  We use an agnostic information-theoretic approach to investigate the
statistical properties of natural images. We introduce the Multiscale Relevance
(MSR) measure to assess the robustness of images to compression at all scales.
Starting in a controlled environment, we characterize the MSR of synthetic
random textures as function of image roughness H and other relevant parameters.
We then extend the analysis to natural images and find striking similarities
with critical (H = 0) random textures. We show that the MSR is more robust and
informative of image content than classical methods such as power spectrum
analysis. Finally, we confront the MSR to classical measures for the
calibration of common procedures such as color mapping and denoising. Overall,
the MSR approach appears to be a good candidate for advanced image analysis and
image processing, while providing a good level of physical interpretability.
