The application of Compressive Sampling (CS) in the medical ultrasound has been widely studied in recent years with the growing requirement of reconstructing high-quality images with smaller data size. Most of the current studies with successful CS reconstruction are mainly focusing on the mathematical applications of CS theory in ultrasound imaging. However, the randomized mechanisms in these studies are hard to be fully fulfilled in hardware. In addition, some of the studies try to discover the sparse representation of signals by ignoring a part of information rather than compressing all data. We propose a new compression scheme for fast image acquisition in ultrasound imaging using a method, which is similar in style to CS. Our scheme is based on the formulation of an inverse scattering problem (ISP), where the Born approximation have been used during its derivation. In our system, the ultrasound image are represented by a collection of hypothetical points, what can be called pixels. These points are identified by their unique spatial impulse responses relative to the elements in the transducer. The randomized linear combinations of the spatial impulse responses from the view of elements can be maintained the uniquenesses of these points, which is similar to the coding techniques in data compression. Hence, our compression scheme can be more controllable than the conventional CS, which can achieve the real-time compression of data during the acquisition stage in hardware. We employ L2-regularization to solve the ill-posed ISP rather than the L1-regularization CS since there is no any assumption of signal sparsity. In our work, we finally achieve the acceptable reconstructions by compressing the raw data to 12.5% of its original size. The results are better than 12.5% with multiplexing the received signals from 12.5% elements in the array and almost as good as 25% with multiplexing the received signals from 25% elements in the array.