Model for sparse sources

In order to model sources with different degrees of sparsity we consider the probability density function (pdf)

$$p_{S_i}(s_i) = p_i\delta(s_i) + (1-p_i)f_{S_i}(s_i),\quad i=1,\dots,n;$$ (1)

where $p_i$ is the probability that a source is inactive, $\delta(\cdot)$ denotes Dirac's delta and $f_{S_i}(s_i)$ is the pdf of the $i$-th source when it is active [8].