FFT-Accelerated Transformation-Domain Image Reconstruction for Electrical Impedance Tomography.

Electrical impedance tomography (EIT) is a promising imaging technique that recovers the conductivity distribution inside a domain from noninvasive electrical measurements on the boundary. In this work, to accelerate the solving of EIT problems in arbitrarily shaped domains and with a large number of unknowns (N), we propose a fast integral-equation-based inversion method. First, by applying the Schwarz-Christoffel (SC) conformal transformation, we map the arbitrarily shaped domain of an EIT problem to a rectangle, on which Green's function can be derived analytically in Fourier series representation. Leveraging such a mathematical structure of Green's function, we then propose a fast Fourier transform (FFT)-based algorithm to compute the multiplication of the associated impedance matrix with vectors, where the time complexity is substantially reduced from O(N-2) to O(N log(N)) and the memory complexity is reduced from O(N-2) to O(N). Using the contrast source inversion method along with the accelerated matrix-vector multiplications, the conductivity profile can be reconstructed much more efficiently in the rectangular transformation domain. As validated by numerical and experimental tests, the proposed FFT-accelerated transformation-domain EIT image reconstruction method can offer significantly reduced computational and memory complexity without sacrificing the image quality.