A hierarchical algorithm for nearfield acoustic imaging

This paper presents a computationally efficient hierarchical nearfield imaging algorithm using a delay and sum beamformer with a random array via pulse-echo techniques. In the conventional imaging of nearfield sources, signals from multiple sensors are delayed and summed to focus at points in the imaging volume. However, the computational burden of implementing the conventional algorithm for arrays with a large number of receivers, due to the distance calculations, requires new suboptimal algorithms. The algorithm described in this paper reduced computational time balanced against a reasonable memory requirement. The key principle of this algorithm is to implement the delay and sum by grouping receivers into various subarrays in a number of stages. Mirroring the hierarchy of subarrays is a decomposition of imaging volume beginning with large voxels and progressively reducing the voxel size. This algorithm introduces two main changes to the conventional algorithm which are (i) subsampling of the received data, which is then compensated by phase interpolations, (ii) a hierarchy of subarrays and subvolumes to combine the data from all the receivers. Comparison of the conventional and the hierarchical algorithms are done in terms of their point spread functions.