We propose a practical approach to JPEG image decoding, utilizing a local implicit neural representation with continuous cosine formulation. The JPEG algorithm significantly quantizes discrete cosine transform (DCT) spectra to achieve a high compression rate, inevitably resulting in quality degradation while encoding an image. We have designed a continuous cosine spectrum estimator to address the quality degradation issue that restores the distorted spectrum. By leveraging local DCT formulations, our network has the privilege to exploit dequantization and upsampling simultaneously. Our proposed model enables decoding compressed images directly across different quality factors using a single pre-trained model without relying on a conventional JPEG decoder. As a result, our proposed network achieves state-of-the-art performance in flexible color image JPEG artifact removal tasks. Our source code is available at https://github.com/WooKyoungHan/JDEC