Amplitude demodulation for electrical capacitance tomography based on singular value decomposition

Amplitude demodulation is essential in image reconstruction for electrical capacitance tomography (ECT). In this paper, an amplitude demodulation method is proposed based on singular value decomposition (SVD), which can substitute the role of phase-sensitive demodulation in ECT. First, an M × N Hankel matrix is constructed based on a set of discrete samples. Then, SVD operation is performed on the matrix. Finally, the mathematical expression between the sinusoid amplitude and effective singular values is given; i.e., the first two singular values are used to estimate the amplitude information of the acquired signal. The proposed method has the following advantages: (1) since no reference signals are needed, the synchronization between the acquired and reference signals is not necessary; (2) this method can obtain the amplitude information of the acquired signal with a high signal-to-noise ratio (SNR), even in the case of non-integrity period sampling; and (3) SVD itself can also implement the filtering function; thus, no additional low-pass filters are required in the signal conditioning module. The demodulation accuracy and feasibility of the proposed method were verified by numerical simulations and experiments, indicating that it can provide amplitude demodulation with excellent SNR and robust performances.