Rank the best FOSS (Free and Open Source) image upscaling algorithms and software for photorealistic images, in order from the best ones.
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.
Give a comparative analysis of these models in terms of quality and the required processing power and memory to use.
Sure, here's a high-level comparison based on the quality and computational resources requirements of the models:

ESRGAN (Enhanced Super-Resolution Generative Adversarial Networks): ESRGAN provides a high-quality output and is known for generating realistic textures in images. However, like most GAN-based models, it's computationally intensive and requires significant GPU memory for optimal operation, especially for high-resolution images.

Waifu2x: Waifu2x provides excellent quality, particularly for images that are more artistic or anime-like. It is less resource-intensive than GAN-based models but still requires a good GPU for efficient operation, especially when dealing with larger images.

Real-ESRGAN: Real-ESRGAN is designed to provide better results on real-world images compared to ESRGAN. Its computational requirements are similar to ESRGAN and it also benefits from a powerful GPU for large, high-resolution images.

FSRCNN (Fast Super-Resolution Convolutional Neural Network): FSRCNN is designed to be faster and less resource-intensive than some other models, making it more suitable for devices with less computational power or memory. Despite its speed, it still produces good quality outputs.

GANPaint Studio: Being a GAN-based model, GANPaint Studio is excellent at preserving and enhancing details but it can be quite resource-intensive. A powerful GPU would be beneficial for using this software efficiently.

Neural Enhance: Neural Enhance uses deep learning to improve image quality. The quality is quite good, but it can be slow and resource-intensive, particularly for larger images.

It's worth noting that, for all of these models, the processing time and memory requirements increase with the resolution of the input image. Additionally, the models generally require less computational resources for inference (i.e., generating upscaled images) than for training the models.