The present paper deals with the problem of the detection of AI-generated images. It first proposes a forensic analysis, based on spatial correlations of the noise present in images, that can be used as fingerprints of both real and generated images. In particular, fingerprints can be extracted in each color channel, and complement each other during detection. The proposed detection scheme is a 3-step classifier, consisting only of a set of simple log-linear classifiers. This scheme is shown to perform much better than a standalone detector. The performance of the method is first assessed in an In-Distribution scenario, where an error probability of less than 1% is achieved on uncompressed images. It is then compared to stateof-the-art detectors in an out-of-distribution scenario, where significant performance gains are achieved. Results highlight the good generalization performances to unseen generators and the liability of color channels, specifically the chrominance CbCr for current state-of-the-art generators. A robustness analysis to JPEG compression also shows promising results for our method.