Low-resolution image restoration using the combination method of sparse representation and PDE model

Abstract

The stable solutions of traditional partial differential equations (PDE) can cause obvious step effects when PDEs are utilized to restore low-resolution images, and the quality of images restored is hardly worse. To solve this problem above-mentioned, a new low-resolution image restoration method, based on the combination method of sparse representation and PDE model based on an enhanced total variation model (ETVM), is proposed in this paper. The dictionary of sparse representation of images is learned by using the K-means based singular value decomposition (K-SVD) algorithm. For images with large noise variance or low-resolution, K-SVD has better denoising robustness. The guiding ideology of low-resolution image restoration is that the K-SVD algorithm is used first to reduce unknown noise existed in low-resolution images, and then the PDE model based on total variation (TV) are utilized to restore the results denoised obtained by K-SVD. In test, a human-made and a real low-resolution image, called millimeter wave (MMW) image, are respectively used to testify our method proposed. Further, compared it with algorithms of K-SVD and PDE, at the same time, the pick signal noise ratio (PSNR) criterion is used to measure restored human-made low-resolution images. Considering different noise variance for a human-made low-resolution image, and in terms of PSNR values and the vision effect of restored images, simulation results show that our method proposed here can efficiently restore low-resolution images, and behave certain theory meaning and practicality. © 2013 Springer-Verlag.