Frequency spectrum regularization for pattern noise removal based on image decomposition

This paper deals with a mixed norm of complex vectors, i.e., the sum of amplitude spectra, and its minimization problem. A combination of this mixed norm and image decomposition problem works well for reduction and decomposition of pattern noise that arises when scanning old photographs with granulated surface. Generally, the spectral distribution of natural images decreases smoothly from low frequency band toward high frequency band, while that of pattern noise is distributed sparsely. Therefore, we assume that an observed image consists of a latent image component and a pattern noise component, and characterize them by using the total variation function and the proposed function, respectively. This enables a reasonable decomposition of the two components. Compared to similar decomposition methods such as Robust PCA, our method has a good decomposition accuracy for this task, and low computational cost.