Abstract:

The existing reconstruction algorithms in compressed sensing (CS) theory commonly cost too much time. A novel reconstruction algorithm based on inner product optimization is proposed to reduce reconstruction time. And also stopping criterion is derived from theory. The proposed algorithm computes the inner product of measurement matrix and the residual only in the first iteration during the reconstruction process. In the remaining iterations, the inner product of vectors instead of matrices is calculated. Then least square calculation is done only once to reconstruct the signal after iterations stopped. Experiments show that the proposed algorithm reduces the reconstruction time largely without degrading the quality of the signal.

Key words: inner product optimization, compressed sensing, reconstruction algorithm