Celebratio Mathematica — Daubechies

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M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies: “Image coding using vector quantization in the wavelet transform domain,” pp. 2297–2300 in International conference on acoustics, speech, and signal processing (Albuquerque, NM, 3–6 April 1990), vol. 4. IEEE (Piscataway, NJ), 1990. incollection

A two-step scheme for image compression that takes into account psychovisual features in space and frequency domains is proposed. A wavelet transform is first used in order to obtain a set of orthonormal subclasses of images; the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains the number of pixels required to describe the image at a constant. Second, according to Shannon’s rate-distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise-shaping bit-allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. The wavelet transform is particularly well adapted to progressive transmission.

Pierre Mathieu	Related
Michel Barlaud	Related
Marc Antonini	Related

M. Antonini, M. Barlaud, P. Mathieu, and I. Daubechies: “Image coding using wavelet transform,” IEEE Trans. Image Proc. 1 : 2 (April 1992), pp. 205–220. article

A scheme for image compression that takes into account psychovisual features both in the space and frequency domains is proposed. This method involves two steps. First, a wavelet transform used in order to obtain a set of biorthogonal subclasses of images: the original image is decomposed at different scales using a pyramidal algorithm architecture. The decomposition is along the vertical and horizontal directions and maintains constant the number of pixels required to describe the image. Second, according to Shannon’s rate distortion theory, the wavelet coefficients are vector quantized using a multiresolution codebook. To encode the wavelet coefficients, a noise shaping bit allocation procedure which assumes that details at high resolution are less visible to the human eye is proposed. In order to allow the receiver to recognize a picture as quickly as possible at minimum cost, a progressive transmission scheme is presented. It is shown that the wavelet transform is particularly well adapted to progressive transmission.

Pierre Mathieu	Related
Michel Barlaud	Related
Marc Antonini	Related