Two numerical methods are proposed to solve the electric impedance tomography (EIT) problem in a domain with arbitrary boundary shape. The rst is the new fast Fourier transform subspace-based optimization method (NFFT-SOM). Instead of implementing optimization within the subspace spanned by smaller singular vectors in subspace-based optimization method (SOM), a space spanned by complete Fourier bases is used in the proposed NFFT-SOM. We discuss the advantages and disadvantages of the proposed method through numerical simulations and comparisons with traditional SOM. The second is the low frequency subspace optimized method (LF-SOM), in which we replace the deterministic current and noise subspace in SOM with low frequency current and space spanned by discrete Fourier bases, respectively. We give a detailed analysis of strengths and weaknesses of LF-SOM through comparisons with mentioned SOM and NFFT-SOM in solving EIT problem in a domain with arbitrary boundary shape.
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