Truncated singular value decomposition for through-the-wall microwave imaging application

We considered differential through-the-wall microwave imaging with different formulations of truncated singular value decomposition (TSVD) method with a non-anechoic experiment. Previous studies employ TSVD with single transmitting/ measuring antenna, while we show how to apply the TSVD in case of a moving linear transmitting/measuring antenna array. Particularly, an averaging scheme is employed for repeated measurements. Three TSVD approaches are tested: (i) TSVD on Contrast Source, (ii) TSVD on Contrast, (iii) multi frequency TSVD on Contrast. For (i), the dimension of inverted matrix is relatively low. After solving equations, a normalisation is proposed for eliminating noise. For (ii), the reconstructions get better compared to (i) since measured data for all excitations are inverted simultaneously. Nevertheless, (ii) requires more time than (i), since the inverted matrix gets larger. Finally, for (iii), to avoid additional calibration, we employ the solutions of (ii). Then, the contrasts are estimated for all frequencies and excitations simultaneously. Thus, the inverted matrix is largest for (iii), accuracy is best, computational time is longest. For testing proposed techniques, a metallic scatterer is deployed behind a wall. Results show trade-off between accuracy and computational time for choosing the suitable inversion method. Moreover, norm type selection is assessed for each method.