Compressive Sensing (CS) framework becomes well known since its ability to recover signal only by using less sampling required by Shanon-Nyquist theorem. The lack of required sampling is no longer constraint for having good reconstruction performance. The load is shifted to the reconstruction procedure instead of the sampling acquisition process. As long as the signal can be guaranteed sparse, the CS based method is able to provide high reconstruction accuracy. One of the CS principle is incoherence property, which can be represented by mutual coherence value. It represents the coherence between the sensing matrix and the sparse base dictionary. The theory said the less coherence between those two parameters, the more precise the reconstruction is. In fact, it is not consistently applied. The research presented on this paper find that, the theory is consistent for reconstruction on compression system, while it is not applied on the reconstruction of measurement system. Other properties are found to be more representative on assigning necessary condition for reconstruction performance on measurement system.
Electrical capacitance volume tomography is a volumetric tomography technique that utilizes capacitance and fringing to capture behavior or perturbation in the sensing domain. One of the crucial issues in developing ECVT technology is the reconstruction algorithm. In practice, ILBP is most used due to its simplicity. However, it still presents elongation errors for certain dielectric contrasts. The high undersampling measurement of the ECVT imaging system, which is mathematically defined as an undetermined linear system, is one of the most challenging issues. Compressive sensing (CS) is a framework that enables the recovery of a sparse signal or a signal that can be represented as sparse in a certain domain, by having a lower dimension of measurement data compared to the Shanon-Nyquist theorem. Thus, mathematically, this framework is promising for solving an undetermined linear system such as the ECVT imaging system. This paper discusses the possibility of developing an ECVT imaging technique for static objects based on a CS framework. Based on the simulation results, Non-optimized CS does not completely succeed in providing better ECVT imaging quality. However, it does provide more localized imaging compared to ILBP. In addition, by having fewer requirements for the measurement data dimension, the CS framework is promising for reducing the number of required electrodes.
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