Signal Processing for Microwave Array Imaging: TDC and Sparse Recovery

Unlike 1-D and 2-D microwave images, 3-D microwave image behaves typical sparsity. Consequently, sparse recovery technique can be used for 3-D microwave signal processing. Three popular signal processing techniques, the time-domain correlation method (TDC), pseudo-inverse method (PI), and compressed sensing method (CS), are discussed in this paper. We find that PI and CS methods can eliminate the side-lobe coupling error of TDC method with the cost of additional noise gains. The performances of TDC, PI, and CS methods are influenced by the autocorrelation matrix of the measurement matrix, which is determined by the distribution of the sparse array and the number of receivers. In general case, the measurement matrix of microwave 3-D imaging cannot be considered as a group of independent identically distributed (i.i.d.) random variables with zero mean. As a result, many properties developed under the i.i.d. Gauss random variable and i.i.d. random variable with zero mean hypotheses cannot explain the microwave 3-D imaging problem accurately. Further discussions on the effects of the image sparsity and number of receivers on TDC, PI, and CS methods are presented in this paper. In usual case, the sparser the image is, the better the imaging result is. In the aspect of the number of receivers (assuming that array size is fixed), when the receiver number is relatively small, increasing it can reduce the coupling error of TDC method and the noise gains of PI and CS methods. When the number of receivers is large enough, increasing it makes less contribution to improving the coupling error or noise gains. Finally, we show that under ill condition, CS method is far more stable than PI method by numerical experiment.