<p>Perfect signal recovery is one of the oldest and most challenging problems in science. Many attempts have been made to conquer the challenges associated with the perfect recovery of signals. Compressive sensing is one such technique that has gained much attention as it allows us to break the bounds of the Nyquist–Shannon sampling theorem. Mathematically, it is possible to achieve perfect signal recovery using the compressive sensing theory. One of the main challenges in compressive sensing is the construction of the sensing matrix, which arises due to the formulation of the system as an underdetermined linear system of equations. Essentially, solving a compressive sensing problem is equivalent to solving an ill-posed problem. In this setup, the sensing matrix plays a vital role in the success of the compressive sensing method. In this paper, two different approaches have been proposed to design a sensing matrix. The first approach is pseudo-random, which is unique in its use of the desirable properties of random matrices and is computationally efficient compared to the existing methods. The second is the deterministic approach. Simulation results have shown a significant improvement for both approaches compared to the existing and well-known methods in the literature.</p>