Most learning-based super-resolution algorithms neglect the illumination problem such as shadows and illumination direction changes. In this paper we propose a logarithmic-wavelet transform (Log-WT) based method to combine super-resolution and shadow removing into a single operation. First intrinsic, illumination invariant features of the image are extracted by exploiting logarithmic-wavelet transform. Then an initial estimation of high resolution image is obtained based on the assumption that small patches in low resolution space and patches in high resolution space share the similar local manifold structure. Finally the target high resolution image is reconstructed by applying the reconstruction constraints in pixel domain. Experimental results demonstrate that the proposed method simultaneously achieves singleimage super-resolution and image enhancement especially shadow removing.