Sparse Boundary Research Articles

Recovering fine details from under-resolved electron tomography data using higher order total variation [formula omitted] regularization

Over the last decade or so, reconstruction methods using ℓ1 regularization, often categorized as compressed sensing (CS) algorithms, have significantly improved the capabilities of high fidelity imaging in electron tomography. The most popular ℓ1 regularization approach within electron tomography has been total variation (TV) regularization. In addition to reducing unwanted noise, TV regularization encourages a piecewise constant solution with sparse boundary regions. In this paper we propose an alternative ℓ1 regularization approach for electron tomography based on higher order total variation (HOTV). Like TV, the HOTV approach promotes solutions with sparse boundary regions. In smooth regions however, the solution is not limited to piecewise constant behavior. We demonstrate that this allows for more accurate reconstruction of a broader class of images – even those for which TV was designed for – particularly when dealing with pragmatic tomographic sampling patterns and very fine image features. We develop results for an electron tomography data set as well as a phantom example, and we also make comparisons with discrete tomography approaches.

Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements

Electromagnetic wave scattering by random surfaces: uncertainty quantification via sparse tensor boundary elements

Semi-automatic segmentation of subcutaneous tumours from micro-computed tomography images

This paper outlines the first attempt to segment the boundary of preclinical subcutaneous tumours, which are frequently used in cancer research, from micro-computed tomography (microCT) image data. MicroCT images provide low tissue contrast, and the tumour-to-muscle interface is hard to determine, however faint features exist which enable the boundary to be located. These are used as the basis of our semi-automatic segmentation algorithm. Local phase feature detection is used to highlight the faint boundary features, and a level set-based active contour is used to generate smooth contours that fit the sparse boundary features. The algorithm is validated against manually drawn contours and micro-positron emission tomography (microPET) images. When compared against manual expert segmentations, it was consistently able to segment at least 70% of the tumour region (n = 39) in both easy and difficult cases, and over a broad range of tumour volumes. When compared against tumour microPET data, it was able to capture over 80% of the functional microPET volume. Based on these results, we demonstrate the feasibility of subcutaneous tumour segmentation from microCT image data without the assistance of exogenous contrast agents. Our approach is a proof-of-concept that can be used as the foundation for further research, and to facilitate this, the code is open-source and available from www.setuvo.com.

Effect of Y content on microstructure and mechanical properties of Mg–2·4Nd–0·2Zn–0·4Zr alloys

The effects of yttrium (0, 2·5, 4·0 and 6·0 wt-%) on the microstructures, age hardening behaviours and mechanical properties of the Mg–2·4Nd–0·2Zn–0·4Zr alloys were investigated. The results demonstrated that the Mg–2·4Nd–0·2Zn–0·4Zr alloy was mainly composed of α-Mg and Mg12Nd phases. When Y was the added into Mg–2·4Nd–0·2Zn–0·4Zr alloy, Mg24Y5 phases formed. The volume fraction of Mg24Y5 phases increased, and the grains were refined with the Y element increasing. Moreover, the additions of Y could improve the peak aged hardness and mechanical properties of the alloys. Mg–2·4Nd–0·2Zn–0·4Zr–6Y alloy exhibited the highest yield strength of 280 MPa in 225°C peak aged condition; Mg–2·4Nd–0·2Zn–0·4Zr–4·0Y alloy exhibited the optimal mechanical properties in the peak aged condition, whose value of ultimate tensile strength, yield strength and elongation were 330 MPa, 265 MPa and 6·5% respectively. The optimal mechanical properties of Mg-2·4Nd-0·2Zn-0·4Zr-4·0Y alloy were mainly attributed to the high volume fraction of fine metastable β′ precipitates in the matrix and the discontinuous distribution of the sparse grain boundary precipitates along grain boundary.

Thin-film sparse boundary array design for passive acoustic mapping during ultrasound therapy

A new 2-D hydrophone array for ultrasound therapy monitoring is presented, along with a novel algorithm for passive acoustic mapping using a sparse weighted aperture. The array is constructed using existing polyvinylidene fluoride (PVDF) ultrasound sensor technology, and is utilized for its broadband characteristics and its high receive sensitivity. For most 2-D arrays, high-resolution imagery is desired, which requires a large aperture at the cost of a large number of elements. The proposed array's geometry is sparse, with elements only on the boundary of the rectangular aperture. The missing information from the interior is filled in using linear imaging techniques. After receiving acoustic emissions during ultrasound therapy, this algorithm applies an apodization to the sparse aperture to limit side lobes and then reconstructs acoustic activity with high spatiotemporal resolution. Experiments show verification of the theoretical point spread function, and cavitation maps in agar phantoms correspond closely to predicted areas, showing the validity of the array and methodology.

Density based pruning for identification of differentially expressed genes from microarray data

MotivationIdentification of differentially expressed genes from microarray datasets is one of the most important analyses for microarray data mining. Popular algorithms such as statistical t-test rank genes based on a single statistics. The false positive rate of these methods can be improved by considering other features of differentially expressed genes.ResultsWe proposed a pattern recognition strategy for identifying differentially expressed genes. Genes are mapped to a two dimension feature space composed of average difference of gene expression and average expression levels. A density based pruning algorithm (DB Pruning) is developed to screen out potential differentially expressed genes usually located in the sparse boundary region. Biases of popular algorithms for identifying differentially expressed genes are visually characterized. Experiments on 17 datasets from Gene Omnibus Database (GEO) with experimentally verified differentially expressed genes showed that DB pruning can significantly improve the prediction accuracy of popular identification algorithms such as t-test, rank product, and fold change.ConclusionsDensity based pruning of non-differentially expressed genes is an effective method for enhancing statistical testing based algorithms for identifying differentially expressed genes. It improves t-test, rank product, and fold change by 11% to 50% in the numbers of identified true differentially expressed genes. The source code of DB pruning is freely available on our website http://mleg.cse.sc.edu/degprune

A poly-region boundary element method for two-dimensional Boussinesq flows

A sparse boundary element method (BEM) for steady non-uniformly heated viscous fluid flow is presented. The new boundary integral formulation with a poly-region approach involves the use of region-based convective velocity along with free-space fundamental solutions with slight compressibility in order to eliminate pressure from the governing equations. The boundary element formulation developed previously by the authors for incompressible isothermal viscous fluid flows is extended for non-isothermal flows governed by Boussinesq equations. The new BEM is then applied to the problem of natural convection in a square enclosure, to the classical Rayleigh–Benard problem and to a stratified flow over a backward-facing step. In all three cases, the boundary element results are in good agreement with published finite difference and finite element solutions. However, in some instances, the boundary element solutions are more accurate, particularly in terms of resolving surface tractions and heat flux. Consequently, results are presented in detail to provide data for future comparison.

Creation of sparse boundary element matrices for 2-D and axi-symmetric electrostatics problems using the bi-orthogonal Haar wavelet

In our previous paper we described the creation of sparse boundary element matrices that arise from Laplace's equation with mixed boundary conditions using an orthogonal wavelet basis. In this paper we examine the properties of wavelet expansions, and propose a way to construct even sparser matrices than the ones we obtained using the conventional Haar wavelet. We observe that the number of 'vanishing moments' of a wavelet qualitatively determines the density of BEM matrices. Then we introduce a way of constructing a wavelet that has more vanishing moments than Haar's wavelet, but still retains a form that is very simple to implement. The time to solution employing the new wavelet is comparable to the Haar wavelet; both are faster than algorithms that rely on a conventional piecewise constant basis. However the quality of the solution is much better, for a given sparsity, the L/sub 2/ error of the source distribution is as much as an order of magnitude lower with the new bi-orthogonal wavelet.

On The Creation Of Sparse Boundary Element Matrices For Two Dimensional Electrostatics Problems Using The Orthogonal Haar Wavelet

This paper describes the creation of sparse boundary element matrices arising from Laplace's equation with mixed boundary conditions using an orthogonal wavelet basis. In contrast to previous work which employed a similarity transform that changed the finite dimensional basis a posteriori, the method described here can produce the sparse matrix directly. This has obvious advantages for large problems, where quadratic growth of the storage space required for the matrix coefficients can be prohibitively expensive.

On the creation of sparse boundary element matrices for two dimensional electrostatics problems using the orthogonal Haar wavelet

This paper describes the creation of sparse boundary element matrices arising from Laplace's equation with mixed boundary conditions using an orthogonal wavelet basis. In contrast to previous work which employed a similarity transform that changed the finite dimensional basis a posteriori, the method described here can produce the sparse matrix directly. This has obvious advantages for large problems, where quadratic growth of the storage space required for the matrix coefficients can be prohibitively expensive.

Sparse Boundary Conditions on Artificial Boundaries for Three-Dimensional Potential Problems

We consider Laplace's equation in three dimensions where the domain is restricted to a finite region with the introduction of an artificial boundaryBon which a boundary condition is imposed. The finite difference method is employed to compare the solution at the nodes inside and on the surfaceBfor four different boundary conditions of which two are local and two are nonlocal. The standard nonlocal (DtN) boundary condition is derived from the solution of the exterior Dirichlet problem, and a discretized (DDtN) version is derived that applies at the nodes onB. However, the coefficients associated with the nodes onBin the system of linear equations for the solution is not sparse. This lack of sparsity is acute for three-dimensional problems owing to the large number of equations. The DDtN boundary condition is approximated to obtain a sparse nonlocal boundary condition, where the coefficients associated with the nodes onBare relatively sparse. We show that the DDtN solution is very accurate. In addition, we present results which indicate that the difference between the DDtN solution and the solution for each of the other three boundary conditions has the correct behavior when the artificial boundary is enlarged.

On the two-grid approximate approach for constructing sparse boundary systems in substructuring

An approximate technique to construct sparse boundary systems in substructure approaches is developed. The technique is based on the introduction of auxiliary coarse grid divisions over superelement boundaries allowing superelement boundary matrices to be constructed on a special basis providing for the possibility of an efficient approximate solution. For the theoretical grounding of the method, a singular integral operator simulation is proposed. Numerical experiments confirming theoretical results and the applicability of the method are presented. Solution strategies with orientation to the standard superelement concept are discussed.

Unimoment Method for Electromagnetic Wave Scattering

A simple problem in 2-dimensional space is used as an example for the application of the unimoment method. The discussion includes fundamentals, mesh generation, loading of equations, sparse matrix inversion and boundary matching. The objective of this paper is to help uninitiated readers understand and apply this method.