A Sequential Down-Sampling Algorithm for Super-Sparse Signal Recovery

When we recovering a sparse signal with the traditional sparse recovery (SR) algorithms, the number of measurements seems to be too large and can be reduced if there is only extremely limited number of nonzero components, i.e. the signal is super-sparse. Down-sampling matrices are built and a sequential down-sampling (SD) algorithm was proposed. The super-sparse signal can be exactly recovered with fewer measurements after sequential observations and reconstructions. The number of measurements is analyzed when reconstructing the super-sparse signal with the proposed SD algorithm and orthogonal matching pursuit (OMP) algorithm, i.e. the SD-OMP algorithm. Experimental results indicate that the proposed SD-OMP requires fewer measurements than OMP when recovering a super-sparse signal.