this model and structural results for the decomposition. The decomposition and structural results enhance the tractability of procedures for determining optimal link control policies. A numerical example is used to illustrate these results.Research supported by ARO Contract No. DAAG-29-85-K0089, NSF Grant No. ECS-8708183, and DCA Contract No. DCA 100-89-C-0031.     

An analytical approach to the partial scan problem

The scan design is the most widely used technique used to ensure the testability of sequential circuits. In this article it is shown that testability is still guaranteed, even if only a small part of the flipflops is integrated into a scan path. An algorithm is presented for selecting a minimal number of flipflops, which must be directly accessible. The direct accessibility ensures that, for each fault, the necessary test sequence is bounded linearly in the circuit size. Since the underlying problem is NP-complete, efficient heuristics are implemented to compute suboptimal solutions. Moreover, a new algorithm is presented to map a sequential circuit into a minimal combinational one, such that test pattern generation for both circuit representations is equivalent and the fast combinational ATPG methods can be applied. For all benchmark circuits investigated, this approach results in a significant reduction of the hardware overhead, and additionally a complete fault coverage is still obtained. Amazingly the overall test application time decreases in comparison with a complete scan path, since the width of the shifted patterns is shorter, and the number of patterns increase only to a small extent.     

An approach to inverse nonlinear control using neural networks

In this paper, we present a strategy for controlling a class of nonlinear dynamical systems using techniques based on neural networks. The proposed strategy essentially exploits the property of neural networks in being able to approximate arbitrary nonlinear maps when suitable learning strategies are applied. For the closed-loop control, such a network is used in conjunction with a technique of inverse nonlinear control to form what we call an inverse nonlinear controller using neural networks, abbreviated as the INC/NN controller. Properties of the controller are discussed, and it is shown that the proposed INC/NN controller allows the closed-loop error dynamics to be specified directly through a set of controller gains. Extensions of the basic INC/NN controller to incorporate integral control action, to higher order systems, and to a class of nonlinear multi-input multi-output dynamical systems are also indicated. Finally, results of some real-time experiments in applying the INC/NN controller to a position control system which has inherent nonlinearities are presented.     

A Bayesian approach to introducing anatomo-functional priors in theEEG/MEG inverse problem

We present a new approach to the recovering of dipole magnitudes in a distributed source model for magnetoencephalographic (MEG) and electroencephalographic (EEG) imaging. This method consists in introducing spatial and temporal a priori information as a cure to this ill-posed inverse problem. A nonlinear spatial regularization scheme allows the preservation of dipole moment discontinuities between some a priori noncorrelated sources, for instance, when considering dipoles located on both sides of a sulcus. Moreover, we introduce temporal smoothness constraints on dipole magnitude evolution at time scales smaller than those of cognitive processes. These priors are easily integrated into a Bayesian formalism, yielding a maximum a posteriori (MAP) estimator of brain electrical activity. Results from EEG simulations of our method are presented and compared with those of classical quadratic regularization and a now popular generalized minimum-norm technique called low-resolution electromagnetic tomography (LORETA)     

Travelling wave expansion: a model fitting approach to the inverse problem of elasticity reconstruction

In this paper, a novel approach to the problem of elasticity reconstruction is introduced. In this approach, the solution of the wave equation is expanded as a sum of waves travelling in different directions sharing a common wave number. In particular, the solutions for the scalar and vector potentials which are related to the dilatational and shear components of the displacement respectively are expanded as sums of travelling waves. This solution is then used as a model and fitted to the measured displacements. The value of the shear wave number which yields the best fit is then used to find the elasticity at each spatial point. The main advantage of this method over direct inversion methods is that, instead of taking the derivatives of noisy measurement data, the derivatives are taken on the analytical model. This improves the results of the inversion. The dilatational and shear components of the displacement can also be computed as a byproduct of the method, without taking any derivatives. Experimental results show the effectiveness of this technique in magnetic resonance elastography. Comparisons are made with other state-of-the-art techniques.     

An adaptive multiscale inverse scattering approach to photothermal depth profilometry

Photothermal depth profilometry is formulated as a nonlinear inverse scattering problem. Starting with the one-dimensional heat diffusion equation, we derive a mathematical model relating arbitrary variation in the depth-dependent thermal conductivity to observed thermal wavefields at the surface of a material sample. The form of the model is particularly convenient for incorporation into a nonlinear optimization framework for is particularly convenient for incorporation into a nonlinear optimization framework for recovering the conductivity based on thermal wave data obtained at multiple frequencies. We develop an adaptive, multiscale algorithm for solving this highly ill-posed inverse problem. The algorithm is designed to produce an accurate, low-order representation of the thermal conductivity by automatically controlling the level of detail in the reconstruction. This control is designed to reflect both (1) the nature of the underlying physics, which says that scale should decrease with depth, and (2) the particular structure of the conductivity profile, which may require a sparse collection of fine-scale components to adequately represent significant features such as a layering structure. The approach is demonstrated in a variety of synthetic examples representative of nondestructive evaluation problems seen in the steel industry.The work of authors E. L. Miller and I. Yavuz was supported by a CAREER Award from the National Science Foundation MIP-9623721, an ODDR&E MURI under Air Force Office of Scientific Research contract F49620-96-1-0028, and the Army Research Office Demining MURI under grant DAAG55-97-1-0013. The work of authors L. Nicolaides and A. Mandelis was supported by a research contract from Material and Manufacturing Ontario (MMO).     

Correction of distortion in endoscope images

Images formed with endoscopes suffer from a spatial distortion due to the wide-angle nature of the endoscope's objective lens. This change in the size of objects with position precludes quantitative measurement of the area of the objects, which is important in endoscopy for accurately measuring ulcer and lesion sizes over time. A method for correcting the distortion characteristic of endoscope images is presented. A polynomial correction formula was developed for the endoscope lens and validated by comparing quantitative test areas before and after the distortion correction. The distortion correction has been incorporated into a computer program that could readily be applied to electronic images obtained at endoscopy using a desk-top computer. The research presented here is a key step towards the quantitative determination of the area of regions of interest in endoscopy.     

反滤波对图像退化的复原研究与实现

在图像退化基础上，根据退化的过程运用了反滤波器进行复原，实验表明，通常在满足一定信噪比时，对退化的图像进行复原的效果有明显改善。     

Accurate alignment of functional EPI data to anatomical MRI using a physics-based distortion model

Mapping of functional magnetic resonance imaging (fMRI) to conventional anatomical MRI is a valuable step in the interpretation of fMRI activations. One of the main limits on the accuracy of this alignment arises from differences in the geometric distortion induced by magnetic field inhomogeneity. This paper describes an approach to the registration of echo planar image (EPI) data to conventional anatomical images which takes into account this difference in geometric distortion. We make use of an additional spin echo EPI image and use the known signal conservation in spin echo distortion to derive a specialized multimodality nonrigid registration algorithm. We also examine a plausible modification using log-intensity evaluation of the criterion to provide increased sensitivity in areas of low EPI signal. A phantom-based imaging experiment is used to evaluate the behavior of the different criteria, comparing nonrigid displacement estimates to those provided by a imagnetic field mapping acquisition. The algorithm is then applied to a range of nine brain imaging studies illustrating global and local improvement in the anatomical alignment and localization of fMRI activations.     

An original genetic approach to the fully automatic gridding of microarray images

Gridding microarray images remains, at present, a major bottleneck. It requires human intervention which causes variations of the gene expression results. In this paper, an original and fully automatic approach for accurately locating a distorted grid structure in a microarray image is presented. The gridding process is expressed as an optimization problem which is solved by using a genetic algorithm (GA). The GA determines the line-segments constituting the grid structure. The proposed method has been compared with existing software tools as well as with a recently published technique. For this purpose, several real and artificial microarray images containing more than one million spots have been used. The outcome has shown that the accuracy of the proposed method achieves the high value of 94% and it outperforms the existing approaches. It is also noise-resistant and yields excellent results even under adverse conditions such as arbitrary grid rotations, and the appearance of various spot sizes.     

A new approach for nonlinear distortion correction in endoscopicimages based on least squares estimation

Images captured with a typical endoscope show spatial distortion, which necessitates distortion correction for subsequent analysis. In this paper, a new methodology based on least squares estimation is proposed to correct the nonlinear distortion in the endoscopic images. A mathematical model based on polynomial mapping is used to map the images from distorted image space onto the corrected image space. The model parameters include the polynomial coefficients, distortion center, and corrected center. The proposed method utilizes a line search approach of global convergence for the iterative procedure to obtain the optimum expansion coefficients. A new technique to find the distortion center of the image based on curvature criterion is presented. A dual-step approach comprising token matching and integrated neighborhood search is also proposed for accurate extraction of the centers of the dots contained in a rectangular grid, used for the model parameter estimation. The model parameters were verified with different grid patterns. The distortion-correction model is applied to several gastrointestinal images and the results are presented. The proposed technique provides high-speed response and forms a key step toward online camera calibration, which is required for accurate quantitative analysis of the images.     

AN EXPANSION AND CORRECTION ALGORITHM FOR PHOTOELECTRIC IMAGE WITH GEOMETRIC DISTORTION

A creepy hotoelectric endoscopy system with good performance is studied,and an expansion and correction algorithm for a compressed photoelectric image with serious geometric distortion is presented.The algorithm can not only correct the geometric geometric distortion,but also restore the gray-level distribution by means of ternary convolution algorithm.The details and the outline in the image are very clear.It is proved to be of high performance in practice.     

An inverse scattering approach based on the differential E-formulation

An inverse scattering technique based on the differential E-formulation in the frequency domain is proposed. The inversion is achieved by minimizing a cost functional, taking into account the discrepancy between measured and estimated field values, while the Helmholtz wave equation is set as constraint. The Fre/spl acute/chet derivatives of the cost functional with respect to the scatterer properties are derived analytically by means of the calculus of variations. Edge elements are used for the numerical treatment of the problem.     

An improved closed-form approximation to the inverse black body radiation problem at microwave frequencies

A function is derived which approximates Planck's black body radiation law more closely at microwave frequencies than either the Rayleigh-Jeans or the recent Hamid-Ragheb approximations. The function leads to an improved closed-form approximation to the inverse black body radiation problem in the microwave region.