Latest research papers on ultrasound tomography feature a new way of performing the scanning procedure that is similar to computed tomography. The underlying work of computed tomography consists of scanning thin slices with a rotating narrow X-ray beam. Usually, one needs a large number of projections for many different angles to reconstruct an image. In this work, we consider the application of the compressive sensing framework together with randomization to arrange an economy representation of the ultrasound diagnostics data without essential loss of performance. Using this approach, we will be able to randomly select the angles of scanning instead of obtaining all possible projections. We start with a brief overview of ultrasound tomography techniques, after that we formulate the problem of our interest, and provide the appropriate decision with results of preliminary computer simulations.