Rapid measurement of ultrasound transducer fields in water employing compressive sensing

The quantitative measurement of acoustic pressure fields in fluids is of crucial interest for the design of medical ultrasound transducers. A new measurement technique for the radiated ultrasound beams using the concept of compressive sensing is introduced. In this approach, a regular grid is defined on a plane oriented perpendicular to the preferred direction of the sound beam. Waveforms are measured at random positions on this grid and are decomposed into their frequency components. The frequency components of missing waveforms in this grid can then be reconstructed exploiting the compressibility of the associated angular spectra. The feasibility of our concept is demonstrated by experiments in a water reservoir with a spherically focused circular single element transducer. Using two different excitation voltages and only 25 % of the recommended number of measurements in literature, the original sound fields could be reconstructed with relative mean squared errors (MSEs) of 11.4 % and 6.86 %, respectively. The relative MSEs obtained by a standard interpolation method were 12.68 % and 7.05 % in these cases.