On optimal transforms in lossy compression of multicomponent images with JPEG2000
Résumé
It is well known in transform coding, that the Karhunen-Loève transform (KLT) is optimal only for Gaussian sources. However, in many applications using JPEG2000 Part 2 codecs, the KLT is generally considered as the optimal linear transform for reducing redundancies between components of multicomponent images. In this paper we present the criterion satisfied by an optimal transform of a JPEG2000 compatible compression scheme, under high resolution quantization hypothesis and without the Gaussianity assumption. We also introduce two variants of the compression scheme and the associated criteria minimized by optimal transforms. Then we give two algorithms, derived of the Independent Component Analysis algorithm ICAinf, that compute the optimal transform, one under the orthogonality constraint and the other without no constraint but invertibility. The computational complexity of the algorithms is evaluated. Finally, comparisons with the KLT are presented on hyperspectral and multispectral satellite images with different measures of distortion, as it is recommended for evaluating the performances of the codec in applications (like classification and target detection). For hyperspectral images, we observe a little but significant gain at medium and high bit-rates of the optimal transforms compared to the KLT. The actual drawback of the optimal transforms is their heavy computational complexity.