Salt and pepper noise removal method based on graph signal reconstruction

Salt and Pepper (SAP) noise is a very common type of impulse noise which frequently arises in image acquisition and transmission. Removing SAP noise is an important task in image restoration. In this paper, we model the SAP removal problem as a graph signal reconstruction problem, so that the information of noisy pixels can also participate in the estimation of their gray values. In the proposed model, the regularization term depends on the Power Spectral Density (PSD) of original signals, which makes the reconstructed signal follows the frequency content of the potential original signal well. Further, an algorithm for estimating the local PSD of an image block is designed and corresponding theoretical analysis is given. Finally, a block SAP noise removal algorithm is proposed. The computational complexity is also discussed. Experimental results on ten commonly used test images demonstrate that the proposed algorithm outperforms the state-of-the-art methods.