Assignment

Soft-Field

You should aim to spend a TOTAL of two days on the assignment. Your time will be spent performing image reconstruction and analysis of prepared data files using EIDORS, according to the guidelines given below, and writing a report in the form. of a paper. It is your responsibility to plan your time ahead during this course module.

Lab space is available to you and there will be demonstrator support. The demonstrators will be instructed to offer guidance but not to do the assignment for you.

The report will be in the form. of a short paper, typical of those that are submitted to international conferences – see Appendix A. Marks will be deducted for not satisfying the format. The marking template is shown in Appendix B. Please follow the exact order of the headings.

This assignment is intended to encourage exploration and appreciation of the strengths and weaknesses of image reconstruction for electrical resistance tomography using EIDORS. You will be given a measurement reference file and measurement data files and will perform. image reconstruction to determine preferred values for the reconstruction parameters. At the end you report what you have done, what you expected to observe compared to what you actually observed and some conclusions – all in 7 pages!

You are strongly advised to divide your time equally between using EIDORS and writing the report. In other words, roughly 1 day on exploring reconstruction with EIDORS and interpreting results and 1 day writing the report.

For submission deadline, please refer to Bb.

Summary of Soft Field Reconstruction so far:

In the laboratory sessions you were introduced to image reconstruction for electrical resistance tomography using EIDORS running under MATLAB. This involved :

· Creating a model of the measurement vessel and generating a mesh to be used for finite element modelling.

· Computing the forward solution to give the boundary voltages that result when a current pattern is applied on the electrodes. Results are displayed as graphs.

· Computing the inverse solution using two reconstruction algorithms, linear back projection and iterative Gauss Newton. Results are displayed as colour-coded cross-sections.

Summary of  useful commands :

· Create the model : create_netgen_model “.geo” file

· Use Netgen to create a Mesh (“.vol” file) from the model (“.geo” file)

· Read in the mesh : FEM_read_model_2

· Calculate the boundary voltages :

[forward_results, forward_parameters]=forward_solution(model_parameters);

· Read in the measurement data :

[measurement_data]=read_lct_data_interactive(forward_results);

· Solve the inverse problem :

[inverse_results, model_parameters] = inverse_solution(forward_results, model_parameters, forward_parameters, measurement_data);

· Display the cross-section :

slicer_plot_n(model_parameters, 0.025, inverse_results.sol_lbp );

The Assignment

You will be allocated 2 personal measurement files corresponding to the same arrangement of 2cm diameter plastic and metal objects in water. These files are different for each student. Your two measurement files correspond to the same arrangement of materials in the vessel but one is acquired with the adjacent strategy and one with the opposite strategy. These may be “full” or “with reciprocity” strategies. You should deduce which strategy has been used by considering the data contained in the file and use the appropriate reference files for reconstructions. Information on the setup for the measurements is given at the start of the data files. This is followed by rows containing measurements of Real Voltage, Imaginary Voltage, Current and Phase for each measurement in the excitation strategy. For our purposes only the Real Voltage is used.

You are to explore the quality of the resulting reconstructed images for these files under a range of conditions.

Explore the number of iterations using Non-linear Gauss Newton. A range of 1 to 100 iterations is suggested.

Explore the smoothing factor. A range from 1 to 1e-8 is suggested

Compare the results for the adjacent and opposite strategies on your data.

Your report should clearly state your strategy in exploring these parameters. For instance :

“It was decided to reconstruct an image for every value for the number of iterations from 1 to 100. Starting with 1 iteration for the opposite and adjacent strategies, then 2 iterations for the adjacent and opposite strategies, and so on up to 100 iterations. Then this was repeated for the following values of the smoothing factor : 1, 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6, 1e-7, 1e-8. This strategy was selected to cover all possible values of the parameters.”

Note : The above strategy is exhaustive but is not recommended as it would involve 100 x 2 x 9 = 1800 reconstructions! So, how did you decide which values to explore?

It is informative to consider noise in the images. This might be evaluated by reconstructing a “noise” file compared to the reference. Select the noise files corresponding to the reference files that you have used. In an ideal world these would give perfectly uniform. images with the same value of conductivity (0.01S/m) for each pixel but, due to the inevitable noise in the measurements, this is not the case.  Evaluation might involve consideration of the images or numerical analysis of the conductivity values in the array  “inverse_results.sol.nlgn”.  You might compare this to the noise in the measurement data.

During your explorations you should consider the following :

What is your best suggestion for the arrangement of objects ? (plastic/metal, position)

What is your estimate of the error on the position ?

Which strategy gives the best results ? (opposite/adjacent)

How many iterations would you recommend ?

Which smoothing factor gives the best results ?

How noisy are the images ?

How do you decide on answers to these issues ?

All measurements have been acquired using the gold vessel as described in the laboratory script. and therefore your model .geo and the mesh .vol from the lab activity do not need to be altered. It is tempting to improve results by using a finer mesh but because of the increased computational demands this is not advisable for the present exercise.

You will need to compute forward solutions (boundary voltages) according to the excitation strategy that is used.

[forward_results, forward_parameters]=forward_solution(model_parameters);

Do you want the ground node at the [t]op or the [b]ottom of the tank

or [u]ser defined: t ….. always “t”

What is the injection current in Amps? 0.001 ….. always 0.001

What is the conductivity of the background in S/m? 0.01 ….. always 0.01

How many planes of electrodes do you have? 1 ….. always 1

Do you want to use an [a]djacent or [o]pposite or [p]seudo-opposite or [c]ross-drive protocol?

Depends on measurement data files a=adj; o=opp

Do you want to take full [b]etween plane, [f]ull planar, planar with [r]eciprocity

or [u]ser defined voltage measurements?

Depends on measurement data files “f” or “r”

Do you want to calculate the Jacobian matrix? [Y/N] y

The data files are located in P:\Assignment files and should be copied into your working directory (P:\”).

Load the data into MATLAB :

[measurement_data]=read_lct_data_interactive(forward_results);

Solve the inverse problem (compute the reconstructed cross-sectional image)

[inverse_results, model_parameters] = inverse_solution(forward_results, model_parameters, forward_parameters, measurement_data);

What type of smoothing do you want? 1 always “1”

What smoothing weight do you want? 1 always “1”

Select the Non-linear Gauss Newton algorithm (nonlin)

Select the smoothing factor

Select the  number of iterations

Points to note :

· In your report you are expected to suggest conclusions regarding the relative performance of the different arrangements. In order to do this effectively you should ensure that you practice “good science”. In other words, when making comparisons, only one parameter should be different. If more than one parameter is changed then it is not possible to identify which one is responsible for any change that is observed.  Therefore at the beginning you should plan your programme of “experiments” and the strategy should be described in the report.

· The assignment aims to explore the quality of image reconstruction. For instance, the more ambitious students might wish to consider the noise in the reconstructed conductivities by processing the appropriate array in the workspace.

· Clearly, the report should be a record of your own work and the reports will be evaluated for similarities. However, discussion with others in the class is encouraged in order to help each other to greater achievements. Note : the images that you reconstruct must be generated from the data files that you are allocated and identified at the top of this script. You can find your allocated data files from blackboard. The excitation strategies of the measured data files are described in the first line of the data files.

· One aim of this assignment is to encourage you to think and work in a way that might be helpful in your dissertation and subsequently if you undertake research that ultimately may result in publications or patents. In this respect an important issue is to draw realistic and justified  conclusions, not just the ones that you might expect - or feel that we might expect! It is good practice, before each experiment, to write down what you expect to happen and why, then compare it to the actual result. If it is different to your expectation, identify the difference and try to suggest the reason. To assist this process you are encouraged to be diligent in maintaining a log of your activities on the assignment.

· You are to submit paper and electronic copies of the report. The electronic version should be placed in the “Software and MRI Coursework drop tray” under “Assignments” on Blackboard.

Remember : You are trying to explore the effect on the results, either reconstructed images or predicted boundary voltages, due to changes in the excitation strategy, iterations or smoothing factor. Also, how do you actually decide on the quality of the results?