The objective of this research is to provide support for the instrumentation concept of a High Resolution Capacitance Imaging System (HRCIS). The work involves the development and evaluation of the mathematical theory and associated models and algorithms which reduce the electronic measurements to valid physical characterizations. The research and development require the investigation of techniques to solve large systems of equations based on capacitance measurements for various electrode configurations in order to estimate densities of materials in a cross-section of a fluidized bed. Capacitance measurements are made for 400 connections of the 32-electrode system; 400 corresponding electric-field curves are constructed by solving a second order partial differential equation. These curves are used to partition the circular disk into 193 regions called pixels, and the density of material in each pixel is to be estimated. Two methods of approximating densities have been developed and consideration of a third method has been initiated. One method (Method 1) is based on products of displacement currents for intersecting electric-field curves on a cross section. For each pixel one point of intersection is chosen, and the product of the capacitance measurements is found. Both the product and the square-root-of-product seem to yield good relative distribution of densities.