Purpose: Electrical capacitance tomography (ECT) and electrical resistance tomography (ERT) are promising techniques for multiphase flow measurement due to their high speed, low cost, non-invasive and visualization features. There are two major difficulties in image reconstruction for ECT and ERT: the “soft-field”effect, and the ill-posedness of the inverse problem, which includes two problems: under-determined problem and the solution is not stable, i.e. is very sensitive to measurement errors and noise. This paper aims to summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide reference for further research and application.Design/methodology/approach: In the past 10 years, various image reconstruction algorithms have been developed to deal with these problems, including in the field of industrial multi-phase flow measurement and biological medical diagnosis.Findings: This paper reviews existing image reconstruction algorithms and the new algorithms proposed by the authors for electrical capacitance tomography and electrical resistance tomography in multi-phase flow measurement and biological medical diagnosis.Originality/value: The authors systematically summarize and evaluate various reconstruction algorithms which have been studied and developed in the word for many years and to provide valuable reference for practical applications.

As an advanced measurement technique of non-radiant, non-intrusive, rapid response, and low cost, the electrical tomography (ET) technique has developed rapidly in recent decades. The ET imaging algorithm plays an important role in the ET imaging process. Linear back projection (LBP) is the most used ET algorithm due to its advantages of dynamic imaging process, real-time response, and easy realization. But the LBP algorithm is of low spatial resolution due to the natural ‘soft field’ effect and ‘ill-posed solution’ problems; thus its applicable ranges are greatly limited. In this paper, an original data decomposition method is proposed, and every ET measuring data are decomposed into two independent new data based on the positive and negative sensing areas of the measuring data. Consequently, the number of total measuring data is extended to twice as many as the number of the original data, thus effectively reducing the ‘ill-posed solution’. On the other hand, an index to measure the ‘soft field’ effect is proposed. The index shows that the decomposed data can distinguish between different contributions of various units (pixels) for any ET measuring data, and can efficiently reduce the ‘soft field’ effect of the ET imaging process. In light of the data decomposition method, a new linear back projection algorithm is proposed to improve the spatial resolution of the ET image. A series of simulations and experiments are applied to validate the proposed algorithm by the real-time performances and the progress of spatial resolutions.

The impedance flow sensors have usually been considered as the competitive components in the multi-flow measurement, primarily due to their advantages of fast response, high dynamic range and sensitivity, non-invasive and/or non-intrusive measurements. In this review, the impedance sensors have been categorized into two categories, i.e. , the probes for local/average parameter measurement and sensor arrays for distributed parameter measurement. Maxwell’s equations and boundary conditions have been referred as a starting point to understand the measuring principle of impedance sensors, from which the sensitivity distribution can be attained. The sensitivity distribution can be utilized to characterize the sensor and employed as an objective function in optimizing the sensor geometry. The EMA models usually offer a way to relate the impedance measurements to individual phase fraction, which have been critically reviewed. In addition, the application range, spatial and temporal resolutions, advantages and disadvantages of the sensor arrays, i.e. , the wire mesh sensor, field focusing sensor, electrical resistance and capacitance tomography sensors have also been provided. Finally, the future trends of impedance sensor development have been briefly discussed.

Process tomography techniques play an important role in visualizing and monitoring industrial processes, which help produce high quality product without affecting the work flow in plants. The industrial process tomography techniques, i.e., electrical tomography and computerized tomography, have been widely applied. Such tomographic tools can be used to investigate various types of multi-phase flows, in which the components may differentiate in density, conductivity, permittivity, etc. In a gasliquid-solid flow, however, it is usually difficult for the existing tomographic tools to visualize the distributions of all three phases. In addition, it is necessary to assume some simplifications, i.e., by viewing two disperse phases as one unified phase. The objective of this research is to provide a dual-modality imaging tool by combining electrical capacitance tomography (ECT) and electromagnetic tomography (EMT). First, an integrated dual-modality sensor was designed and implemented on the same cross-section of the process vessel. Subsequently, dual-modality tomographic measurements were collected by a custom-built multi-channel impedance measurement system. The performance of the dual-modality sensor was verified by numerical simulations and experimental tests, showing that it can produce reliable ECT and EMT measurements at a satisfying signal-to-noise ratio. The complementary tomographic images can be obtained from ECT and EMT, and the distributions of two disperse phases, i.e., gas and solid phases, can be observed. Preliminary image fusion results were also given by combining the information from both the ECT and EMT images.