Extraction of patterns from images using a model of combined frequency localization spaces

Abstract

An algorithm for image decomposition and separation of superposed stationary contributions is proposed. It is based on the concept of sparse-to-sparse domain representation achieved through a relationship between block-based and full-size discrete cosine transform. The L-statistics is adapted to discard nonstationary components from the frequency domain vectors, leaving just a few coefficients associated with stationary pattern. These fewer stationary components are then used under the compressive sensing framework to reconstruct the stationary pattern. The original image is observed as a nonstationary component, acting as a non-desired part at this stage of the procedure, while the stationary pattern is observed as a “desired part” that should be extracted through the reconstruction process. The problem of interest is formulated as underdetermined system of equations resulting from a relationship between the two considered transformation spaces. Once the stationary pattern is reconstructed, it can be removed entirely from the image. Furthermore, it will be shown that the efficiency of pattern extraction cannot be affected, even when image contains additional nonstationary disturbance (here, the noisy image is observed as nonstationary undesired part). The proposed approach is motivated by challenges in removing Moiré-like patterns from images, enabling some interesting applications, including extraction of hidden sinusoidal signatures.