Image super resolution via combination of two dimensional quaternion valued singular spectrum analysis based denoising, empirical mode decomposition based denoising and discrete cosine transform based denoising methods

Abstract

This paper formulates the image super resolution problem as various denoising problems. In particular, the discrete cosine transform zero padding approach is used to generate an initial high resolution image. Then, three different time frequency analysis based denoising methods are applied iteratively to improve the quality of the super resolution image. In particular, the two dimensional quaternion valued singular spectrum analysis (2DQSSA) based denoising method, the empirical mode decomposition (EMD) based denoising method and the discrete cosine transform based denoised method are applied. For the 2DQSSA based denoising method, the luminance plane is used as the real part of the quaternion valued image. Since different color planes in the quaternion valued image are fused together via the quaternion valued operation, some high frequency information missing in one color plane can be generated using those in other color planes. On the other hand, for the EMD based denoising method, the selection of the intrinsic mode functions (IMFs) is formulated as a binary linear programming problem. Here, the high frequency components generated by the aliasing are removed by discarding some IMFs. The computer numerical simulation results show that our proposed method can achieve the super resolution performance better than those without performing any one of the above three time frequency analysis based denoising.