Image denoising is a fundamental problem in image processing and many powerful algorithms have been developed. However, they often rely on the knowledge of the noise distribution and its parameters. We propose a fully blind denoising method that first estimates the noise level function then uses this estimation for automatic denoising. First we perform the non-parametric detection of homogeneous image regions in order to compute a scatterplot of the noise statistics, then we estimate the noise level function with the least absolute deviation estimator. The noise level function parameters are then directly re-injected into an adaptive denoising algorithm based on the non-local means with no prior model fitting. Results show the performance of the noise estimation and denoising methods, and we provide a robust blind denoising tool.