A Correlation - Dependent Model for Denoising viaNonorthogonal Wavelet

In many applications it is desirable to study nonorthogonal wavelet transforms. A translation-invariant wavelet transform is a nonorthogonal variant of the classical wavelet transform which plays an important role in denoising algorithms. However, it has been observed in many experiments that the thresholding scheme for the orthogonal DWT should be slightly modiied for use in the translation-invariant setting. These observations motivate us to study denoising schemes for nonorthogonal wavelet transforms. In this paper we derive a thresholding scheme for denoising that incorporates correlations between nonorthogonal wavelet coeecients and specify these thresholds for translation-invariant and biorthogonal wavelet systems. The new scheme includes a scale-and wavelet-dependent threshold which is larger than the one normally used in combination with the orthogonal discrete wavelet transform.