Jiehua Zhu

• PhD
• Professor (Full) at Georgia Southern University

Manually annotating liver tumor contours is a time-consuming and labor-intensive task for clinicians. Therefore, automated segmentation is urgently needed in clinical diagnosis. However, automatic segmentation methods face certain challenges due to heterogeneity, fuzzy boundaries, and irregularity of tumor tissue. In this paper, a novel deep learni...

Medical image segmentation is a crucial step in clinical treatment planning. However, automatic and accurate medical image segmentation remains a challenging task, owing to the difficulty in data acquisition, the heterogeneity and large variation of the lesion tissue. In order to explore image segmentation tasks in different scenarios, we propose a...

Sparse representation (SR) has been widely studied and successfully applied to many areas of computer science in recent years. However, whether sparsity is essential to improve the classification performance is still an open question. Some studies reveal that it is the collaborative representation (CR) rather than SR that truly improves the classif...

Spectral CT utilizes spectral information of X-ray sources to reconstruct energy-resolved X-ray images and has wide medical applications. Compared with conventional energy-integrated CT scanners, however, spectral CT faces serious technical difficulties in hardware, and hence its clinical use has been expensive and limited. The goal of this paper i...

The l1-norm regularization has attracted attention for image reconstruction in computed tomography. The l0-norm of the gradients of an image provides a measure of the sparsity of gradients of the image. In this paper, we present a new combined l1-norm and l0-norm regularization model for image reconstruction from limited projection data in computed...

The nonmonotone alternating direction algorithm (NADA) was recently proposed for effectively solving a class of equality-constrained nonsmooth optimization problems and applied to the total variation minimization in image reconstruction, but the reconstructed images suffer from the artifacts. Though by the l0 -norm regularization the edge can be ef...

Different aspects of harmonic analysis, complex analysis, sampling theory, approximation theory and related topics are covered in this volume. The topics included are Fourier analysis, Padè approximation, dynamical systems and difference operators, splines, Christoffel functions, best approximation, discrepancy theory and Jackson-type theorems of a...

Dictionary learning (DL) methods are widely used for pattern recognition in recent years. In most DL methods, the [Formula presented] norm is employed to promote sparsity of the coding. However, the usage of the sparse coding based methods is limited since solving the [Formula presented] based sparse coding is very time-consuming. In this paper, a...

The generalized $l_1$ greedy algorithm was recently proposed and shown to outperform the standard reweighted l1- minimization and $l_1$ greedy algorithms for image reconstruction in Computed Tomography (CT). Herein this algorithm is extended as a semisoft generalized $l_1$ greedy algorithm by adapting the wavelet technique of semisoft thresholding....

A full row-rank system matrix generated by scans along two directions in discrete tomography was recently studied. In this paper, we generalize the result to multiple directions. Let be a reduced binary linear system generated by scans along three directions. Using geometry, it is shown in this paper that the linearly dependent rows of the system m...

Nonlinear dimensionality reduction (DR) algorithms can reveal the intrinsic characteristic of the high dimensional data in a succinct way. However, most of these methods suffer from two problems. First, the incremental dimensionality reduction problem, which means the algorithms cannot compute the embedding of new added data incrementally. Second,...

Sparse solutions for an underdetermined system of linear equations can be found more accurately by -minimization type algorithms, such as the reweighted -minimization and greedy algorithms, than with analytical methods, in particular in the presence of noisy data. Recently, a generalized greedy algorithm was introduced and applied to signal and ima...

The block cyclic projection method in the compressed sensing framework (BCPCS) was introduced for image reconstruction in computed tomography and its convergence had been proven in the case of unity relaxation (λ=1). In this paper, we prove its convergence with underrelaxation parameters λ∈(0,1). As a result, the convergence of compressed sensing b...

The sparse vector solutions for an underdetermined system of linear equations Ax=bAx=b have many applications in signal recovery and image reconstruction in tomography. Under certain conditions, the sparsest solution can be found by solving a constrained l1l1 minimization problem: min||x||1min||x||1 subject to Ax=bAx=b. Recently, the reweighted l1l...

The generalized l1 greedy algorithm was recently introduced and used to reconstruct medical images in computerized tomography in the compressed sensing framework via total variation minimization. Experimental results showed that this algorithm is superior to the reweighted l1-minimization and l1 greedy algorithms in reconstructing these medical ima...

The power and flexibility of polynomial surfaces are unleashed when their degrees are no longer restricted to four or lower, as they are used in early CT phantoms. They have proved useful and appropriate for geometric simulation of human and animal anatomy. In this paper a general algorithm is presented for the x-ray transform of any polynomial sur...

A full row-rank system matrix generated by the strip-based projection model along one scanning direction was studied recently in [9]. In this paper, we generalize the result to multiple directions. Let Cu=h be a reduced binary linear system generated along two distinct scanning directions by the strip-based projection model in discrete tomography,...

The constrained total variation minimization has been developed successfully for image reconstruction in com- puterized tomography. The convergence of the block cyclic projection and Cimmino algorithms for compressed sensing based tomography have been proved recently. In this paper, a block component averaging algorithm incorporation to the total v...

In this paper, we propose a block diagonally-relaxed orthogonal projection algorithm incorporated into the total variation minimization for computed tomography image recon- struction in the compressed sensing framework and derive its convergence. A numerical experiment is performed to illustrate the convergence of the new algorithm. Index Terms—com...

Let Cu=k be an underdetermined linear system generated by the strip-based projection model in discrete tomography, where C is row-rank deficient. In the case of one scanning direction the linear dependency of the rows of C is studied in this paper. An index set H is specified such that if all rows of C with row indices in H are deleted then the row...

Let the system matrix of a linear system be p-cyclic and consistently ordered. Under the assumption that the pth power of the associated Jacobi matrix has only non-positive eigenvalues, it is known that the optimal spectral radius of the SOR-k iteration matrix is strictly increasing as k increases from 2 to p. In this paper, we first show that the...

Analytic simulation in computed tomography(CT) generates projection data for evaluating and improving CT image reconstruction algorithms and has played an important role in the research and development of x-ray CT. The simulation is desired to be as realistic as possible while the computation needs to be efficient and accurate. Early primitive equa...

The amalgamated projection method for convex feasibility and optimization problems has recently been proposed and the stable convergence under summable perturbations has been derived. As an application in computerized tomography (CT), the accuracy and the rate of convergence of the cyclic projection method and Cimmino algorithm incorporated with to...

Analytic simulation in computed tomography(CT) generates projection data for evaluating and improving CT image reconstruction algorithms and has played an important role in the research and development of x-ray CT. The simulation is desired to be as realistic as possible while the computation needs to be efficient and accurate. Early primitive equa...

The amalgamated projection method for convex feasibility and optimization problems has recently been proposed and the stable convergence under summable perturbations has been derived. As an application in computerized tomography (CT), the accuracy and the rate of convergence of the cyclic projection method and Cimmino algorithm incorporated with to...

Abstract Discrete tomography,deals with image reconstruction of an object with finitely many,gray levels (such as two). Different approaches,are used to model,the raw detector reading. The most popular models,are line projection with a lattice of points and strip projection with a lattice of pixels/cells. The line-based projection model,fits some,a...

The line projection with a lattice of points and the strip projection with a lattice of cells are popularly used in modeling the raw detector reading in discrete tomography (DT). In the strip-based projection model for a 2D rectangular region, the projection equations are formulated according to the fractional areas of the intersection of each stri...

In this paper,we consider the singular boundary value problems for second order quasilinear ordinary differential equations and prove existence and convergence on second order perturbation terms.The result is applied to solve the Riemann problem for 2×2 hyperbolic conservation laws,which is a partial differential equation arising in applied mathema...

The projection equations in the research of discrete tomography are obtained by either counting the number of points that each line passes or computing the fractional areas of the intersection of each strip and the grid. In this work, a system of linear equations for strip-based projections with rational slopes is obtained. The linear dependency nu...

Accurate and efficient simulation of an x-ray transform for representative structures plays an important role in research and development of x-ray CT, for the evaluation and improvement of CT image reconstruction algorithms, in particular. Superquadrics are a family of three-dimensional objects, which can be used to model a variety of anatomical st...

In this paper, we perform numerical studies on Feldkamp-type and Katsevich-type algorithms for cone-beam reconstruction with a nonstandard spiral locus to develop an electron-beam micro-CT scanner. Numerical results are obtained using both the approximate and exact algorithms in terms of image quality. It is observed that the two algorithms produce...

The goal is to perform geometric studies on cone-beam CT scanning along a three-dimensional (3D) spiral of variable radius. First, the background for variable radius spiral cone-beam scanning is given in the context of electron-beam CT/micro-CT. Then, necessary and sufficient conditions are proved for existence and uniqueness of PI lines inside the...

The goal of this paper is to study Cone-beam CT scanning along a helix of variable pitch. First the rationale and applications in medical imaging of variable pitch CT reconstruction are explained. Then formulas for the minimum detection window are derived. The main part of the paper proves a necessary and sufficient condition for the existence and...

Accurate simulation of X-ray transforms of representative objects plays an important role in the evaluation and improvement of CT reconstruction algorithms. In this paper, we formulate the X-ray transform and 3D Radon transform for ellipsoids and tetrahedra, and verify the resulting formulas by numerical simulation. Here the ellipsoids and tetrahed...

Computed tomography (CT) is one of the most important areas in the modern science and technology. The most popular approach for image reconstruction is filtered backprojection. It is essential to understand the limit behavior of the filtered backprojection algorithms. The classic results on the limit of image reconstruction are typically done in th...

In this report, we present a number-theory-based approach for discrete tomography (DT),which is based on parallel projections of rational slopes. Using a well-controlled geometry of X-ray beams, we obtain a system of linear equations with integer coefficients. Assuming that the range of pixel values is a(i, j) = 0, 1,..., M-1, with M being a prime...

This paper addressed the standardization of tongue diagnosis using image processing approach. To analyze the tongue features locally, a tongue image is divided into a number of blocks with size 36 * 36. Two algorithms are developed to analyze the color and texture features of each block. A hierarchical K-means clustering algorithm in CIE L * u * v...

Printout. Thesis (Ph. D.)--University of Iowa, 2005. Includes bibliographical references (leaves 123-129).