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eitcom / pyEIT

Python based toolkit for Electrical Impedance Tomography
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Question regarding Jacobians #25

Closed akarshp28 closed 2 years ago

akarshp28 commented 2 years ago

Hello @liubenyuan,

I hope you are doing well. First of all, thank you so much for developing and sharing your pyEIT library with everyone. I am fairly new to using your library so, I have some questions for you with regards to the Forward class provided below. https://github.com/liubenyuan/pyEIT/blob/eaa0b7981b6ab0735e25ba079c1ecc209604c438/pyeit/eit/fem.py#L17

If I understand correctly, you provide the Jacobian of the body with respect to the electric potential "u" and conductivity "sigma" using solve and solve_eit functions respectively from the above Forward class. So, "solve" computes the forward problem by outputting the point wise potential u values and Jacobian of u. While, "solve_eit" computes the inverse problem by outputting the Jacobian of sigma, boundary voltages at electrodes and Smear matrix. Please correct my understanding if I am wrong here.

I am particularly interested in the Jacobian information from your library. My main questions are:

  1. These Jacobians are w.r.t the simplex triangles i.e, df(body, sigma)/d sigma and df(body, u)/d u at each triangle on the mesh correct?
  2. Do you know if there is a way I can compute the individual gradients du/dx, du/dy, d sigma/dx and d sigma/dy for each x, y on the mesh?

Any advice is greatly appreciated,

Thank you so much,

liubenyuan commented 2 years ago

Hi, Yes you are right.

1, The detailed Jacobian calculation code is based on "Direct EIT Jacobian calculations for conductivity change and electrode movement", which can be download at https://iopscience.iop.org/article/10.1088/0967-3334/29/6/S08/pdf

2, You mean position jacobian? If so, you may refer this article, "Methods for calculating the electrode position Jacobian for impedance imaging", https://iopscience.iop.org/article/10.1088/1361-6579/aa5b78