<p>This paper proposes a two dimensional (2D) fractional singular spectrum analysis (2DFSSA) based method for performing image interpolation. First, the low-resolution image is truncated in three different directions and the corresponding delayed matrix in each direction is generated. Second, the trajectory matrices of both the truncated image and the delayed matrix in each direction are constructed. Third, the singular value decomposition (SVD) is performed on each trajectory matrix. Fourth, the designs of both the left unitary matrix and the right unitary matrix of a new trajectory matrix corresponding to the fractional delay of the low-resolution image in each direction are formulated as quadratically constrained quadratic programming problems. After finding the solution to the optimization problem via the SVD approach and performing the diagonal averaging operation, the 2DFSSA components are obtained. Finally, the selected components are used for performing the image interpolation. Since the 2DFSSA operations are nonlinear and adaptive, our proposed method is a kind of nonlinear and adaptive approach for performing image interpolation. Besides, by discarding some of these 2DFSSA components, the joint image interpolation and image denoising can be performed simultaneously.</p>