This disclosure relates to systems and methods for solving generic inverse problems by providing a coupled representation architecture using transform learning. Convention solutions are complex, require long training and testing times, reconstruction quality also may not be suitable for all applications. Furthermore, they preclude application to real-time scenarios due to the mentioned inherent lacunae. The methods provided herein require involve very low computational complexity with a need for only three matrix-vector products, and requires very short training and testing times, which makes it applicable for real-time applications. Unlike the conventional learning architectures using inductive approaches, the CASC of the present disclosure can learn directly from the source domain and the number of features in a source domain may not be necessarily equal to the number of features in a target domain.