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Wavelet transform is a powerful tool for multiresolution time-frequency analysis. It has been widely adopted in many image processing tasks, such as denoising, enhancement, fusion, and especially compression. Wavelets lead to the successful image coding standard JPEG-2000. Traditionally, wavelets were designed from the signal processing theory with certain assumption on the signal, but natural images are not as ideal as assumed by the theory. How to design content-adaptive wavelets for natural images remains a difficulty. Inspired by the recent progress of convolutional neural network (CNN), we propose iWave as a framework for deriving wavelet-like transform that is more suitable for natural image compression. iWave adopts an update-first lifting scheme, where the prediction filter is a trained CNN, to achieve wavelet-like transform. The CNN can be embedded into a deep network that is analogous to an auto-encoder, which is trained end-to-end. The trained wavelet-like transform still possesses the lifting structure, which ensures perfect reconstruction, supports multiresolution analysis, and is more interpretable than the deep networks trained as “black boxes.” We perform experiments to verify the generality as well as the speciality of iWave in comparison with JPEG-2000. When trained with a generic set of natural images and tested on the Kodak dataset, iWave achieves on average 4.4% and up to 14% BD-rate reductions. When trained and tested with a specific kind of textures, iWave provides as high as 27% BD-rate reduction.
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