Directional quasi-analytic wavelet packets for image restoration
Amir Z. Averbuch, Pekka Neittaanmäki, Valery A. Zheludev, Moshe Salhov, Jonathan Hauser · arXiv (Cornell University) · 2020
The paper addresses the problems of image denoising and impainting by using the directional quasi-analytic wavelet packets (qWPs) and new developments described in the paper.The qWPs and the transform schemes are designed in [1]. The obtained results for both problems are quite competitive with the best state-of-the-art algorithms. These results are achieved due to the exceptional properties of qWPs such as: directionality of waveforms with unlimited number of orientations, (anti-)symmetry of waveforms and windowed oscillating structure of waveforms with a variety of frequencies. The denoising procedure consists of qWP decomposition of the degraded image, application of adaptive localized soft thresholding of the transform coefficients using the Bivariate Shrinkage algorithm (BSA) and restoration of the image from the thresholded coefficients from several decomposition levels. The inpainting is implemented by an iterative scheme, which,in essence, is the Split Bregman Iteration (SBI) procedure supplied by a BSA-based adaptive thresholding. The numerical denoising experiments demonstrate that qWP-based algorithm performance is competitive with the performance of the best existing denoising algorithms such as BM3D, Directional Tensor Product Complex Tight Framelets (TP-CTF) and Digital Affine Shear Filter Transform with 2-Layer Structure (DAS-2). specially, it is true for texture-rich images. In the inpainting experiments, performance comparison between the qWP-based methods and the state-of-the-art algorithms that are based on Digital Affine Shear (DAS-1), DAS-2 and TP-CTF transforms takes place. For texture images, qWP-based methods significantly outperform the mentioned algorithms in PSNR and SSIM and by visual perception. In most experiments with cartoon images the qWP-based methods produced the highest SSIM values and demonstrated the best resolution of fine details