A Study of Multi-Static Ultrasonic Tomography Using Propagation and Back-Propagation Method

This paper considers a time domain ultrasonic tomographic imaging method in a multi-static configuration using the propagation and backpropagation (PBP) method. Under this imaging configuration, ultrasonic excitation signals from the sources probe the object imbedded in the surrounding medium. The scattering signals are recorded by the receivers. Starting from the nonlinear ultrasonic wave propagation equation and using the recorded time domain signals from all the receiver sensors, the object is to be reconstructed. The conventional PBP method is a modified version of the Kaczmarz method that iteratively updates the estimates of the object acoustical potential distribution within the image area. Each source takes turns to excite the acoustical field until all the sources are used. The proposed multi-static image reconstruction method utilizes a significantly reduced number of sources that are simultaneously excited. We consider two imaging scenarios with regard to source positions. In the first scenario, sources are uniformly positioned on the perimeter of the imaging area. In the second scenario, sources are randomly positioned. By numerical experiments we demonstrate that the proposed multi-static tomographic imaging method using the multiple source excitation schemes results in fast reconstruction and achieves high resolution imaging quality.