Rigorous coupled wave transform coding of images
Nai-Jen Chang, C.J. Kuo · 2003
Image coding based on a linear transform has been extensively studied. On the other hand, the only nonlinear transform used for image coding, to our best knowledge, is the fractal coding. We proposed a rigorous coupled wave (RCW) nonlinear transform for image coding. Here, we model the image as a surface relief grating where the gray-scale value of the image pixel is directly converted to the pixel's depth of the grating. When a uniform light wave is shined through the grating, the amplitude of the backward- and forward-diffracted waves are quantized and recorded, while the phase of the backward- and forward-diffracted waves can be calculated based on some a priori boundary conditions. Then these quantized diffraction waves can be used to reconstruct the depth of the grating (or image signal) based on Maxwell's equations. Scalar quantizations (SQ) combined with variable length coding are tested. Respectively, the PSNR of the SQ coded RCW transformed image at a low bit rate (0.1 bit/pixel) is 30.83 dB, while the state-of-the-art JPEG-2000 only achieves 28.61 dB.