Compressed Sensing Performance of Random Bernoulli Matrices with High Compression Ratio

This letter studies the sensing performance of random Bernoulli matrices with column size $n$ much larger than row size $m$. It is observed that as the compression ratio $n/m$ increases, this kind of matrices tends to present a performance floor regarding the guaranteed signal sparsity. The performance floor is effectively estimated with the formula ${1 \over 2}(\sqrt {\pi m/2} + 1)$. To the best of our knowledge, it is the first time in compressed sensing, a theoretical estimation is successfully proposed to reflect the real performance.