In this paper, we introduce a new image modeling method by getting benefit from both sparsity and multiscale characteristics of transform-domain modeling, along with the geometrical representation of the graph-based models. The proposed method is named bandlet on an oriented graph (BOG) and improves directional selectivity property of the bandlets. The conventional wavelet in the bandlet design is substituted with a new non-orthogonal wavelet. The replaced wavelet is defined on a graph. In order to adjust the orientation of the wavelet atoms with the corresponding edges in the image pixels, a directed graph is constructed. The resultant wavelets in discrete scales can be considered as a frame and are created to build a tight frame. To show the effectiveness of this new atomic representation, we demonstrated the performance of the new model in noise alleviation of the optical coherence tomography (OCT) images (from the retina) and microscopic images. Denoising results on OCT are reported on 72 slices, selected arbitrarily out of OCT dataset from Topcon device. The combined method provided an enhancement of contrast to noise ratio (CNR) (from 27.82 to 30.11), and improvement of the equivalent number of looks (ENL) (from 2183.26 to 2217.37) over the state-of-the-art in OCT noise reduction. In the denoising of microscopic images, PSNR improvement (from 26.33 to 35.24) over the original image is shown along with the improvement in next steps of feature extraction.