Projection matrix design for compressive sensing

The mechanism of linear projections of the signal into a projection matrix to acquire the signal directly in already compressed form is well known as Compressive sensing (CS). In CS, the multiplication between projection matrix and sparsifying dictionary which is used to represent the signal is called equivalent dictionary. The equivalent dictionary plays an important role in designing an optimal projection matrix. The commonly used method to optimize projection matrix is minimizing the coherence between the columns of the equivalent dictionary. This paper proposes the optimal design of projection matrix for CS system by making the Gram matrix of equivalent dictionary close to identity matrix. This approach will result a set of solutions where alternating projection based on tight frames and iterative shrinkage method is used to find the optimum solution. The experimental results show that the projection matrix obtained by the proposed method improves the performance of CS System in terms of signal reconstruction accuracy and outperforms the previous methods.