This paper proposes a joint two dimensional (2D) singular spectrum analysis (SSA) with the generalized singular value decomposition (GSVD) and the binary linear programming based method for performing the super-resolution. For a given low resolution image, first both the upsampling operation and a lowpass filtering are applied on each column of the image to obtain an enlarged image. Second, apply the 2D Hankelization to both the low resolution image and the enlarged image to obtain their corresponding trajectory matrices. Third, both the GSVD and the 2D de-Hankelization are applied to these two trajectory matrices to obtain their corresponding sets of the de-Hankelized 2D SSA components. Here, it is proved that the exact perfect reconstruction is achieved. In order to enhance the high frequency contents of the enlarged image, the selection of the de-Hankelized 2D SSA components is formulated as a binary linear programming problem. Computer numerical simulation results show that the proposed method outperforms the state of art methods.