Radio Tomographic Imaging with Extremely Sparse and Location-Uncertain Transmitters

Radio tomographic imaging (RTI) is an imaging technique that only uses received signal strength (RSS) measurements, classically on a dense mesh of transmitter-receiver (TX-RX) pairs with precisely known positions. However, in many practical scenarios, TX locations may be uncertain due to deployment constraints, mobility, or reliance on ambient RF sources. This paper investigates RTI in an extremely sparse setting, where only a few TXs (potentially just one) with uncertain positions are available, leading to a severe reduction in the number of TX-RX links and increased reconstruction challenges. We formulate the joint image reconstruction and TX localization problem and propose both optimal and suboptimal algorithms. The suboptimal algorithm, in particular, achieves near-optimal performance while maintaining linear complexity with respect to the number of TXs, in contrast to the exponential complexity of the optimal approach. Comparative evaluations against worst-case and stochastic robust approximation methods demonstrate the superior reconstruction accuracy of our proposed techniques.