Digital Reconstruction of Acoustic Holograms in the Space Domain with a Vector Space Approximation
We have developed a computer-assisted ultrasonic underwater imaging system. Until recently, we used back-propagation to reconstruct images. This method, accurate both in the near and far fields of the object, is an inverse filtering technique that operates in the spatial frequency domain and requires the taking of two Discrete Fourier transforms (DFT’s).
Here, we present a method based on back-projection, an alternative reconstruction technique which operates in the space domain and reconstructs images without any DFT’s. Back-projection is computationally as fast as a single DFT, and it is accurate in both the near and far fields. This new algorithm works because the spatial propagation of a point-source is known, and any object is a linear combination of point-sources. We, therefore, can construct a spatial propagation matrix which maps the object-wave field into a field at the receiver plane. To use the received data to obtain the object wave field requires the inverse matrix. The back-projection algorithm applies an approximation technique from vector-space algebra to estimate the inverse matrix and reconstruct an acceptable image of an unknown object.
We not only present computer simulations which demonstrate the feasibility of back-projection, but we also use a modified version of the above algorithm to correct simulated data that has been degraded by motion of the object during data acquisition. Results from simulated data are compared with those from experimental data.
KeywordsDiscrete Fourier Transform Motion Correction Space Domain Inverse Filter Array Position
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