Sampling Design of Synthetic Volume Arrays for Three-Dimensional Microwave Imaging

In this paper, sampling design of three-dimensional (3-D) synthetic array (i.e., synthetic volume array) for microwave imaging is considered. Generally, the spatial sampling criteria for one- or two-dimensional arrays can be determined based on some narrowband/ultrawideband array theories. However, for 3-D arrays, where antennas are located in a volume instead of over a surface, these existing array theories are no longer straightforwardly applicable. To address the spatial sampling problem of 3-D arrays, we formulate it as a sensor/observation selection problem in this paper. Although some selection approaches exist and are conveniently applicable to small-scale problems, they are either less efficient or provide less optimal results for selection problems with data dimensions of hundreds or even thousands which is typical for microwave imaging. To get the (near-) optimal spatial sampling scheme for 3-D arrays, a greedy algorithm named clustered maximal projection on minimal eigenspace (CMPME) is proposed to select the most informative sampling positions based on some optimality criteria. This algorithm attempts to select the fewest sampling positions by considering an error threshold for the estimated images. Moreover, it has higher computational efficiency compared to the existing approaches. Finally, its effectiveness and selection performances are demonstrated through some imaging examples.