This work generalizes an existing framework of nonseparable oversampled lapped transforms (NSOLTs) to effectively represent complex-valued images. The original NSOLTs are lattice-structure-based redundant transforms, which satisfy the linear-phase, compact-supported and real-valued property. The lattice structure is able to constitute a Parseval tight frame with rational redundancy and to generate a dictionary with directional atomic images. In this study, a generalized structure of NSOLTs is proposed to cover complex-valued atomic images. The novel transform is referred to as a complex NSOLT (CNSOLT). The effectiveness of the structure is verified by evaluating the sparse approximation performance using the iterative hard thresholding (IHT) algorithm for a millimeter wave radar image.