Denoising Real Images Using Complex-Valued Wavelets

Although the details are more complicated in two dimensions, the basic ideas behind (1) and (2) are the same: a function is described in terms of scaled and shifted copies of the “building blocks” and . More details can be found in (e.g.) Vidakovic (1999). The two families of compactly supported wavelets described by Daubechies (1992) are by far the most commonly used. These “extremal phase” and “least asymmetric” wavelets have been applied to statistical problems such as nonparametric regression, density estimation, time series analysis, signal processing and image analysis. Less well known are the complex-valued Daubechies wavelets (cDws) introduced by Lawton (1993) and Lina and Mayrand (1995). A selection of cDws are shown in figure 1. These cDws have seen relatively little use in the literature compared to the real-valued Daubechies’ wavelets. Belzer, Lina and Villasensor (1995) have used the real parts only of “nearly real” cDws in image compression, while Lina and MacGibbon (1997) and Lina (1997)