Compressive sensing (CS) has recently gained a lot of attention in the domains of applied mathematics, computer science, and electrical engineering by offering compression of data below the Nyquist rate. The particle swarm optimization (PSO) reconstruction algorithm is considered one of the most widely used evolutionary optimization techniques in CS. The self-tuned PSO parameters control can greatly improve its performance. In this paper, we propose a self-tuned PSO parameter control based on a sigmoid function in the CS framework. In the proposed approach, PSO parameters are adjusted by the evaluation at each iteration. The proposed self-tuned PSO parameter control approach involves two PSO parameters. First, acceleration coefficients, which are considered very effective parameters in enhancing the performance of the algorithm, second, inertia weight, which is used to accelerate the movement of particles towards the optimum point or slow down the particles so that they converge to the optimum. In contrast to conventional PSO, the proposed self-tuned PSO parameters control algorithm governs the convergence rate, resulting in a fast convergence to an optimal solution and very precise recovery of the original signal. A simulation study validates the effectiveness of the proposed method as compared to the conventional PSO algorithm.