Mathematical concepts for image reconstruction in tomography

Kim, S.; Khambampati, Anil Kumar

doi:10.1016/b978-1-78242-118-4.00012-5

Cited by 12 publications

(6 citation statements)

References 63 publications

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“…In practice, algorithms based on the Kalman filter are used, for example, in the restoration of satellite and radar images [ 17 , 24 , 30 ] or various medical images (MRI, CT, ultrasound, ...) [ 4 , 9 , 20 , 27 , 29 ] and can be used even for color image restoration [ 10 , 21 , 26 ]. Moreover, the Kalman filter can be employed also in related tasks such as estimating image model parameters [ 37 ] etc.…”

Section: Practical Demonstration and Obtained Resultsmentioning

confidence: 99%

Kalman Filter Employment in Image Processing

Fronckova

Slaby

2020

Lecture Notes in Computer Science

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The Kalman filter is a classical algorithm of estimation and control theory. Its use in image processing is not very well known as it is not its typical application area. The paper deals with the presentation and demonstration of selected possibilities of using the Kalman filter in image processing. Particular attention is paid to problems of image noise filtering and blurred image restoration. The contribution presents the reduced update Kalman filter algorithm, that can be used to solve both the tasks. The construction of the image model, which is the necessary first step prior to the application of the algorithm itself, is briefly mentioned too. The described procedures are then implemented in the MATLAB software and the results are presented and discussed in the paper.

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Section: Practical Demonstration and Obtained Resultsmentioning

confidence: 99%

Kalman Filter Employment in Image Processing

Fronckova

Slaby

2020

Lecture Notes in Computer Science

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“…As a consequence, a simulated measurement set was obtained, which was used to attempt the image reconstruction afterwards. For the solution of the inverse problem, the iterative Gauss–Newton algorithm was applied [2,28].…”

Section: Methodsmentioning

confidence: 99%

Assessment of the Spatial Distribution of Moisture Content in Granular Material Using Electrical Impedance Tomography

Porzuczek

2019

Sensors

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This paper presents a method for the online determination of the spatial distribution of the moisture content in granular material. It might be essential for the monitoring and optimal control of, for example, drying processes. The proposed method utilizes Electrical Impedance Tomography (EIT). As an exemplary material for experimental research, the black chokeberry (Aronia melanocarpa) was used. The relationship between the electrical impedance of the chokeberry and its moisture content was determined for a wide range of frequencies (20 Hz–200 kHz). The EIT research consisted of both simulation and experimental investigation. Experimental studies of the spatial distribution of the moisture content were performed in a cylindrical vessel equipped with 8 electrodes circumferentially arranged. The voltage signal from the electrodes was acquired simultaneously using the data acquisition module. Due to the high impedance of the chokeberries, exceeding 109 Ω for the dried matter, extraordinary instrumentation was necessary to be applied. On the other hand, raw chokeberry was characterized by a several orders of magnitude lower impedance (103–104 Ω), especially for high frequencies. The wide range of the observed impedance was able to be measured owing to its use of the voltage stimulation instead of the current stimulation (which is most common for EIT). The image reconstruction problem was solved using an iterative Gauss–Newton algorithm and the EIDORS (Electrical Impedance Tomography and Diffuse Optical Tomography Reconstruction Software) package. The obtained results showed a satisfactory ability to localize an insufficiently dried part of the material. Prospective ways to improve the imaging quality are also discussed.

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“…As reported from the Kalman filter approaches studied in [56]- [58], the unknown boundary shape or conductivity distribution is regarded as state variables, whereby the EIT problem is transformed into a state estimation problem. In this work, we treat the unknown state parameters µ as a stochastic process which has an evolution model…”

Section: Extended Kalman Filter Modelmentioning

confidence: 99%