Sparse representation based super resolution deals with the problem of reconstructing a high resolution image from one or several of its low resolution counterparts. In this case the low resolution image is modelled as the down-sampled version of its high resolution counterpart after blurring. When the blurring kernel is the Dirac delta function, i.e. the low resolution image is directly down sampled from its high resolution counterpart without blurring and the super-resolution problem becomes an image interpolation problem. In such cases, the conventional sparse representation models become less effective, because the data fidelity term fails to constrain the image local structures. In natural images, the given image patch can be modelled as the linear combination of nonlocal similar neighbours. In this paper image nonlocal self-similarity for image interpolation is introduced. More specifically, wavelet based a nonlocal autoregressive model (NARM) is proposed and taken as the data fidelity term in sparse representation model. Our experimental results on benchmark test images clearly demonstrate that the proposed wavelet-NARM based image interpolation method outperforms the reconstruction of edge structures and suppression of jaggy/ringing artefacts, achieving the best image interpolation results so far in terms of PSNR as well as perceptual quality metrics such as structural similarity index and structural content. The proposed method is applied on bio medical images to emphasis on diagnostic information.