Displaying high-quality images on edge devices, such as augmented reality devices, is essential for enhancing the user experience. However, these devices often face power consumption and computing resource limitations, making it challenging to apply many deep learning-based image compression algorithms in this field. Implicit Neural Representation (INR) for image compression is an emerging technology that offers two key benefits compared to cutting-edge autoencoder models: low computational complexity and parameter-free decoding. It also outperforms many traditional and early neural compression methods in terms of quality. In this study, we introduce a new Mixed AutoRegressive Model (MARM) to significantly reduce the decoding time for the current INR codec, along with a new synthesis network to enhance reconstruction quality. MARM includes our proposed AutoRegressive Upsampler (ARU) blocks, which are highly computationally efficient, and ARM from previous work to balance decoding time and reconstruction quality. We also propose enhancing ARU's performance using a checkerboard two-stage decoding strategy. Moreover, the ratio of different modules can be adjusted to maintain a balance between quality and speed. Comprehensive experiments demonstrate that our method significantly improves computational efficiency while preserving image quality. With different parameter settings, our method can achieve over a magnitude acceleration in decoding time without industrial level optimization, or achieve state-of-the-art reconstruction quality compared with other INR codecs. To the best of our knowledge, our method is the first INR-based codec comparable with Hyperprior in both decoding speed and quality while maintaining low complexity.