The weak-$\ell^p$ norm can be used to define a measure $s$ of sparsity. When we compute $s$ for the discrete cosine transform coefficients of a signal, the value of $s$ is related to the information content of said signal. We use this value of $s$ to define a reference-free index $\mathcal{E}$, called the sparsity index, that we can use to predict with high accuracy the quality of signal reconstruction in the setting of compressed sensing imaging. That way, when compressed sensing is framed in the context of sampling theory, we can use $\mathcal{E}$ to decide when to further partition the sampling space and increase the sampling rate to optimize the recovery of an image when we use compressed sensing techniques.