Accelerated MRI involves a trade-off between sampling sufficiency and acquisition time. Although supervised and self-supervised deep learning approaches have shown promise in reconstructing under-sampled MR images, they typically rely on large-scale training datasets. This dependence increases the risk of overfitting and hallucinated features, particularly when training data diverges from test-time distributions. In this paper, we propose PixelINR, a scan-specific, self-supervised reconstruction method based on implicit neural representations (INR) that requires only a single under-sampled scan for training. By eliminating the need for external training databases, scan-specific PixelINR mitigates hallucination risks and improves generalization to diverse acquisition settings. To further enhance image quality, we incorporate anti-blurriness regularization in the image domain and a frequency-domain inpainting loss, guiding the model to recover sharp structures and plausible k-space content. Experimental results demonstrate that PixelINR outperforms existing scan-specific approaches in both reconstruction accuracy and robustness.