Maximum likelihood estimation of length of secret message embedded using ±k steganography in spatial domain

Abstract

In this paper, we propose a new method for estimating the number of embedding changes for non-adaptive ±K embedding in images. The method uses a high-pass FIR filter and then recovers an approximate message length using a Maximum Likelihood Estimator on those stego image segments where the filtered samples can be modeled using a stationary Generalized Gaussian random process. It is shown that for images with a low noise level, such as decompressed JPEG images, this method can accurately estimate the number of embedding changes even for K=1 and for embedding rates as low as 0.2 bits per pixel. Although for raw, never compressed images the message length estimate is less accurate, when used as a scalar parameter for a classifier detecting the presence of ±K steganography, the proposed method gave us relatively reliable results for embedding rates as low as 0.5 bits per pixel.