Feature preserving lossy image compression using nonlinear PDE's

For very noisy images, high loss wavelet compression usually results in feature loss since edges generate high frequencies and they are removed along with the noise. This paper suggest a feature-retaining denoising method, followed by wavelet hard thresholding compression to get a high ratio compression which still keeps the features. In particular, the total variation (TV) denoising method which can smooth out the high frequency noise while keeping the edges is considered. Numerical experiments indicate that the more wavelet coefficients of the TV-denoised images are closer to zero so that they can be eventually removed in the compression process while the coefficients that are generated by the edges are still relatively big and therefore automatically retained.