Wavelet transforms and compression of seismic data

Let us briefly outline the role of each step. The role of the transform step is to decorrelate the data. Namely, the transform will take a data set with a more or less flat histogram and produce a data set which has just a few large values and a very high number of near zero or zero values. In short, this step prepares the data for quantization. It has been observed that a much better compression is achieved by quantizing the decorrelated data than the original data. There are several transforms that can be used for decorrelation. For example, the Karhunen-Loeve transform achieves decorrelation but at a very high computational cost. It turns out that the wavelet, wavelet-packet or local cosine transforms can be used instead. These transforms are fast and provide a local time-scale (or time-frequency) data representation, resulting in a relatively few large coefficients and a large number of small coefficients. At the second step the coefficients of transformed data are quantized, i.e., mapped to a discrete data set. The quantization can take two forms, either scalar quantization, or vector quantization. In the case of scalar quantization every transform coefficent is quantized separately whereas in the case of vector quantization a block of coefficients is quantized simultaneously. Based on practical experience with seismic data it appears that the transformed coefficents tend to be reasonably decorrelated, thus pointing to scalar quantization as a good option. The most straightforward type of scalar quantization is uniform quantization, where the range of the coefficient values is divided into intervals of equal lehgth (bins), except possibly for a separate bin near zero (zero bin). Since the quantization step is the only lossy step of the process, a certain level of optimization has to take place in order to accommodate the target compression ratio (or the target bit budget).