Modeling the distribution of DCT coefficients for JPEG reconstruction

In the paper, the one moment (OM) method for the estimation of the shape parameter of generalized Gaussian distribution (GGD) is derived from the two moments method in the case when the moments converge in the limits to the same value. The one moment method reduces to the maximum likelihood (ML) method in the special case when the moment equals the shape parameter. The proposed method exhibits smaller complexity of calculations over ML keeping the same error.Assuming Laplacian distribution, there exists a method for optimally biasing the reconstruction levels for the quantized AC discrete cosine transform (DCT) coefficients using only the quantized ones available at the JPEG decoder J.R. Price, M. Rabbani, Biased reconstruction for JPEG decoding, IEEE Signal Process. Lett. 6 (12) (1999) 297–299; R. Krupiński, J. Purczyński, First absolute moment and variance estimators used in JPEG reconstruction, IEEE Signal Process. Lett. 11 (8) (2004) 674–677].Many researchers stated that the subset of images can be modeled with GGD with the shape parameter lower than 1. By assuming a source signal with GGD with the exponent 0.5, equations in a closed form for the centroid reconstruction can be obtained as it cannot be done for a GGD model. The ML method of discrete GGD 0.5 is derived, which requires the estimation of only one parameter. For selected images, the values of PSNR coefficients are compared for both distributions.