The automated analysis of retinal images is a widely researched area which can help to diagnose several diseases like diabetic retinopathy in early stages of the disease. More specifically, separation of vessels and lesions is very critical as features of these structures are directly related to the diagnosis and treatment process of diabetic retinopathy. The complexity of the retinal image contents especially in images with severe diabetic retinopathy makes detection of vascular structure and lesions difficult. In this paper, a novel framework based on morphological component analysis (MCA) is presented which benefits from the adaptive representations obtained via dictionary learning. In the proposed Bi-level Adaptive MCA (BAMCA), MCA is extended to locally deal with sparse representation of the retinal images at patch level whereas the decomposition process occurs globally at the image level. BAMCA method with appropriately offline learnt dictionaries is adopted to work on retinal images with severe diabetic retinopathy in order to simultaneously separate vessels and exudate lesions as diagnostically useful morphological components. To obtain the appropriate dictionaries, K-SVD dictionary learning algorithm is modified to use a gated error which guides the process toward learning the main structures of the retinal images using vessel or lesion maps. Computational efficiency of the proposed framework is also increased significantly through some improvement leading to noticeable reduction in run time. We experimentally show how effective dictionaries can be learnt which help BAMCA to successfully separate exudate and vessel components from retinal images even in severe cases of diabetic retinopathy. In this paper, in addition to visual qualitative assessment, the performance of the proposed method is quantitatively measured in the framework of vessel and exudate segmentation. The reported experimental results on public datasets demonstrate that the obtained components can be used to achieve competitive results with regard to the state-of-the-art vessel and exudate segmentation methods.