Background: With advanced design and smaller electronic components, pocket-sized ultrasound systems are becoming a useful diagnostic tool. However, the demand for higher resolution and improved image quality requires more elements in the transducer, thus increasing the associated data flow and in turn the size of the device, its battery consumption and cost. Methods: In this work, we introduce an efficient approach to the design of smaller portable ultrasound devices with enhanced image quality that may be used practically as mobile systems. A compact efficient transducer in which the beamformed signals are multiplied and processed to form an image is demonstrated and considered. Results: Our analysis shows that the beam pattern of this compact simplified transducer provides the same resolution as an array used in ordinary complex transducers that has significantly more receiving elements. For example, our tests show that two sub-arrays of 8 elements each together with associated image processing techniques to compensate for the SNR reduction, produce better imaging results than the original imaging produced by a 64-element array. The multiplicative element-reduction method is not limited to a single step and can be continued recursively until all subarrays have only 2 elements. Conclusion: The proposed input-channel reduction enables the implementation of computationally complex algorithms that were previously unrealistic for real-time ultrasound devices (Coherence Factor Multiplication, Strong Reflectors Separation as well as Short-Lag Spatial Coherence). As a result, our technique allows reduced costs and size, as well as lowering battery power consumption, while increasing image quality and resolution.