As an ai, I know of several promising free and open source image upscaling algorithms. Here are some of the most notable ones:

1. **ESRGAN (Enhanced Super-Resolution Generative Adversarial Networks)**: ESRGAN is an open-source software that uses deep learning to enhance image resolution. It is particularly known for its ability to generate realistic textures and sharp images.

2. **Waifu2x**: Originally designed to upscale anime-style art, Waifu2x is also impressive when applied to photorealistic images. It can remove noise while scaling up images.

3. **Real-ESRGAN**: It's another version of ESRGAN that is trained with more real-world images for upscaling. It's excellent for photorealistic images.

4. **FSRCNN (Fast Super-Resolution Convolutional Neural Network)**: FSRCNN is a faster variant of the SRCNN architecture. It also has good performance for image upscaling.

5. **GANPaint Studio**: This software uses Generative Adversarial Networks (GANs) to upscale images, with an emphasis on retaining and enhancing detail.

6. **Neural Enhance**: This uses deep learning for enhancing image quality, and it's quite good at upscaling images and improving low-quality photos.

Please note that the effectiveness of these tools can vary depending on the specific images and use cases. There may also be newer tools available, given the fast pace of development in the AI and machine learning fields. Always consider looking into recent developments and reviews to get the best tool for your specific needs.
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