Reconstruction of compressed samples in shift-invariant space base on matrix factorization

According to the model of compressed sampling in shift-invariant space, the over-complete dictionary is usually a function matrix, which increases the complexity of reconstructing samples. In order to reduce the complexity of reconstructing samples, this paper proposes a reconstruction method based on matrix factorization. The method transforms over-complete dictionary into the multiplication of a reversible function matrix and a constant matrix using least squares error, and converts the samples reconstruction into the computing of constant matrix, which reduces the complexity of samples reconstruction. Meanwhile, the feasibility and convergence of method is analyzed in theory. Finally, the convergence and reconstruction error of the method is validated by simulation; and it is shown that the method is effective.