Parametric Haar-Like Transforms in Image Denoising

In our recent work, a class of parametric transforms, including family of Haar-like transforms, was introduced and studied in application to image compression. Parametric Haar-like transform (PHT) is a discrete orthogonal transform such that it may be computed with a fast algorithm in a structure similar to that of classical fast Haar transform and such that its matrix contains arbitrary predefined vector in its first row. The aim of this paper is to study a potential use of parametric Haar-like transforms in image denoising. A PHT-based post-processing method is proposed which may improve a denoising method based on fixed transforms. In particular, it is shown that the proposed method may significantly improve the performance of wavelet thresholding based image denoising.