稀疏最小化技术提升水-气流层析成像分辨率

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"基于稀疏最小化的水-气流层析X射线网状成像" 在当前的研究论文中，作者探讨了如何利用稀疏最小化技术来提高水-气流层析X射线网状成像的分辨率。网状传感器在两相流测量中广泛应用，因其高时间分辨率、成本效益和对流态影响的强鲁棒性而受到青睐。然而，其固有的低空间分辨率是其主要限制之一。论文中提出了一种新的层析方法，以解决这一问题。这种方法通过构建线性观测模型，并结合网状传感器的原始数据，对网状图像进行重构，从而提高空间分辨率。在这个过程中，他们引入了一种折叠凹形罚函数的稀疏最小化方法来解决图像重建问题。稀疏最小化是现代信号处理和图像恢复领域的一个关键工具，它假设信号或图像可以用一个相对较小的系数集合来表示。在这种情况下，折叠凹形罚函数可以促进稀疏解的形成，即找到一个能够以最少的非零元素精确表示图像的解决方案。这有助于减少重建图像中的伪影，同时清晰地分辨出不同相的界面。实验结果证实，所提出的算法能够生成具有更高分辨率、更少噪声和更明显相界线的网状图像，这在理论上为观察和分析复杂水-气流动提供了可能性。这对于理解和优化工业过程中的两相流，如热交换器、燃烧系统或环境气象学中的云动力学等，具有重要意义。此外，该研究还可能推动网状传感器技术的发展，未来可能应用于其他领域，如医疗成像、地质探测或材料科学中的结构分析。通过改进现有的成像技术，可以获取更详尽的数据，帮助科学家和工程师们更好地理解和控制各种物理现象。因此，这项工作不仅在技术上具有创新性，而且对实际应用具有广泛的影响。

IEEE SENSORS JOURNAL, VOL. 17, NO. 24, DECEM BER 15, 2017 8187

Tomographic Wire-Mesh Imaging of Water–Air

Flow Based on Sparse Minimization

Shangjie Ren, Member, IEEE, Hongcheng Liu, Chao Tan, Senior Member, IEEE,

and Feng Dong, Senior Member, IEEE

Abstract— The wire-mesh sensor is widely used in the measure-

ment of two-phase ﬂow. Comparing with the other ﬂow imaging

methods, the wire-mesh method has the advantages of high tem-

poral resolution, cost efﬁciency, and with high robustness against

effects of ﬂow patterns, but suffers from the comparatively low

resolution. In this paper, a tomographic method was proposed

to enhance the spatial resolution of the wire-mesh sensor. The

wire-mesh image is reﬁned through reconstruction with a linear

observation model and the raw data from the wire-mesh sensor.

The sparse minimization method with folded concave penalty

was p resented to solve the i mage reconstruction problem. The

numerical and experimental results show that the proposed

method can produce the resolution-enhanced wire-mesh images

with less artifacts and distinct phase interfaces, and thus gives

a theoretically possibility to observing the details of the target

ﬂow conditions.

Index Terms— Wire-mesh sensor, tomographic imaging

method, image reconstruction, sparse minimization, folded

concave penalty.

I. INTRODUCTION

IRE-MESH sensor is one of the powerful tools for

the measurement of multi-phase ﬂow. The concept

of wire-mesh sensor was introduced by Prasser et al. [1] in

an earlier time. Two planes of orthogonal distributed wire

electrodes were spanned over a cross section of a pipeline. The

local instantaneous conductance at the crossing points (sensing

points) of the wire electrodes was measured for producing

the cross-sectional images of the distributions of the ﬂow

parameter, such as: the phase concentrations and the bubble

sizes. Due to the advantages of high time reso lution, cost

efﬁciency and robust to ﬂow regimes, such a wire-mesh

imaging method was widely studied in the ﬁeld of multi-

phase ﬂow, and has been proved to be accurate by comparing

Manuscript received June 28, 2017; revised August 17, 2017 and

September 6, 2017; accepted September 6, 2017. Date of publication

September 14, 2017; date of current version November 22, 2017. This work

was supported in part by the National Natural Science Foundation of China

under Grant 61401304, in part by the joint project through the National

Natural Science Foundation of China and the Royal Society of Edinburgh

under Grant 6151101270, in part by the Natural Science Foundation of Tianjin

under Grant 17JCQNJC03500, and in part by the Science and Technology

Innovation Plan of Tianjin under Grant 16PTSYJC00060. The associate editor

coordinating the review of this paper and approving it for publication was

Dr. Marco J. Da Silva. (Corresponding author: Chao Tan.)

S. Ren, C. Tan, and F. Dong are with the Tianjin Key Laboratory of Process

Measurement and Control, School of Electrical and Information Engineer-

ing, Tianjin University, Tianjin 300072, China (e-mail: rensjie@tju.edu.cn;

tanchao@tju.edu.cn; fdong@tju.edu.cn).

H. Liu is with Industrial and Systems Engineering, University of Florida,

Gainesville, FL 32611 USA (e-mail: liu.h@uﬂ.edu).

Digital Object Identiﬁer 10.1109/JSEN.2017.2752226

with the other ﬂow imaging methods, such as: the ultra-fast

x-ray CT [2], [3], the electrical resistance tomography [4],

the electrical capacitance tomography [5] and the conductive

needle-probes [6]. By far, the wire-mesh imaging method is

not only used to measure the ﬂow parameters [7], but also

used to discover the dynamic characteristic of the different

ﬂow pattern s [8].

Currently, the most commonly used wire-mesh imaging

methods are non-tomographic. For a wire-mesh sensor consists

of L transmitter and L receiver electrodes, a L × L image

is directly conducted from the L × L wire-mesh sensor

data. The resolution of a wire-mesh image is limited to

the electrode pitch. This makes it d ifﬁcult to observe the

small bubbles or slight interfaces ﬂuctuations with wire-mesh

technique. A straightforward method to improve the resolution

of a wire-mesh sensor is to decrease the wire separation. For

example, da Silva et al. [9] reported a wire-mesh sensor with

2.8 mm electrode pitch and 24 × 24 measurements per frame

of data. However, the decreased wire separation will increase

the mechanical load at the wire electro des.

Another kind of methods to improve the resolution is based

on the phase in terface extraction technique. A high reso lution

binarization of the image was conducted by segmenting the

bubbles in the raw wire-mesh images with the individually

assigned thresholds [10]. The method was improved for sep-

arating the nearby bubbles that affect a number of crossing

points simultaneously [11]. Recently, a similar idea was used

to extract the stratiﬁed phase interfaces in horizontal two-phase

ﬂow [12]. The interface extraction method has a high com-

putational efﬁciency, and provide high-resolution, even full-

resolution, wire-mesh images. However, they are developed

for a speciﬁc ﬂow pattern, e.g. bubbly ﬂow [10] or stratiﬁed

ﬂow [12]. An additional ﬂow pattern recognition procedure,

such as: [13], is necessary when these methods are applied in

variant ﬂow conditions.

The tomographic wire-mesh imaging method is a promising

resolution enhancement method that is robust to ﬂow patterns.

In 1996, Reinecke et al. [14] proposed a tomographic wire-

mesh imaging system. Three planes of thin wires were used to

obtain the projections of the conductivity distribution along the

different directions. A high-resolution image with 1000 pixels

was reconstructed from 84 measurements. Since the number

of given measurements is much less than the number of

unknown pixels, the tomographic wire-mesh imaging problem

was highly ill-posed, and thus was suffering (or suffered) fro m

the instability of the solution. In 2011, Sun and Wang [15]

See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

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