Summary: Process tomography is the investigation and imaging of a physical process in region of interest (RoI), such as fluid flow for example, on time and spatial scales around those of the process dynamics. The data gathered from the RoI may be utilized for diverse purposes such as characterization of industrial monitoring and control, design and optimization of industrial hardware, combustion flame imaging, and flow imaging, to name just a few. Due to nature of these applications, the associated sensors often need to be operated in harsh environments under very high pressure and/or temperature conditions. This reduces the currently available sensing modalities to a handful of choices as the possible candidates. Among these modalities, electrical capacitance tomography (ECT) holds great potential due to its relatively fast, non-invasive, non-intrusive imaging characteristics in addition to lightweight and inexpensive hardware. These attractive characteristics also carry over to electrical capacitance volume tomography (ECVT) which find applications in petroleum, chemical, and biochemical industries. Despite all these benefits, ECT and ECVT systems also have a few challenges that demand research efforts. First, typical operational frequencies are below 10 MHz, which make these "soft-field" modalities yield relatively low resolution compared with "hard-field" imaging counterparts such as X-ray. Second, current hardware design imply a high degree of correlation between mutual capacitance measurements and therefore an highly ill-conditioned inverse (imaging) problem. In addition, with the increasing demand for volume tomography, more challenging applications are being sought after by industry such as exploration of larger RoI with better resolutions. Therefore, these scenarios imply increased computational costs for the volumetric imaging problem and make it more difficult real-time ECVT imaging applications.In this dissertation, we introduce displacement-current phase tomography (DCPT) for process tomography. The operation principle of DCPT is based on the imaging of the imaginary part of the permittivity inside the RoI, which is complementary to real-part permittivity imaging obtained by ECT. While using the same ECT hardware, DCPT provides better resolution for certain classes of applications involving lossy media. This method is also extended to 3D volume tomography based on the use of ECVT hardware. DCPT is also extended to velocimetry applications, where the objective is to image the flow velocity in the RoI, based on ECVT hardware. Finally, a faster reconstruction approach for ECT/ECVT systems based on sparse representation of images in the Fourier domain is proposed and studied to facilitate real-time imaging for applications involving volumetric RoIs.