Polynomial Wavelet Regression for Images With Irregular Boundaries

In this paper, we focus on denoising images for which observations are equally spaced except around the boundaries which are irregular. Such images are very common in many fields, for example in geophysics. The advantages of adding a low-order polynomial term when implementing a wavelet regression for such images are presented. Besides removing the classical restriction of having a dyadic of number of observations, this strategy reduces the bias at the edges without significantly increasing the risk. In addition, this method is simple to implement, fast and efficient. Its utility is illustrated with simulation studies and a real example.