Pyramidal Dual-tree Directional Filter Bank Research Articles

Fusing PDTDFB magnitude and relative phase modeling for geometrical correction-based image watermarking

Robustness, which refers to the ability that watermark signal survives various attacks, like additive noise, compression, rotation, etc., has played extremely important role in the multiple applications of digital watermarking. As one of the most difficult kinds of signal processing operations for a digital watermark to survive, geometric distortions have become a central problem in image watermarking research. Therefore, developing a greatly robust digital image watermarking approach, which can withstand geometrical distortions, remains a quite challenging work. In this paper, a new geometrical correction-based image watermarking approach using PDTDFB magnitude and relative phase modeling is proposed. This approach consists of digital watermark embedding, geometric distortions correction, and digital watermark extraction. In the watermark embedding process, PDTDFB (Pyramidal dual-tree directional filter bank) decomposition is performed on the original host image, followed by the low-pass subband partitioning. Watermark bit is inserted into low-pass subband block by modifying (quantization index modulation, QIM) the set of low-pass PDTDFB coefficients. In the geometric correction, the PDTDFB magnitude and relative phase are modeled by using Weibull distribution and Vonn distribution, respectively. Utilizing the compact statistical model parameters, the LS-SVR (Least squares support vector regression) correction is performed to estimate the geometrical distortions parameters. After LS-SVR geometrical correction, the watermark bits are extracted from the watermarked low-pass subband by employing the inverse QIM. Experimental results confirm that, under various well-known practical attacks, including common signal processing operations and geometrical distortions, the proposed approach performs well compared to conventional image watermarking methods.

Adaptive tube wave suppression and elastic down-going and up-going separation in VSP data using pyramidal dual-tree directional filter bank

ABSTRACTTube wave suppression and the separation of elastic up-going and down-going waves are the most important steps in vertical seismic profile (VSP) data processing. Different methods have been developed to suppress tube waves and separate wave fields. In this work, we use a pyramidal dual-tree directional filter bank as a multi-directional and multi-scale method. We then design two different adaptive algorithms to suppress tube waves and aliased tube waves, and to separate elastic up-going and down-going waves. In the first proposed algorithm, subscales containing tube waves and aliased tube waves were detected adaptively through energy calculation in the 2D Fourier domain, through which the filtered VSP were achieved by zeroing these subscales. When applied to field VSP data with strong tube waves, the proposed filter can attenuate both the tube wave and aliased tube wave successfully, with results outperforming those of f–k filtering, singular value decomposition and median filtering. Similarly, following tube wave and aliased tube wave suppression in the second designed algorithm, subscales with elastic up-going waves were detected fully. By reconstructing these subscales and subtracting them from the original VSP data, the wave fields were separated successfully. The performance of both algorithms in the presence of random noise was investigated and none of the algorithms were found to be highly sensitive.

Color image segmentation using PDTDFB domain hidden Markov tree model

The pyramidal dual-tree directional filter bank (PDTDFB) transform is a new image decomposition, which has many advantages, such as multiscale and multidirectional transform, efficient implementation, high angular resolution, low redundant ratio, and shiftable subbands. In this paper, we present a new color image segmentation algorithm based on PDTDFB domain hidden Markov tree (HMT) model. Firstly, the joint statistics and mutual information of the PDTDFB coefficients are studied. Then, the PDTDFB coefficients are modeled using a HMT model with Gaussian mixtures, which can effectively capture the intra-scale, inter-scale, and inter-direction dependencies. Finally, a color image segmentation using PDTDFB domain HMT model is developed, in which expectation–maximization (EM) parameter estimation, Bayesian multiscale raw segmentation, context based multiscale fusion, and majority-vote based color component fusion are used. Experimental evidence shows that the proposed color image segmentation algorithm has very effective segmentation results in comparison with the state-of-the-art segmentation methods recently proposed in the literature.

Relative phase in dual tree shearlets

The relative phase is an efficient approach to exploit the phase information of complex wavelet coefficients. However, the relative phase original generated from the pyramidal dual tree directional filter bank (PDTDFB) has three defaults. Firstly, its texture retrieval performance does not simultaneously improve in general as the scale increases. Secondly, it is not accurate enough when the directional subbands are not uniformly downsampled along row and column. Thirdly, its 2n number of directions are not optimal. In this paper, we propose a new multiscale and multidirection transform for relative phase, named as dual tree shearlets. The transform is based on the discrete shearlet transform, but a dual tree Laplacian pyramid is adopted to create a real-imaginary pair structure for deriving phase information under multiscale framework. The dual tree shearlets have the properties of uniform downsampled subbands; higher directional sensitivity and the 2-D Hilbert transform relationship between two channels like the dual tree complex wavelet transform (DTCWT). The numerical experiments presented in this paper demonstrate that the relative phase of our proposed method outperforms that of the PDTDFB in texture retrieval application both in terms of performance and computational efficiency. The results show that relative phase of the dual tree shearlets amends the above mentioned defaults.

Image denoising using bilateral filter and Gaussian scale mixtures in shiftable complex directional pyramid domain

For image denoising, the main challenge is how to preserve the information-bearing structures such as edges and textures to get satisfactory visual quality when improving the signal-to-noise-ratio (SNR). Edge-preserving image denoising has become a very intensive research topic. In this paper, we describe a method for removing noise from digital images, based on bilateral filter and Gaussian scale mixtures (GSM) in shiftable complex directional pyramid (also named Pyramidal Dual-Tree Directional Filter Bank, PDTDFB) domain. Firstly, the noisy image is decomposed into different subbands of frequency and orientation responses using a PDTDFB transform. Secondly, the bilateral filter, which is a nonlinear filter that does spatial averaging without smoothing edges, is applied on the approximation subband. Finally, the distribution of detail subbands of PDTDFB coefficients is modeled with GSM, and the statistical model is then used to obtain the denoised detail coefficients from the noisy image decomposition by Bayes least squares estimator. Extensive experimental results demonstrate that our method can obtain better performances in terms of both subjective and objective evaluations than those state-of-the-art denoising techniques. Especially, the proposed method can preserve edges very well while removing noise.

A study of relative phase in complex wavelet domain: Property, statistics and applications in texture image retrieval and segmentation

In this paper, we develop a new approach which exploits the probabilistic properties from the phase information of 2-D complex wavelet coefficients for image modeling. Instead of directly using phases of complex wavelet coefficients, we demonstrate why relative phases should be used. The definition, properties and statistics of relative phases of complex coefficients are studied in detail. We proposed von Mises and wrapped Cauchy for the probability density function (pdf) of relative phases in the complex wavelet domain. The maximum-likelihood method is used to estimate two parameters of von Mises and wrapped Cauchy. We demonstrate that the von Mises and wrapped Cauchy fit well with real data obtained from various real images including texture images as well as standard images. The von Mises and wrapped Cauchy models are compared, and the simulation results show that the wrapped Cauchy fits well with the peaky and heavy-tailed pdf of relative phases and the von Mises fits well with the pdf which is in Gaussian shape. For most of the test images, the wrapped Cauchy model is more accurate than the von Mises model, when images are decomposed by different complex wavelet transforms including dual-tree complex wavelet (DTCWT), pyramidal dual-tree directional filter bank (PDTDFB) and uniform discrete curvelet transform (UDCT). Moreover, the relative phase is applied to obtain new features for texture image retrieval and segmentation applications. Instead of using only real or magnitude coefficients, the new approach uses a feature in which phase information is incorporated, yielding a higher accuracy in texture image retrieval as well as in segmentation. The relative phase information which is complementary to the magnitude is a promising approach in image processing.

The Shiftable Complex Directional Pyramid—Part II: Implementation and Applications

In Part I ["The shiftable complex directional pyramid-Part I: Theoretical Aspects," IEEE TRANSACTIONS on Signal Processing, vol. 56, no. 10, October 2008], we proposed a novel image decomposition called the shiftable complex directional pyramid. The shiftable, multiresolution and multidirectional image decomposition is constructed by the pyramidal dual-tree directional filter bank (PDTDFB). In this Part II, we consider the design and implementation issues of the PDTDFB and its applications in image processing. The PDTDFB is composed of a multiresolution filter bank (FB) and a pair of directional filter banks (DFB); the design of each FB is considered separately. The binary tree structure of the DFB is modified to minimize the phase delay factor in order to reduce the border artifact in case symmetric extension is used. The filters presented in this paper are designed in frequency domain, and approximated by finite-impulse-response (FIR) filters. Numerical experiments show that the filters from the dual branches approximate the Hilbert transform of those from the primal ones, and the resulting PDTDFB yields acceptable shiftability. The shiftable pyramid decomposition is then tested in image processing applications, including image denoising, texture retrieval and seismic image migration.