Electrical Capacitance Volume Tomography static imaging using Compressive Sensing with l₁ sparse recovery

Compressive Sensing (CS) framework is mathematical framework to recover the signal by having less measurement data compared to Shannon-Nyquist theorem. It indicates the underdetermined linear system where the dimension of measurement data is much lower compared to dimension of the projected data. The basic idea of CS is to shift the sensing load into image reconstruction load. Thus, even though the sensing process produces less measurement data subject to the recovery data dimension, the CS theoretically is able to perform good signal recovery. Theoretically, CS should be working for natural sparse signal or sparse in transform domain. Electrical Capacitance Volume Tomography (ECVT) imaging forms naturally underdetermined linear system since the dimension of capacitance as the measurement data is much lower compared to dimension of predicted permittivity distribution. In addition, the ECVT signal is naturally sparse. Thus, the compressive sensing framework is theoretically promising for ECVT imaging. This paper will introduce ECVT static imaging based on compressive sensing framework. The early simulations show that compressive sensing with l₁ optimization on the sparse recovery succeed to eliminate the elongation error on ECVT imaging by ILBP (Iterative Learning Back Propagation).