No abstract

The Karhunen-Loève Transform (KLT) is optimal for transform coding of Gaussian sources, however it is no more optimal, in general, for non Gaussian sources. Furthermore, under the high resolution quantization hypothesis, nearly everything is known about the performance of a transform coding with entropy constrained scalar quantization and mean square distortion. It is then straightforward to find a criterion that, when minimized, gives the optimal linear transform under the above mentioned conditions. However, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculus. In this paper, we present the above mentioned criterion as a contrast of Independent Component Analysis modified by an additional term which is a penalty to nonorthogonality. Then we adapt the icainf algorithm by Pham in order to compute the transform minimizing the criterion either with no constraint or with the orthogonality constraint. Finally, experimental results show that the transforms we introduced can 1) outperform the KLT on synthetic signals, 2) achieve slightly better PSNR for high-rates and better visual quality (preservation of lines and contours) for medium-to-low rates than the KLT and 2-D DCT on grayscale natural images.

No abstract

Recently, Narozny et al [1] proposed a new viewpoint in variable high-rate transform coding. They showed that the problem of finding the optimal 1-D linear block transform for a coding system employing entropy-constrained uniform quantization may be viewed as a modified independent component analysis (ICA) problem. By adopting this new viewpoint, two new ICA-based algorithms, called GCGsup and ICAorth, were then derived for computing respectively the optimal linear transform and the optimal orthogonal transform. In this paper, we show that the transforms returned by GCGsup and ICAorth can achieve better visual image quality (better preservation of lines and contours) than the KLT and 2-D Discrete Cosine Transform (DCT) when applied to the compression of well-known grayscale images.