Rigorous coupled wave transform coding of images

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.