In this paper, a new approach (scheme) to the analysis of quad-trees in the discrete wavelet spectrum of a digital image is proposed. During the pre-scanning phase, the proposed scheme generates problem-oriented binary codes for the whole set of quad-tree roots (wavelet coefficients) and thereby accumulates information on the significance of respective descendants (wavelet coefficients comprising quad-trees on the view). The developed scheme can be efficiently applied to any zero-tree based image coder, such as the embedded zero-tree wavelet (EZW) algorithm of Shapiro and set partitioning in hierarchical trees (SPIHT) by Said and Pearlman. Fairly impressive performance of the proposed quad-tree analysis scheme, in the sense of image encoding times, is demonstrated using the SPIHT algorithm and the discrete Le Gall wavelet transform.

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In this paper, a modified version of the discrete reversible (integer-to-integer) Le Gall wavelet transform (DLGT), distinguishing itself by apparently improved space localization properties and visibly extended potential capabilities, is proposed. The key point of the proposal-ensuring full decorrelation of Le Gall wavelet coefficients across the lower scales. Based on the latter circumstance, a novel exceptionally fast procedure for computing the integer DLGT spectra of the selected image blocks (regions of interest-ROI) is presented. It is shown that the new developments can be efficiently applied to progressive encoding and transmission of image blocks. Progressive encoding and transmission of image blocks is achieved by first transmitting a "rough" estimate of the original image, then sending further details related to one or another image block (ROI). To translate the idea into action, the zero-treebased encoder SPIHT (Set Partitioning in Hierarchical Trees) with an improved quad-tree analysis scheme is employed.

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In this paper, a novel wavelet-based approach to the detection of defects in grey-level texture images is proposed. This new approach (system) explores specific properties of the discrete wavelet transform (DWT), evaluates the statistical analysis results associated with well-defined and task-oriented subsets of DWT spectral coefficients, and generates defect detection criteria which, in their turn, evaluate many-sided nature of potential defects in texture images and leave space for controlling the risk, i.e. for controlling the percentage of false positives and/or false negatives in a particular class of texture images. The experimental results demonstrating the use of the proposed system for the visual inspection of ceramic tiles, obtained from the real factory environment, and textile fabric scraps are also presented.