Image boundary extension with mean values for cosine-sine modulated filter banks

We present a mean value extension for cosine-sine modulated filter banks (CSMFBs), which are a class of dual-tree complex wavelet transforms (DTCWTs) and provide rich directional selectivity in image processing. The conventional signal extensions for CSMFBs yield annoying artifacts at the image boundaries due to the directionality being ignored. To mitigate the artifacts, we extend the image boundaries with the mean values of the pixel values around the boundaries. The proposed extension method is implemented by non-expansive convolution. We apply CSMFBs with the mean value extension to non-linear approximation (NLA) and the denoising of images and show the usefulness of the extension.