الگوریتم کدگزاری آماری برای فشرده سازی تصویر سلسله مراتبی Statistical Encoding Algorithm for Hierarchical Image Compression

1. INTRODUCTION In the present time, body of data related to images increases permanently. As an example, we can mention growth of video data obtained when shooting the Earth’s surface from aircrafts [1–3]. If earlier, they have to deal only with images obtained from airplanes and satellites, now the researchers are concerned with multispectral and hyperspectral data that can contain hundreds of large format high-resolution channels. Mass application of unmanned aerial vehicles adds to the problem of storage of such image data. Of course, there are other examples except the Earth’s surface shooting. Increase in resolution and number of images takes place in different branches of knowledge, such as geoinformatics, medicine, printing industry, science of crime detection, and so on. In this situation, compression of images has no alternative, and the necessity to increase the efficiency of image compression methods is obvious. Many image compression methods use decorrelation techniques [4]. Then data are quantized [5] and encoded (finish compression is performed) [6, 7]. For example, in the framework of the differential methods [8] of image compression they perform the decorrelation by transition to a residual signal (difference between incoming and predicted values of pixels). After that, the residual signal is quantized and encoded. In the case of transform coding based on the discrete cosine transforms [9] (JPEG [10]) or the wavelet transforms [11] (JPEG-2000 [12]) a quantized field of the transforms (the results of transformation) has to be encoded. When applying a hierarchical grid interpolation (HGI) for compression of images [13, 14] we interpolate pixels of an image basing on thinned versions of the same image and quantize and encode interpolation errors (post- interpolation remainders). In all the examples discussed above, finally we need to encode a quantized signal. Of course, at a decorrelation step of any compression method it is necessary to construct the quantized signal most suitable for encoding (“final compression”). This is why as a rule the quantized signal has a specific (strongly nonuniform) distribution of probabilities. To make the best use of this non-uniformity for increasing the coefficient of compression, usually the quantized signal is statistical encoded [6, 7] allowing one to reduce data volume with the aid of an unequal-probability of the signal readings.