Jianhua Luo

Hierarchical modularity of nested bow-ties in metabolic networks

BackgroundThe exploration of the structural topology and the organizing principles of genome-based large-scale metabolic networks is essential for studying possible relations between structure and functionality of metabolic networks. Topological analysis of graph models has often been applied to study the structural characteristics of complex metabolic networks.ResultsIn this work, metabolic networks of 75 organisms were investigated from a topological point of view. Network decomposition of three microbes (Escherichia coli, Aeropyrum pernix and Saccharomyces cerevisiae) shows that almost all of the sub-networks exhibit a highly modularized bow-tie topological pattern similar to that of the global metabolic networks. Moreover, these small bow-ties are hierarchically nested into larger ones and collectively integrated into a large metabolic network, and important features of this modularity are not observed in the random shuffled network. In addition, such a bow-tie pattern appears to be present in certain chemically isolated functional modules and spatially separated modules including carbohydrate metabolism, cytosol and mitochondrion respectively.ConclusionThe highly modularized bow-tie pattern is present at different levels and scales, and in different chemical and spatial modules of metabolic networks, which is likely the result of the evolutionary process rather than a random accident. Identification and analysis of such a pattern is helpful for understanding the design principles and facilitate the modelling of metabolic networks.

Modular co-evolution of metabolic networks

BackgroundThe architecture of biological networks has been reported to exhibit high level of modularity, and to some extent, topological modules of networks overlap with known functional modules. However, how the modular topology of the molecular network affects the evolution of its member proteins remains unclear.ResultsIn this work, the functional and evolutionary modularity of Homo sapiens (H. sapiens) metabolic network were investigated from a topological point of view. Network decomposition shows that the metabolic network is organized in a highly modular core-periphery way, in which the core modules are tightly linked together and perform basic metabolism functions, whereas the periphery modules only interact with few modules and accomplish relatively independent and specialized functions. Moreover, over half of the modules exhibit co-evolutionary feature and belong to specific evolutionary ages. Peripheral modules tend to evolve more cohesively and faster than core modules do.ConclusionThe correlation between functional, evolutionary and topological modularity suggests that the evolutionary history and functional requirements of metabolic systems have been imprinted in the architecture of metabolic networks. Such systems level analysis could demonstrate how the evolution of genes may be placed in a genome-scale network context, giving a novel perspective on molecular evolution.

Highly Undersampled Magnetic Resonance Image Reconstruction Using Two-Level Bregman Method With Dictionary Updating

In recent years Bregman iterative method (or related augmented Lagrangian method) has shown to be an efficient optimization technique for various inverse problems. In this paper, we propose a two-level Bregman Method with dictionary updating for highly undersampled magnetic resonance (MR) image reconstruction. The outer-level Bregman iterative procedure enforces the sampled k-space data constraints, while the inner-level Bregman method devotes to updating dictionary and sparse representation of small overlapping image patches, emphasizing local structure adaptively. Modified sparse coding stage and simple dictionary updating stage applied in the inner minimization make the whole algorithm converge in a relatively small number of iterations, and enable accurate MR image reconstruction from highly undersampled k-space data. Experimental results on both simulated MR images and real MR data consistently demonstrate that the proposed algorithm can efficiently reconstruct MR images and present advantages over the current state-of-the-art reconstruction approach.

Correction of bias field in MR images using singularity function analysis

A new approach for correcting bias field in magnetic resonance (MR) images is proposed using the mathematical model of singularity function analysis (SFA), which represents a discrete signal or its spectrum as a weighted sum of singularity functions. Through this model, an MR images low spatial frequency components corrupted by a smoothly varying bias field are first removed, and then reconstructed from its higher spatial frequency components not polluted by bias field. The thus reconstructed image is then used to estimate bias field for final image correction. The approach does not rely on the assumption that anatomical information in MR images occurs at higher spatial frequencies than bias field. The performance of this approach is evaluated using both simulated and real clinical MR images.

Augmented Lagrangian based Sparse Representation Method with Dictionary Updating for Image Deblurring

This paper presents an efficient alternating direction method with patch-based dictionary updating, ADMDU-DEB, for sparse representation regularization framework of image deblurring. The main idea of the proposed method is to reformulate the variational problem as a linear equality constrained problem and then minimize its augmented Lagrangian function. The alternating direction method decouples the minimization by alternately iterating the pixel-based regularization and the patch-based sparse representation. Typically, accelerated sparse coding and simple dictionary updating applied in the sparse representation stage enable the whole algorithm to converge at a relatively small number of iterations. Additionally, the approach is readily extended to solve the same kind of variational problem with a nonnegativity constraint. Experimental results on benchmark test images consistently validate the superiority of the proposed approach and demonstrate that it achieves very competitive deblurring performance, co...

Gabor feature based nonlocal means filter for textured image denoising

The nonlocal means (NLM) filter has distinct advantages over traditional image denoising techniques. However, in spite of its simplicity, the pixel value-based self-similarity measure used by the NLM filter is intrinsically less robust when applied to images with non-stationary contents. In this paper, we use Gabor-based texture features to measure the self-similarity, and thus propose the Gabor feature based NLM (GFNLM) filter for textured image denoising. This filter recovers noise-corrupted images by replacing each pixel value with the weighted sum of pixel values in its search window, where each weight is defined based on the Gabor-based texture similarity measure. The GFNLM filter has been compared to the classical NLM filter and four other state-of-the-art image denoising algorithms in textured images degraded by additive Gaussian noise. Our results show that the proposed GFNLM filter can denoise textured images more effectively and robustly while preserving the texture information.

Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI

Diffusion tensor interpolation is an important issue in the application of diffusion tensor magnetic resonance imaging (DT-MRI) to the human heart, all the more as the points representing the myocardium of the heart are often sparse. We propose a feature-based interpolation framework for the tensor fields from cardiac DT-MRI, by taking into account inherent relationships between tensor components. In this framework, the interpolation consists in representing a diffusion tensor in terms of two tensor features, eigenvalues and orientation, interpolating the Euler angles or the quaternion relative to tensor orientation and the logarithmically transformed eigenvalues, and reconstructing the tensor to be interpolated from the interpolated eigenvalues and tensor orientations. The results obtained with the aid of both synthetic and real cardiac DT-MRI data demonstrate that the feature-based schemes based on Euler angles or quaternions not only maintain the advantages of Log-Euclidean and Riemannian interpolation as for preserving the tensors symmetric positive-definiteness and the monotonic determinant variation, but also preserve, at the same time, the monotonicity of fractional anisotropy (FA) and mean diffusivity (MD) values, which is not the case with Euclidean, Cholesky and Log-Euclidean methods. As a result, both interpolation schemes remove the phenomenon of FA collapse, and consequently avoid introducing artificial fiber crossing, with the difference that the quaternion is independent of coordinate system while Euler angles have the property of being more suitable for sophisticated interpolations.

MR image reconstruction from truncated k-space using a Layer singular point extraction technique

A new approach to image reconstruction in magnetic resonance imaging is proposed using the mathematical model of singularity function analysis (SFA). Through this model, any discrete signal is expressed as a weighted sum of singularity functions. A layer extraction technique based on SFA is then developed to determine the singular points as well as the weighting coefficients from the acquired k-space data. Images are finally reconstructed using the obtained model parameters. This reconstruction methodology differs fundamentally from existing methods, and is particularly suitable for reconstructing images from truncated k-space. Experiments on both simulated and physical data revealed significant advantages of the present method over conventional reconstruction methods.

A novel predual dictionary learning algorithm

Dictionary learning has been a hot topic fascinating many researchers in recent years. Most of existing methods have a common character that the sequences of learned dictionaries are simpler and simpler regularly by minimizing some cost function. This paper presents a novel predual dictionary learning (PDL) algorithm that updates dictionary via a simple gradient descent method after each inner minimization step of Predual Proximal Point Algorithm (PPPA), which was recently presented by Malgouyres and Zeng (2009) [F. Malgouyres, T. Zeng, A predual proximal point algorithm solving a non negative basis pursuit denoising model, Int. J. Comput. Vision 83 (3) (2009) 294-311]. We prove that the dictionary update strategy of the proposed method is different from the current ones because the learned dictionaries become more and more complex regularly. The experimental results on both synthetic data and real images consistently demonstrate that the proposed approach can efficiently remove the noise while maintaining high image quality and presents advantages over the classical dictionary learning algorithms MOD and K-SVD.

An augmented Lagrangian multi-scale dictionary learning algorithm

Learning overcomplete dictionaries for sparse signal representation has become a hot topic fascinated by many researchers in the recent years, while most of the existing approaches have a serious problem that they always lead to local minima. In this article, we present a novel augmented Lagrangian multi-scale dictionary learning algorithm (ALM-DL), which is achieved by first recasting the constrained dictionary learning problem into an AL scheme, and then updating the dictionary after each inner iteration of the scheme during which majorization-minimization technique is employed for solving the inner subproblem. Refining the dictionary from low scale to high makes the proposed method less dependent on the initial dictionary hence avoiding local optima. Numerical tests for synthetic data and denoising applications on real images demonstrate the superior performance of the proposed approach.