Singular Value Decomposition of Images of Structural Textures and Their Reconstruction using Periodicity

Abstract

Singular Value Decomposition (SVD) based image compression involves decomposition of an image into several subspace images of different details and reconstruction of an approximate image using initial few subspace images. In this paper, a periodicity-based approach is presented for effectively reconstructing images of structural textures that are decomposed using SVD. It is proved that irrespective of the size of the input image of a structural texture, the number of subspace images required for reconstruction of the approximate image (low-rank image) is equal to texture-periodicity itself. Effectiveness of the present approach is demonstrated using experiments on various real-world natural images with the help of performance parameters such as energy ratio between the reconstructed image and the original image, root mean square error, universal image quality index and compression ratio.