If the behavior of signal $x$ was known, it would be easy to determine the optimal dictionary. However, the aim is to measure this signal, i.e., derive this knowledge. This is ultimately the limitation of using the basis set as the projection matrix, which is the case when using Hadamard patterns, and requires a way of incorporating nonbinary dictionaries to be developed. The sampling of signal $x$ can be considered using an $M\xd7N$ projection matrix $\varphi $, which generates a series of voltages $y$, i.e., $y=\varphi x$. This can be rewritten as $y=\varphi \psi c$ and we can now describe the PV as a simple linear equation $y=\theta c$, in terms of a measurement matrix $\theta =\varphi \psi $, and a series of sparse coefficients $c$. By probing the PV sample with binary sampling patterns $\varphi $, the original signal $x$ can be determined by performing compressed sensing in the transformed domain of the dictionary $\psi $. The matrix $\theta $ is an $M\xd7N$ matrix, which allows all rows of the dictionary to be addressed by an incomplete series of measurements and thus avoids the dilemma produced using Hadamard mapping, where exclusion of important measurements may occur through lack of prior knowledge.