Image denoising via lossy compression and wavelet thresholding

Some past work has proposed to use lossy compression to remove noise, based on the rationale that a reasonable compression method retains the dominant signal features more than the randomness of the noise. Building on this theme, we 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. The method of quantization is facilitated by a criterion similar to Rissanen's minimum description length principle. An important issue is the threshold value of the zero-zone (and of wavelet thresholding). For a natural image, it has been observed that its subband coefficients can be well modeled by a Laplacian distribution. With this assumption, we derive a threshold which is easy to compute and is intuitive. Experiments show that the proposed threshold performs close to optimal thresholding.