Fundamenta Informaticae

We present the most popular image and video coding standards. We concentrate on lossy compression techniques and ISO and ITU-T standards. JPEG image compression standard is described and its successor, currently developed JPEG-2000 is mentioned. For video, there are several standards aimed at different applications. We describe them starting with ISO MPEG-1 and continuing with MPEG-2, MPEG-4, H.261 and H.263.

A novel compression method called MBWT (modified basic wavelet technique) for efficient medical image compression is presented. MBWT is based on classic wavelet compression scheme with dyadic decomposition, uniform scalar quantisation and entropy coding of wavelet coefficients. By exploiting of space-frequency data characteristics in wavelet domain, an algorithm of adaptive quantisation and separable context-based binary coding with two (bitewise and wordwise) arithmetic coders are proposed. Also the most suitable filter banks selection is included. Quantisation step size evaluation is done for each subband on the basis of two items: established image quality level and wavelet coefficients variance estimation. Additionally adaptive threshold data selection is performed to reduce of unimportant coefficients in noisy areas. 9-order noncausal context model depicts the importance of the data from spatial correlations. The significance of parent node is also taken into account as a frequency aspect of data dependence. The idea of entropy coding includes three main elements: a) the construction of a decomposition tree with significant and insignificant nodes, b) pruning the tree - modified zerotree construction with four symbols of alphabet, c) separate arithmetic coding of two distinct data streams - a set of significant coefficients and a significant root node map with the signs of significant data. The MBWT algorithm seems to be simpler than the majority of efficient wavelet compression techniques and the effectiveness of our method is competitive with the best algorithms in the literature across diverse classes of medical images. Objective and subjective image quality evaluation supports this conlusion. Significant efficiency improvement over SPIHT algorithm is irrefutable for all images tested.

A new image coding scheme based on multiresolution image representation and entropy-constrained vector quantisation is proposed. The proposed technique is evaluated using a series of images. The results show a performance improvement over the previously proposed multiresolution scheme at relatively high bitrates. The reasons for worse performance at low bitrates are discussed.

In the last few years Vector Quantisation has become an important technique in speech and image compression and recognition. The jump from one dimension to the multiple ones allows wealth of new ideas, concepts, techniques and applications. In this paper there is enclosed a desription of vector quantisation idea, the design techniques, optimization methods and practical implementations.

The technique of image compression using Iterative Function System (IFS) is known as fractal image compression. An extension of IFS theory is called as Partitioned or local Iterative Function System (PIFS) for coding the gray level images. The theory of PIFS appears to be different from that of IFS in the sense of application domain. Assuming the theory of PIFS is the same as that of IFS, several techniques of image compression have been developed. In the present article we have studied the PIFS scheme as a separate one and proposed a mathematical formulation for the existence of its attractor. Moreover the results of a Genetic Algorithm (GA) based PIFS technique [1] is presented. This technique appears to be efficient in the sense of computational cost.

The convergence of fractal operator F used in image compression is investigated by analysis of block influence graph and pixel influence graph. The graph stability condition in block influence graph implies eventual contractivity condition which is sufficient for the operator iteration convergence. The graph stability condition in pixel influence graph appears to be sufficient and necessary for convergence of selecting fractal operators.

It is shown that the discrete time dynamical system defined by the Oja-RLS algorithm is stable in the closed ring K(0,9/8) – $\overline{K}$ (0,8/9) if only the initial gain β₀ is bounded by (2B)⁻¹, where B = b² and b is the bound for the learning sequence. It is rigorously proved that automatically computed gains β_n in Oja-RLS scheme converge to zero with the rate 1/n, almost surely.

The wavelet compression method is one of the most effective techniques of digital image compression. Efficiency of this method strongly depends on the filters used in two-dimensional wavelet transform. The fundamental way of construction of finite impulse response filters was given by I. Daubechies. The paper contains foundations of technique for wavelet image compression and presents a new proof of the fact that the Daubechies filters satisfy the conditions of a perfect signal reconstruction.

We present a simple proof of Mallat's theorem about wavelet and multiresolution analysis. We do not use Fourier transform and the proof is accesible even for younger undergraduate students.