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Sometimes image processing units inherit images in raster bitmap format only, so that processing is to be carried without knowledge of past operations that may compromise image quality (e.g., compression). To carry further processing, it is useful to not only know whether the image has been previously JPEG compressed, but to learn what quantization table was used. This is the case, for example, if one wants to remove JPEG artifacts or for JPEG re-compression. In this paper, a fast and efficient method is provided to determine whether an image has been previously JPEG compressed. After detecting a compression signature, we estimate compression parameters. Specifically, we developed a method for the maximum likelihood estimation of JPEG quantization steps. The quantizer estimation method is very robust so that only sporadically an estimated quantizer step size is off, and when so, it is by one value.