Lossy compression and wavelet thresholding for image denoising
S. Grace Chang, Bin Yu, Martin Vetterli · 1998
In recent work, it was proposed to use lossy compression to remove noise from corrupted signals, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. To further understand and substantiate this theory, we first explain why compression (via coefficient quantization) is appropriate for filtering noise from signal by making the connection that quantization of transform coefficients approximates the operation of wavelet thresholding for denoising. That is, denoising is mainly due to the zero-zone and that the full precision of the thresholded coefficients is of secondary importance. Secondly, under the realistic assumption that wavelet coefficients follow a Generalized Gaussian distribution, we derive an optimal threshold value (and thus the zero-zone width) from minimizing the mean squared error among soft-threshold estimators. We propose an adaptive threshold which is easy to compute and nearly o...