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Adaptive Compression of Images

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We propose an adaptive compression enhancement scheme for images, that faithfully preserves edges that exist at certain scales. The image gradient is decomposed in a wavelet basis to locate edges at specific scales. Based on their location, the corresponding wavelet coefficients in the wavelet decomposition of the image are earmarked for preservation. A scale-space localized implementation of the gradient operator is derived in the wavelet transform domain, based on the Lemarie-Rieusset diagonalization of the derivative operator for functions of one variable. By decomposing an image with respect to a standard biorthogonal wavelet basis, we succeed in obtaining the gradient edge information in the image with respect to associated hybrid biorthogonal wavelet bases at certain desired scales only. There are several advantages to and applications of such a localized implementation of the gradient, apart from its computational efficiency. Adaptive compression of images based on edge-strengths at specific scales becomes possible, so that compression can be less in the neighborhood of edges at those scales at which its characteristics are best represented. Such preferential compression capability is useful for the compression of vast databases of oceanographic and astronomical images faint edges characterizing interfaces between warm and cold ocean currents in satellite oceanographic images, and boundaries between interstellar dust and nebulae of subtly varying luminosities in astronomical images are important image features that need to be preserved with minimum distortion, while achieving significant compression in other parts of these images that correspond to known features such as land-ocean boundaries or familiar stars.

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  • Cybernetics

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