Algorithm 2: Data Aggregation Using Compressed Sensing Theory

Input: Sensor data $d$ = {$d$1, $d$2,…, $d$n}

Output: Compressed data y

1:Compute the data aggregation fromPN1 to DODAG root

$y_1={\displaystyle \sum }_{i=1}^k{r}_{1i}\times d_i$

2:Compute the data aggregation in DODAG root from the M paths

$\left[\begin{array}{c}{y}_1\\ y_2\\ .\\ .\\ y_M\end{array}\right]=\left[\begin{array}{ccccc}{r}_{11}& r_{12}& ..& ..& r_{1N}\\ r_{21}& r_{22}& ..& ..& r_{2N}\\ .& .& ..& ..& .\\ .& .& ..& ..& .\\ r_{M1}& r_{M2}& ..& ..& r_{MN}\end{array}\right]\left[\begin{array}{c}{d}_1\\ d_2\\ .\\ .\\ d_N\end{array}\right]$

3: Return the aggregated data y.