On optimal orthogonal transforms at high bit-rates using only second order statistics in multicomponent image coding with JPEG2000

• Published in: Signal processing 2010-03, Vol.90 (3), p.753-758
• Main Authors: Bita, Isidore Paul Akam, Barret, Michel, Pham, Dinh-Tuan
• Format: Article
• Language: English
• Subjects: Algorithms; Applied sciences; Coding, codes; Computer Science; Criteria; Documents; Engineering Sciences; Exact sciences and technology; High rate transform coding; Hyperspectral image coding; Image processing; Independent component analysis; Information, signal and communications theory; JPEG2000; Karhunen–Loève transform; Miscellaneous; Multicomponent image coding; Multispectral image coding; Optimization; Signal and communications theory; Signal and Image processing; Signal processing; Spectra; Statistics; Telecommunications and information theory; Transforms
• ISSN: 0165-1684; 1872-7557
• DOI: 10.1016/j.sigpro.2009.08.008

We study a JPEG2000 compatible multicomponent image compression scheme, which consists in applying a discrete wavelet transform (DWT) to each component of the image and a spectral linear transform between components. We consider the case of a spectral transform which adapts to the image and a 2-D DWT with fixed coefficients. In Akam Bita et al. (accepted for publication, [6]) we gave a criterion minimized by optimal spectral transforms. Here, we derive a simplified criterion by treating the transformed coefficients in each subband as having a Gaussian distribution of variance depending on the subband. Its minimization under orthogonality constraint is shown to lead to a joint approximate diagonalization problem, for which a fast algorithm ( JADO) is available. Performances in coding of the transform returned by JADO are compared on hyper- and multi-spectral images with the Karhunen–Loève transform (KLT) and the optimal transform (without Gaussianity assumption) returned by the algorithm OrthOST introduced in Akam Bita et al. (accepted for publication, [6]). For hyper- (resp. multi-) spectral images, we observe that JADO returns a transform which performs appreciably better than (resp. as well as) the KLT at medium to high bit-rates, nearly attaining (resp. slightly below) the performances of the transform returned by OrthOST, with a significantly lower complexity than the algorithm OrthOST.