Adaptive k-space sampling design for edge-enhanced DCE-MRI using compressed sensing

The critical challenge in dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI) is the trade-off between spatial and temporal resolution due to the limited availability of acquisition time. To address this, it is imperative to under-sample k-space and to develop specific reconstruction techniques. Our proposed method reconstructs high-quality images from under-sampled dynamic k-space data by proposing two main improvements; i) design of an adaptive k-space sampling lattice and ii) edge-enhanced reconstruction technique. A high-resolution data set obtained before the start of the dynamic phase is utilized. The sampling pattern is designed to adapt to the nature of k-space energy distribution obtained from the static high-resolution data. For image reconstruction, the well-known compressed sensing-based total variation (TV) minimization constrained reconstruction scheme is utilized by incorporating the gradient information obtained from the static high-resolution data. The proposed method is tested on seven real dynamic time series consisting of 2 breast data sets and 5 abdomen data sets spanning 1196 images in all. For data availability of only 10%, performance improvement is seen across various quality metrics. Average improvements in Universal Image Quality Index and Structural Similarity Index Metric of up to 28% and 24% on breast data and about 17% and 9% on abdomen data, respectively, are obtained for the proposed method as against the baseline TV reconstruction with variable density random sampling pattern.     

Reduced aliasing artifacts using shaking projection k-space sampling trajectory

Radial imaging techniques, such as projection-reconstruction （PR）, are used in magnetic resonance imaging （MRI） for dynamic imaging, angiography, and short-T2 imaging. They are less sensitive to flow and motion artifacts, and support fast imaging with short echo times. However, aliasing and streaking artifacts are two main sources which degrade radial imaging quality. For a given fixed number of k-space projections, data distributions along radial and angular directions will influence the level of aliasing and streaking artifacts. Conventional radial k-space sampling trajectory introduces an aliasing artifact at the first principal ring of point spread function （PSF）. In this paper, a shaking projection （SP） k-space sampling trajectory was proposed to reduce aliasing artifacts in MR images. SP sampling trajectory shifts the projection alternately along the k-space center, which separates k-space data in the azimuthal direction. Simulations based on conventional and SP sampling trajectories were compared with the same number projections. A significant reduction of aliasing artifacts was observed using the SP sampling trajectory. These two trajectories were also compared with different sampling frequencies. ASP trajectory has the same aliasing character when using half sampling frequency （or half data） for reconstruction. SNR comparisons with different white noise levels show that these two trajectories have the same SNR character. In conclusion, the SP trajectory can reduce the aliasing artifact without decreasing SNR and also provide a way for undersampling recon- struction. Furthermore, this method can be applied to three-dimensional （3D） hybrid or spherical radial k-space sampling for a more efficient reduction of aliasing artifacts.     

一种面向信息带宽的频谱感知方法研究

本文利用频带宽度先验信息,提出一种面向信息带宽的自适应调制宽带转换器结构.该结构的总采样率为信号信息带宽的四倍,远小于信号的奈奎斯特采样频率,从而更有效利用采样资源,降低采样数据量,提高处理实时性.通过对该结构中随机波形函数周期的选择,可以实现对系统采样率和系统物理实现复杂度的权衡取舍,从而适应不同场合中的应用.本文通过理论分析给出了该结构实现信号精确重构的充分条件.引入多重信号分类算法,分析了该结构适用此算法的充分条件.本文通过仿真实验对上述分析进行了有效性验证.该系统可以应用于隐形装备的吸波材料的前端特性分析、认知无线电的频谱感知.     

On a Class of Generalized Sampling Functions

In this note, we discuss a class of so-called generalized sampling functions. These functions are defined to be the inverse Fourier transform of a family of piecewise constant functions that are either square integrable or Lebegue integrable on the real number line. They are in fact the generalization of the classic sinc function. Two approaches of constructing the generalized sampling functions are reviewed. Their properties such as cardinality, orthogonality, and decaying properties are discussed. The interactions of those functions and Hilbert transformer are also discussed.     

On optimal wavelet reconstructions from Fourier samples: Linearity and universality of the stable sampling rate

In this paper we study the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling. Our first result demonstrates that using generalized sampling one obtains a stable and accurate reconstruction, provided the number of Fourier samples grows linearly in the number of wavelet coefficients recovered. For the class of Daubechies wavelets we derive the exact constant of proportionality.Our second result concerns the optimality of generalized sampling for this problem. Under some mild assumptions we show that generalized sampling cannot be outperformed in terms of approximation quality by more than a constant factor. Moreover, for the class of so-called perfect methods, any attempt to lower the sampling ratio below a certain critical threshold necessarily results in exponential ill-conditioning. Thus generalized sampling provides a nearly-optimal solution to this problem.     

Generalized loop‐erased random walks and approximate reachability

In this paper we extend the loop‐erased random walk (LERW) to the directed hypergraph setting. We then generalize Wilson's algorithm for uniform sampling of spanning trees to directed hypergraphs. In several special cases, this algorithm perfectly samples spanning hypertrees in expected polynomial time. Our main application is to the reachability problem, also known as the directed all‐terminal network reliability problem. This classical problem is known to be # P‐complete, hence is most likely intractable (Ball and Provan, SIAM J Comput 12 (1983) 777–788). We show that in the case of bi‐directed graphs, a conjectured polynomial bound for the expected running time of the generalized Wilson algorithm implies a FPRAS for approximating reachability. Copyright © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 44, 201‐223, 2014     

Consensus of heterogeneous multi-agent systems based on sampled data with a small sampling delay

In this paper, consensus problems of heterogeneous multi-agent systems based on sampled data with a small sampling delay are considered. First, a consensus protocol based on sampled data with a small sampling delay for heterogeneous multi-agent systems is proposed. Then, the algebra graph theory, the matrix method, the stability theory of linear systems, and some other techniques are employed to derive the necessary and sufficient conditions guaranteeing heterogeneous multi-agent systems to asymptotically achieve the stationary consensus. Finally, simulations are performed to demonstrate the correctness of the theoretical results.     

Characterization of a novel particle into liquid sampler for analysis of single fluorescent aerosol particles through capillary electrophoresis

An approach to sample and analyze single aerosolized droplets (<10 nL) of solutions containing fluorescein isothiocyanate (FITC) labeled glycine (GLY) and glutamic acid (GLU) is demonstrated. The sampling approach is based on inertial impaction in which the sample particle is accelerated through a nozzle and directly into a small drop of buffered solution (20 mM borate, pH = 10) suspended at the end of a coaxial tube of stainless steel and a fused silica capillary. A spherical light scattering cell and laser (λ = 532 nm) is used to detect the arrival of particles at the buffered droplet. Upon dissolution and/or mixing, a portion of the sample is injected onto the fused silica capillary for subsequent chemical analysis by capillary electrophoresis (CE) and detection by laser-induced fluorescence (LIF). It was found that the inertial impaction approach sampled particles >1 μm diameter with an efficiency of 80% or greater. At 15 kV applied potential, the FITC conjugates of GLY and GLU could be resolved in less than 120 s allowing qualitative analysis of the contents of single dispersed particles. However, the extent to which the sample is diluted into the buffer droplet varied significantly on a per-particle basis that caused >80% R.S.D. in fluorescence peak heights. This aspect of the method would necessitate the use of internal standards for quantitative analysis of materials present within the particles. It is envisaged that further improvements to the device described may ultimately lead to analysis of the contents of single particles dispersed in earth's atmosphere.     

Predictive modeling and analysis of HfO2 thin film process based on Bayesian information criterion using PCA‐based neural networks

Principal component analysis (PCA)‐based neural network (NNet) models of HfO₂ thin films are used to study the process of efficient model selection and develop an improved model by using multivariate functional data such as X‐ray diffraction data (XRD). The accumulation capacitance and the hysteresis index input parameters, both characteristic of HfO₂ dielectric films, were selected for the inclusion in the model by analyzing the process conditions. Standardized XRD were used to analyze the characteristic variations for different process conditions; the responses and the electrical properties were predicted by NNet modeling using crystallinity‐based measurement data. A Bayesian information criterion (BIC) was used to compare the model efficiency and to select an improved model for response prediction. Two conclusions summarize the results of the research documented in this paper: (i) physical or material properties can be predicted by the PCA‐based NNet model using large‐dimension data, and (ii) BIC can be used for the selection and evaluation of predictive models in semiconductor manufacturing processes. Copyright © 2013 John Wiley & Sons, Ltd.