  Wireless tomography is a technique for inferring a physical environment
within a monitored region by analyzing RF signals traversed across the region.
In this paper, we consider wireless tomography in a two and higher
dimensionally structured monitored region, and propose a multi-dimensional
wireless tomography scheme based on compressed sensing to estimate a spatial
distribution of shadowing loss in the monitored region. In order to estimate
the spatial distribution, we consider two compressed sensing frameworks:
vector-based compressed sensing and tensor-based compressed sensing. When the
shadowing loss has a high spatial correlation in the monitored region, the
spatial distribution has a sparsity in its frequency domain. Existing wireless
tomography schemes are based on the vector-based compressed sensing and
estimates the distribution by utilizing the sparsity. On the other hand, the
proposed scheme is based on the tensor-based compressed sensing, which
estimates the distribution by utilizing its low-rank property. We reveal that
the tensor-based compressed sensing has a potential for highly accurate
estimation as compared with the vector-based compressed sensing.
