Reconstruction system and methods for impedance imaging

Claim 1

A method of displaying an image of the interior of a structure having a plurality of surfaces and comprising regions of different conductivities which differentially affect electrical signals transmitted therethrough, said method comprising the steps of: (a) applying electrical input currents at a plurality of selected current input sites of said structures, each of said electrical input currents flowing within at least one of said regions and exiting from said structure at a selected current output site thereof; (b) measuring the voltages generated by each of said applied currents at a plurality of selected voltage measuring sites of said structure with respect to a voltage reference point, each of said selected voltage measuring sites being remote from the current input and output sites through which flows the current generating said voltages; (c) calculating the voltages φ at a plurality of locations within said structure, including said selected voltage measuring sites, with respect to said voltage reference point from the equation -∇·κ∇φ=f, where κ is a value of conductivity assumed for each of said locations and f is the density of each of the electrical input currents at said current input and output sites, the current traversing the surfaces of said structure except at said current input and output sites being assumed equal to zero; (d) calculating the electrical current flux density J at each of the locations for which the voltage was calculated in step (c) from the equation J=-κ∇φ; (e) comparing the voltages calculated in step (c) for each of said selected voltage measuring sites of said structure and the corresponding voltages measured at said selected sites in step (b); (f) repeating steps (c) and (d) when the difference between the voltages compared in step (e) are greater than a predetermined amount, the voltages measured in step (b) then being substituted at said selected voltage measuring sites for the voltages calculated in step (c); (g) calculating new values for κ for each of said locations when the squared residual sum R equals ##EQU7## where V is the region over which the imaging is being performed and X represents the excitations over which the sum is taken, by determining the values of κ which minimize R throughout said structure; (h) repeating steps (f) and (g) until the voltages compared in step (e) do not exceed said predetermined amount; and (i) displaying the values of κ calculating in step (h) thereby providing an image of the interior of said structure.

Claim 2

A method of displaying an image of the interior of a structure having a plurality of surfaces and comprising regions of different conductivities which differentially affect electrical signals transmitted therethrough, said method comprising the steps of: (a) applying electrical input currents at a plurality of selected current input sites of said structures, each of said electrical input currents flowing within at least one of said regions and exiting from said structure at a selected current output site thereof; (b) measuring the voltages generated by each of said applied currents at a plurality of selected voltage measuring sites of said structure with respect to a voltage reference point, each of said selected voltage measuring sites being remote from the current input and output sites through which flows the current generating said voltages; (c) calculating the voltages φ at a plurality of locations within said structure, including said selected voltage measuring sites, with respect to said voltage reference point from the equation -∇·κ∇φ=f, where κ is a value of conductivity assumed for each of said locations and f is the density of each of the electrical input currents at said current input and output sites, the current traversing the surfaces of said structure except at said current input and output sites being assumed equal to zero; (d) calculating the electrical current flux density J at each of the locations for which the voltage was calculated in step (c) from the equation J=-κ∇φ; (e) comparing the voltages calculated in step (c) for each of said selected voltage measuring sites of said structure and the corresponding voltages measured at said selected sites in step (b); (f) repeating steps (c) and (d) when the difference between the voltages compared in step (e) are greater than a predetermined amount, the voltages measured in step (b) then being substituted at said selected voltage measuring sites for the voltages calculated in step (c); (g) calculating new values for κ for each of said locations when the squared residual sum R equals ##EQU7## where V is the region over which the imaging is being performed and X represents the excitations over which the sum is taken, by determining the values of κ which minimize R throughout said structure; (h) repeating steps (f) and (g) until the voltages compared in step (e) do not exceed said predetermined amount; and (i) displaying the values of κ calculating in step (h) thereby providing an image of the interior of said structure.