Modified ICA algorithms for finding optimal transforms in transform coding

Discrete Wavelet Transform and Optimal Spectral Transform Applied to Multicomponent Image Coding

“…Nevertheless, the optimal transform computation is generally considered as a difficult task and the Gaussian assumption is then used in order to simplify the calculation. Recently, the problem of computing the optimal coding transform associated with scalar variable-rate quantizers for still images was resolved under high-resolution quantization hypothesis, with mean square error as distortion and without the Gaussian assumption (Narozny et al, 2005;. However, for the JPEG2000 Part2 compression scheme, the previous optimal transform computation cannot be directly applied to obtain the optimal spectral transform, because of the 2D DWT presence-see the criterion (15) in Section 4, which depends on subband statistics-.…”

ICA-Based Algorithms Applied to Image Coding

“…By adopting this new viewpoint, two new modified ICA algorithms, called GCGsup and ICAorth, were then derived for computing respectively the optimal 1-D linear transform and the optimal 1-D orthogonal transform. Unlike other more intuitive attempts of applying ICA to transform coding [5,6], the work of Narozny et al [1], which relies on a theoretical analysis, revealed one underlying link between ICA and transform coding. This paper aims at assessing the performances of algorithms GCGsup and ICAorth when applied to the compression of well-known grayscale images (Lenna, Mandrill, Peppers and Boat) each of size 512×512 pixels and coded using 8 bits per pixel (bpp).…”

“…

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.

…”

Spatio-chromatic decorrelation for color image compression

“…However, while ICA has been widely used for classification, implications of ICA for multimedia compression have not been greatly studied, and usually have been discussed in simple terms of dimensional reduction. Studies including a bit allocation scheme have so far considered only audio [17], and grayscale imagery [18][19][20][21], with inclusion of color in still imagery only in our previous preliminary papers [22,23]. When color is included, our patch vectors become N × N × 3 structures, for RGB images.…”