Enhancing low resolution images via super-resolution or image synthesis for cross-resolution face recognition has been well studied. Several image processing and machine learning paradigms have been explored for addressing the same. In this research, we propose Synthesis via Deep Sparse Representation algorithm for synthesizing a high resolution face image from a low resolution input image. The proposed algorithm learns multi-level sparse representation for both high and low resolution gallery images, along with an identity aware dictionary and a transformation function between the two representations for face identification scenarios. With low resolution test data as input, the high resolution test image is synthesized using the identity aware dictionary and transformation which is then used for face recognition. The performance of the proposed SDSR algorithm is evaluated on four databases, including one real world dataset. Experimental results and comparison with existing seven algorithms demonstrate the efficacy of the proposed algorithm in terms of both face identification and image quality measures.