Robust Structured Sparsity-Based Fused Lasso Estimator With Sensor Position Uncertainty

In radio tomographic imaging (RTI), targets induce attenuation of radio waves and cause shadowing of radio links. The radio maps generated due to shadowing phenomena are known as spatial loss fields (SLFs). One of the concerns for SLF estimation is improvement in sparsity. Furthermore, the improvement of sparsity in estimated SLF becomes challenging with uncertain sensor position information. This problem is handled by the stochastic robust approximation (SRA) technique using
$\boldsymbol {l}_{1}$
-norm, i.e.,
$\boldsymbol {l}_{1}$
-SRA. However, the
$\boldsymbol {l}_{1}$
-SRA cannot simultaneously enhance the sparsity and smoothness features of the SLF. To handle such a scenario, a robust fused lasso
$(\mathbf {FL})$
-based SRA technique, i.e.,
$\mathbf {FL}$
-SRA, is proposed in this brief. However, the proposed
$\mathbf {FL}$
-SRA estimator has a higher computational cost, which is quadratic with the number of pixels. Therefore, in the second part of this brief, a support vector regression (SVR)-based estimator with sensor position uncertainty,
$\mathbf {UFL}$
-SVR, is proposed.
$\mathbf {UFL}$
-SVR has a lower computational cost than
$\mathbf {FL}$
-SRA, whose cost is quadratic with the number of links. The results of
$\mathbf {FL}$
-SRA and
$\mathbf {UFL}$
-SVR are compared to verify the findings.