A new theory is proposed for the reconstruction of curl-free vector field, whose divergence serves as acoustic source. The theory is applied to reconstruct vector acoustic sources from the scalar acoustic signals measured on a surface enclosing the source area. It is shown that, under certain conditions, the scalar acoustic measurements can be vectorized according to the known measurement geometry and subsequently be used to reconstruct the original vector field. Theoretically, this method extends the application domain of the existing acoustic reciprocity principle from a scalar field to a vector field, indicating that the stimulating vectorial source and the transmitted acoustic pressure vector (acoustic pressure vectorized according to certain measurement geometry) are interchangeable. Computer simulation studies were conducted to evaluate the proposed theory, and the numerical results suggest that reconstruction of a vector field using the proposed theory is not sensitive to variation in the detecting distance. The present theory may be applied to magnetoacoustic tomography with magnetic induction (MAT-MI) for reconstructing current distribution from acoustic measurements. A simulation on MAT-MI shows that, compared to existing methods, the present method can give an accurate estimation on the source current distribution and a better conductivity reconstruction.
Bibliographical noteFunding Information:
Manuscript received September 29, 2008; revised October 20, 2008. First published February 10, 2009; current version published April 29, 2009. This work was supported in part by the National Institutes of Health (NIH) under Grant R21EB006070, Grant R01EB007920, and Grant R01HL080093, and in part by the National Science Foundation (NSF) under Grant BES-0602957. Asterisk indicates corresponding author.
- Current density imaging
- Electrical impedance imaging
- Magnetoacoustic imaging