In this paper, we propose a mathematical model to estimate the sparsity degree κ of exactly κ-sparse signals acquired through Compressed Sensing (CS). Our method does not need to recover the signal to estimate its sparsity, and is based on the use of sparse sensing matrices. We exploit this model to propose a CS acquisition system where the number of measurements is calculated on-the-fly depending on the estimated signal sparsity. Experimental results on block-based CS acquisition of black and white images show that the proposed adaptive technique outperforms classical CS acquisition methods where the number of measurements is set a priori.