Greedy steep slope finder: The fast impulsive noise rejection for compressed measurement image signals

Impulsive noise in a compressed measurement signal can be detected by the energy distribution of the reconstructed sparse signal. In this paper, the fast preprocessing for impulsive noise rejection for a compressed measurement image signal is proposed. An image is sparsified by octave-tree wavelet transform with db8 as the mother wavelet. The impulsive noise is detected via the change in the ratio of the energy leaking out of the third level subband to the total energy of the sparse signal. Since the information in the image is redundant, the number of the noisy element is estimated within +g of the actual value. g is defined in the unit of the percent of the size of the compressed measurement signal. The experiment shows that the proposed method effectively rejected noise with large magnitude. It provided the comparable performance to the method that rejected the exact number of noisy elements but required less computational time.