Pyramidal Coder Research Articles

Optimal pyramidal decomposition for progressive multidimensional signal coding using optimal quantizers

Optimal hierarchical coding is sought, for progressive or scalable multidimensional signal transmission, by minimizing the variance of the error difference between the original image and its lower resolution renditions. The optimal, according to the above criterion, pyramidal coders are determined for images quantized using the optimal vector Lloyd-Max quantizers. A rigorous general statistical model of a vector Lloyd-Max quantizer is used, consisting of a linear time-invariant filter followed by additive noise uncorrelated with the input. Given arbitrary analysis filters, the optimal synthesis filters are found. The optimal analysis filters are subsequently determined, leading to formulas for globally optimal structures for pyramidal multidimensional signal decompositions. These structures produce replicas of the original image, which at lower resolutions retain as much similarity to the original as possible. This is highly useful for the progressive coding of two- or three-dimensional (2-D or 3-D) images needed in applications such as fast browsing through image databases. Furthermore, the minimization of the variance of the error image leads to minimization of the variance of the quantization noise for this image and, hence, to its optimally efficient compression. Experimental results illustrate the implementation and performance of the optimal pyramids in application for the coding of still 2-D images.

Human visual weighted quantization : a unified approach for subband and pyramidal image coders

In the field of the coding of digital video signals, the concept of hierarchical coding is of real interest. Decorrelation operators fulfilling that hierarchical requirement are subband operators and pyramidal systems. The aim of this paper is show that the same methodology can be used to solve the quantization problem in subband and pyramidal coders. The criterion considered here takes into account the eye sensitivity to spatial frequencies. An analytical approach is presented in that paper for the cases of fixed bit allocation and quantizer followed by an entropy coder.