"In  the problem of computing the optimal transform for still images is resolved under high-rate entropy constraint scalar quantization hypothesis. More, in  these optimal transforms are applied to multi-and hyper-spectral images for reducing spectral redundancy when the quasi-orthonormal 2D discrete wavelet decomposition (DWT) — known as Daubechies (9,7) — is applied to each component for reducing spatial redundancy. Further, for multicomponent images and under the same hypothesis as above, the authors clarified in  the criterion that, when minimized, gives the optimal linear transform for reducing spectral redundancy when it is associated with the Daubechies (9,7) 2D DWT, according to a compression scheme compatible with the JPEG2000 Part 2 standard. "
[Show abstract][Hide abstract] ABSTRACT: In previous works, we defined the Optimal Transform Code (OTC) assuming high rate coding and using the asymptotical Bennett approximation of the rate. We showed that the OTC gives the optimal linear transform of a multicomponent image compression scheme which consists in applying a linear transform that adapts to the encoded image for reducing the spectral redundancy and a fixed 2-D Discrete Wavelet Transform (DWT) per component for reducing the spatial redundancy. The performances in terms of rate vs PSNR (Peak of Signal to Noise Ratio) are very attractive when evaluated with the Verification Model version 9 of the JPEG2000 committee which is a JPEG2000 codec (coding-decoding). The transform in OTC performs better than the Karhunen Loeve Transform (KLT). The drawback of the OTC is its high computing complexity, since the optimal linear transform must be computed for each encoded image. In order to implement the OTC in an on- board satellite real-time codec system, we propose to pass round the problem of computing complexity by learning only one fixed transform with the OTC algorithms from a set of images instead of computing a new transform for each image. We call the fixed transform computed in this way an exogenous quasi-optimal linear transform. In this paper, we focus the study on hyperspectral images. Our set of images is constituted of ten Hyperion3 hyperspectral images. We have separated the VNIR and the SWIR bands (since they are obtained with two different sensors on- board) and we just focus on the VNIR spectral bands.
[Show abstract][Hide abstract] ABSTRACT: 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.
Signal Processing 03/2010; 90(3-90):759-773. DOI:10.1016/j.sigpro.2009.09.011 · 2.21 Impact Factor
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