What is hallucinations_invpb?

This repository is the code that accompanies a research paper titled On Hallucinations in Inverse Problems: Fundamental Limits and Computable Bounds. Inverse problems are a type of task where you try to reconstruct a full, clean signal, like an image, from partial or noisy data. Hallucinations here means confident but wrong details that a reconstruction method invents when it fills in missing information. The paper studies mathematical limits on how bad these invented details can be, and this repository lets others reproduce the paper's experiments. The code covers three separate applications: sharpening low-resolution Sentinel 2 satellite images, speeding up MRI scans by reconstructing them from less raw data than usual, and increasing the resolution of MNIST handwritten digit images. It relies on a separate library called AccuracyBounds for computing the kernel sizes used in the underlying calculations. Because the three applications need different, sometimes conflicting Python packages, the instructions set up two separate virtual environments: one shared between the MRI and MNIST experiments, and one for the satellite image experiments. Each application then needs its own dataset downloaded separately, the satellite data from a Hugging Face dataset, the MRI data from the official Fast MRI website, and the MNIST data automatically through torchvision. Running an experiment typically means computing an operator specific to that problem, running a script that pastes in extra detail to visualize where hallucinations occur, and then working through a Jupyter notebook that walks through the remaining analysis with adjustable parameters such as patch size, noise level, and batch size. For MRI experiments, preparing the dataset alone can take one to two hours on a CPU. The project is released under the MIT license and is aimed at researchers working on inverse problems, image reconstruction, or the reliability of machine learning models.