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Rescaling digital images for display on various devices, while simultaneously removing noise, has increasingly become a focus of attention. However, limited research has been done on a unified framework that can efficiently perform both tasks. In response, we propose INDIRECT (INvertible and Discrete noisy Image Rescaling with Enhancement from Case-dependent Textures), a novel method designed to address image denoising and rescaling jointly. INDIRECT leverages a jointly optimized framework to produce clean and visually appealing images using a lightweight model. It employs a discrete invertible network, DDR-Net, to perform rescaling and denoising through its reversible operations, efficiently mitigating the quantization errors typically encountered during downscaling. Subsequently, the Case-dependent Texture Module (CTM) is introduced to estimate missing high-frequency information, thereby recovering a clean and high-resolution image. Experimental results demonstrate that our method achieves competitive performance across three tasks: noisy image rescaling, image rescaling, and denoising, all while maintaining a relatively small model size. [ABSTRACT FROM AUTHOR]