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Segmentation of Images from Fourier Spectral Data

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Communications in Computational Physics 2009年第2期5卷 326-349页

作者： anne gelb Dennis Cates Department of Mathematics and Statistics Arizona State UniversityTempeArizona 85287 USA

This paper designs a segmentation method for an image based on its Fourier spectral *** edge map is generated directly from the Fourier coefficients without first reconstructing the image in pixelated *** the internal boundaries of the edge map are not blurred by any(filtered)Fourier *** edge map is then processed with an edge linking segmentation *** include examples from magnetic resonance imaging(MRI).Our results illustrate some potential benefits of using high order methods in imaging.

关键词： Fourier coefficients edge detection segmentation

ACCURATE AND EFFICIENT IMAGE RECONSTRUCTION FROM MULTIPLE MEASUREMENTS OF FOURIER SAMPLES

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Journal of Computational Mathematics 2020年第5期38卷 797-826页

作者： T.Scarnati anne gelb Air Force Research Laboratory WPAFBOH 45433USA Dartmouth College HanoverNH 03755USA

Several problems in imaging acquire multiple measurement vectors(MMVs)of Fourier samples for the same underlying *** recovery techniques from MMVs aim to exploit the joint sparsity across the measurements in the sparse *** is typically accomplished by extending the use of`1 regularization of the sparse domain in the single measurement vector(SMV)case to using`2,1 regularization so that the“jointness”can be accounted *** effective,the approach is inherently coupled and therefore computationally *** method also does not consider current approaches in the SMV case that use spatially varying weighted`1 regularization *** recently introduced variance based joint sparsity(VBJS)recovery method uses the variance across the measurements in the sparse domain to produce a weighted MMV method that is more accurate and more efficient than the standard`2,1 *** efficiency is due to the decoupling of the measurement vectors,with the increased accuracy resulting from the spatially varying *** by these results,this paper introduces a new technique to even further reduce computational cost by eliminating the requirement to first approximate the underlying image in order to construct the *** this preprocessing step moreover reduces the amount of information lost from the data,so that our method is more *** examples provided in the paper verify these benefits.

关键词： Multiple measurement vectors Joint sparsity Weighted`1 Edge detection Fourier data

A High Order Method for Determining the Edges in the Gradient of a Function

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Communications in Computational Physics 2009年第2期5卷 694-711页

作者： Rishu Saxena anne gelb Hans Mittelmann Department of Mathematics and Statistics Arizona State UniversityTempeArizona 85287USA

Detection of edges in piecewise smooth functions is important in many *** order reconstruction algorithms in image processing and post processing of numerical solutions to partial differential equations require the identification of smooth domains,creating the need for algorithms that will accurately identify discontinuities in a given function as well as those in its *** work expands the use of the polynomial annihilation edge detector,(Archibald,gelb and Yoon,2005),to locate discontinuities in the gradient given irregularly sampled point values of a continuous *** idea is to preprocess the given data by calculating the derivative,and then to use the polynomial annihilation edge detector to locate the jumps in the *** compare our results to other recently developed methods.

关键词： Multivariate edge detection derivative discontinuities piecewise smooth functions polynomial annihilation non-uniform grids

The Discrete Orthogonal Polynomial Least Squares Method for Approximation and Solving Partial Differential Equations

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Communications in Computational Physics 2008年第3期3卷 734-758页

作者： anne gelb Rodrigo B.Platte W.Steven Rosenthal Department of Mathematics and Statistics Arizona State UniversityTempeArizona 85287USA

We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential *** focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential *** results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in *** time stability,small corrections near the ends of the interval are computed using local polynomial *** numerical experiments illustrate the performance of the method.

关键词： Discrete least-squares orthogonal polynomials spectralmethods high order numerical methods uniform grid.