Optical proximity correction (OPC) is an extensively used resolution enhancement technique (RET) in optical lithography. To date, the computational efficiency has become a big issue for pixelated OPC techniques due to the increasing complexity of lithographic masks in modern integrated circuits. This paper is the first to apply nonlinear compressive sensing (CS) theory to break through the computational efficiency of gradient-based pixelated OPC methods. The proposed method reduces the dimensionality of the OPC problem by downsampling the layout pattern. Then, a nonlinear cost function is established to guarantee the lithography imaging performance on the downsampled layout. Under the sparsity assumption of the mask, the OPC problem is formulated as an inverse nonlinear CS reconstruction problem. The iterative hard thresholding (IHT) algorithm is then used to solve for the OPC problem. The proposed method proves to improve the computational efficiency of traditional gradient-based OPC methods, while improving the process windows of the lithography systems. Benefiting from the sparse property of the mask patterns, the mask manufacturability can also be improved compared to traditional methods.