Transparent Composite Model for DCT Coefficients: Design and Analysis

The distributions of discrete cosine transform (DCT) coefficients of images are revisited on a per image base. To better handle, the heavy tail phenomenon commonly seen in the DCT coefficients, a new model dubbed a transparent composite model (TCM) is proposed and justified for both modeling accuracy and an additional data reduction capability. Given a sequence of the DCT coefficients, a TCM first separates the tail from the main body of the sequence. Then, a uniform distribution is used to model the DCT coefficients in the heavy tail, whereas a different parametric distribution is used to model data in the main body. The separate boundary and other parameters of the TCM can be estimated via maximum likelihood estimation. Efficient online algorithms are proposed for parameter estimation and their convergence is also proved. Experimental results based on Kullback-Leibler divergence and χ² test show that for real-valued continuous ac coefficients, the TCM based on truncated Laplacian offers the best tradeoff between modeling accuracy and complexity. For discrete or integer DCT coefficients, the discrete TCM based on truncated geometric distributions (GMTCM) models the ac coefficients more accurately than pure Laplacian models and generalized Gaussian models in majority cases while having simplicity and practicality similar to those of pure Laplacian models. In addition, it is demonstrated that the GMTCM also exhibits a good capability of data reduction or feature extraction-the DCT coefficients in the heavy tail identified by the GMTCM are truly outliers, and these outliers represent an outlier image revealing some unique global features of the image. Overall, the modeling performance and the data reduction feature of the GMTCM make it a desirable choice for modeling discrete or integer DCT coefficients in the real-world image or video applications, as summarized in a few of our further studies on quantization design, entropy coding design, and ima- e understanding and management.