We propose a unique mathematical framework to deblur, denoise and compress natural images. Images are decomposed in a wavelet packet basis adapted both to the deblurring filter and to the denoising process. Effective denoising is performed by thresholding small wavelet packet coefficients while deblurring is obtained by multiplying the coefficients with a deconvolution kernel. This representation is compressed by quantizing the remaining coefficients and by coding the values using a context-based entropy coder. We present examples of such treatments on a satellite image chain. The results show a significant improvement compared to separate treatments with up-to-date compression approach.
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