This paper addresses mathematical modelling for a hard-field tomography application, in which forward and inverse problems are discussed in detail in terms of the projection modelling and image reconstruction algorithm. The forward modelling of the ultrasonic prototype system is discussed to predict the sensor output for constructing cross-sectional images. Besides that, this paper also discusses the image algorithms to solve the inverse problem for tomogram reconstruction. Event-driven software applications were designed as the solutions to both forward and inverse problems. The applications are discussed with the supporting programming flow charts. Simulations were performed in forward and inverse applications respectively, and results were analysed using an image quality assessment technique called the Mean Structural Similarity Index, MSSIM. The results which indicated high MSSIM ( > 90%) in image analysis concluded that the designed forward and inverse modelling applications can be deployed in real-time systems.
