In this paper we present a new lossless image compression algorithm. To achieve the high compression speed we use a linear prediction, modified Golomb–Rice code family, and a very fast prediction error modeling method. We compare the algorithm experimentally with others for medical and natural continuous tone grayscale images of depths of up to 16 bits. Its results are especially good for big images, for natural images of high bit depths, and for noisy images. The average compression speed on Intel Xeon 3.06 GHz CPU is 47 MB/s. For big images the speed is over 60 MB/s, i.e., the algorithm needs less than 50 CPU cycles per byte of image. KEY WORDS: lossless image compression; predictive coding; adaptive modeling; medical imaging; Golomb–Rice codes 1

Abstract. Image processing and analysis based on the continuous or discrete image transforms are classic techniques. The image transforms are widely used in image filtering, data description, etc. Nowadays the wavelet theorems make up very popular methods of image processing, denoising and compression. Considering that the Haar functions are the simplest wavelets, these forms are used in many methods of discrete image transforms and processing. The image transform theory is a well known area characterized by a precise mathematical background, but in many cases some transforms have particular properties which are not still investigated. This paper for the first time presents graphic dependences between parts of Haar and wavelets spectra. It also presents a method of image analysis by means of the wavelets–Haar spectrum. Some properties of the Haar and wavelets spectrum were investigated. The extraction of image features immediately from spectral coefficients distribution were shown. In this paper it is presented that two–dimensional both, the Haar and wavelets functions products man be treated as extractors of particular image features. Furthermore, it is also shown that some coefficients from both spectra are proportional, which simplify slightly computations and analyses.

November 23. Address correspondence to H.R. (e-mail:

OR � odds ratio PACS � picture archiving and communication system ROC � receiver operating characteristic