复轮廓波包变换及其在SAR图像去斑中的应用

利用解析的双树复小波包变换(DT-CWPT)与非抽样方向滤波器组(NSDFB),构造了一种复轮廓波包变换(CCPT),并将其应用于合成孔径雷达(SAR)图像去斑。新的变换由于对信号的低频和高频部分都进行了分解,因此除了具有多分辨率、局部性、方向性和各向异性的特点外,还具有平移不变性和更丰富的方向分量。实验结果表明,本文构造的CCPT能够有效地抑制斑点噪声,达到较好的边缘保持效果,并且在图像的细节和纹理表现方面具有一定的优势。     

基于非下采样轮廓小波变换的图像去噪

针对采用下采样滤波器结构的轮廓波、轮廓小波在图像去噪过程中会引入伪吉布斯现象,利用小波变换(WT)和非下采样方向滤波器组(NDFB)构造了一种新的多尺度、多分辨率图像的非下采样轮廓小波变换(NWCT)。WT去除了拉普拉斯金字塔滤波器(LPF)的计算冗余,NDFB保证了该变换具有平移不变性。为了验证该变换的有效性,对其进行了图像去噪实验。实验结果表明,所提出方法能获得比WT、轮廓波变换(CT)、轮廓小波变换(WCT)更高的峰值信噪比(PSNR),并且能够很好地抑制伪吉布斯现象。     

The nonsubsampled contourlet transform: theory, design, and applications.

In this paper, we develop the nonsubsampled contourlet transform (NSCT) and study its applications. The construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks. The result is a flexible multiscale, multidirection, and shift-invariant image decomposition that can be efficiently implemented via the à trous algorithm. At the core of the proposed scheme is the nonseparable two-channel nonsubsampled filter bank (NSFB). We exploit the less stringent design condition of the NSFB to design filters that lead to a NSCT with better frequency selectivity and regularity when compared to the contourlet transform. We propose a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases. In addition, our design ensures that the corresponding frame elements are regular, symmetric, and the frame is close to a tight one. We assess the performance of the NSCT in image denoising and enhancement applications. In both applications the NSCT compares favorably to other existing methods in the literature.     

Multiresolution Image Representation Using Combined 2-D and 1-D Directional Filter Banks

In this paper, effective multiresolution image representations using a combination of 2-D filter bank (FB) and directional wavelet transform (WT) are presented. The proposed methods yield simple implementation and low computation costs compared to previous 1-D and 2-D FB combinations or adaptive directional WT methods. Furthermore, they are nonredundant transforms and realize quad-tree like multiresolution representations. In applications on nonlinear approximation, image coding, and denoising, the proposed filter banks show visual quality improvements and have higher PSNR than the conventional separable WT or the contourlet.     

The contourlet transform: an efficient directional multiresolution image representation.

The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In this paper, we pursue a "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information. The main challenge in exploring geometry in images comes from the discrete nature of the data. Thus, unlike other approaches, such as curvelets, that first develop a transform in the continuous domain and then discretize for sampled data, our approach starts with a discrete-domain construction and then studies its convergence to an expansion in the continuous domain. Specifically, we construct a discrete-domain multiresolution and multidirection expansion using nonseparable filter banks, in much the same way that wavelets were derived from filter banks. This construction results in a flexible multiresolution, local, and directional image expansion using contour segments, and, thus, it is named the contourlet transform. The discrete contourlet transform has a fast iterated filter bank algorithm that requires an order N operations for N-pixel images. Furthermore, we establish a precise link between the developed filter bank and the associated continuous-domain contourlet expansion via a directional multiresolution analysis framework. We show that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing applications. Index Terms-Contourlets, contours, filter banks, geometric image processing, multidirection, multiresolution, sparse representation, wavelets.     

A new family of nonredundant transforms using hybrid wavelets and directional filter banks.

We propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks. We convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks, where we form a nonredundant transform family, which exhibits both directional and nondirectional basis functions. We demonstrate the potential of the proposed transforms using nonlinear approximation. In addition, we employ the proposed family in two key image processing applications, image coding and denoising, and show its efficiency for these applications.     

非下抽样抗混叠Contourlet变换及其自适应阈值去噪

针对Contourlet变换在频谱混叠及平移不变性方面存在的局限性,提出了一种非下抽样抗混叠Contourlet变换(NS-NACT),其由非下抽样抗混叠塔式滤波器组(NS-NPFB)和非下抽样方向滤波器组(UDFB)构成。基于此,研究了一种基于自适应阈值调节的去噪算法。实验研究结果表明,当噪声方差σ=30时,通过本文算法去噪后的图像,不仅峰值信噪比(PSNR)较非抽样小波和Contourlet分别高出0.65dB和3.47dB,而且有效抑制了Contourlet变换去噪后的Gibbs现象,同时还可以更好地保留图像的边缘和细节,去噪效果更佳。     

A Mapping-Based Design for Nonsubsampled Hourglass Filter Banks in Arbitrary Dimensions

Multidimensional hourglass filter banks decompose the frequency spectrum of input signals into hourglass-shaped directional subbands, each aligned with one of the frequency axes. The directionality of the spectral partitioning makes these filter banks useful in separating the directional information in multidimensional signals. Despite the existence of various design techniques proposed for the 2-D case, to our best knowledge, the design of hourglass filter banks in 3-D and higher dimensions with finite impulse response (FIR) filters and perfect reconstruction has not been previously reported. In this paper, we propose a novel mapping-based design for the hourglass filter banks in arbitrary dimensions, featuring perfect reconstruction, FIR filters, efficient implementation using lifting/ladder structures, and a near-tight frame construction. The effectiveness of the proposed mapping- based design depends on the study of a set of conditions on the frequency supports of the mapping kernels. These conditions ensure that we can still get good frequency responses when the component filters used are nonideal. Among all feasible choices, we then propose an optimal specification for the mapping kernels, which leads to the simplest passband shapes and involves the fewest number of frequency variables. Finally, we illustrate the proposed techniques by a design example in 3-D, and an application in video denoising.     

Translation-invariant contourlet transform and its application to image denoising.

Most subsampled filter banks lack the feature of translation invariance, which is an important characteristic in denoising applications. In this paper, we study and develop new methods to convert a general multichannel, multidimensional filter bank to a corresponding translation-invariant (TI) framework. In particular, we propose a generalized algorithme à trous, which is an extension of the algorithme à trous introduced for 1-D wavelet transforms. Using the proposed algorithm, as well as incorporating modified versions of directional filter banks, we construct the TI contourlet transform (TICT). To reduce the high redundancy and complexity of the TICT, we also introduce semi-translation-invariant contourlet transform (STICT). Then, we employ an adapted bivariate shrinkage scheme to the STICT to achieve an efficient image denoising approach. Our experimental results demonstrate the benefits and potential of the proposed denoising approach. Complexity analysis and efficient realization of the proposed TI schemes are also presented.     

Bayesian texture classification based on contourlet transform and BYY harmony learning of Poisson mixtures

As a newly developed 2-D extension of the wavelet transform using multiscale and directional filter banks, the contourlet transform can effectively capture the intrinsic geometric structures and smooth contours of a texture image that are the dominant features for texture classification. In this paper, we propose a novel Bayesian texture classifier based on the adaptive model-selection learning of Poisson mixtures on the contourlet features of texture images. The adaptive model-selection learning of Poisson mixtures is carried out by the recently established adaptive gradient Bayesian Ying-Yang harmony learning algorithm for Poisson mixtures. It is demonstrated by the experiments that our proposed Bayesian classifier significantly improves the texture classification accuracy in comparison with several current state-of-the-art texture classification approaches.     

Enhancement of blood vessels in retinal imaging using the nonsubsampled contourlet transform

This paper presents an enhancement method for blood vessels in retinal images based on the nonsubsampled contourlet transform (NSCT). The NSCT is a shift-invariant version of the contourlet transform built upon the nonsubsampled pyramid filter banks and the nonsubsampled directional filter banks. The proposed method uses the NSCT to decompose the input retinal image into eight directions from coarser to finer scales, and then analyzes and classifies the image pixels into three categories: vessel, uncertainty, and non-vessel pixels, according to the NSCT coefficients. Then, we modify the NSCT coefficients according to the class of each pixel using a nonlinear mapping function, and reconstruct the enhanced image from the modified NSCT coefficients. The experimental results show that the proposed method can obviously increase the contrast of retinal vessels and thus outperform other enhancement methods.     

基于解析轮廓波变换的图像稀疏表示及其在压缩传感中的应用

 提出了具有平移不变性的低冗余度解析轮廓波变换.在该变换中圆对称滤波器组首先将图像分解为多个不同分辨率的细节子带和一个低频子带,再对细节子带进行希尔伯特变换形成二维解析信号.最后用方向滤波器组对二维解析信号进行分解,实现具有平移不变性多尺度多方向的解析轮廓波变换.解析轮廓波变换基函数的实部和虚部与Gabor小波的实部和虚部类似,符合人眼视觉特性.实验结果表明解析轮廓波变换在图像去噪和压缩传感方面具有明显优势.     

A reduced-complexity image coding scheme using decision-directed wavelet-based contourlet transform

Recently the wavelet-based contourlet transform (WBCT) is adopted for image coding because it matches better image textures of different orientations. However, its computational complexity is very high. In this paper, we propose three tools to enhance the WBCT coding scheme, in particular, on reducing its computational complexity. First, we propose short-length 2-D filters for directional transform. Second, the directional transform is applied to only a few selected subbands and the selection is done by a mean-shift-based decision procedure. Third, we fine-tune the context tables used by the arithmetic coder in WBCT coding to improve coding efficiency and to reduce computation. Simulations show that, at comparable coded image quality, the proposed scheme saves over 92% computing time of the original WBCT scheme. Comparing to the conventional 2-D wavelet coding schemes, it produces clearly better subjective image quality.     

基于支持向量值轮廓波变换的遥感影像融合

 本文研究基于支持向量值轮廓波变换的遥感影像融合.首先将支持向量值滤波器和方向滤波器组进行合理搭配,构造支持向量值轮廓波变换,该变换具有平移不变、泛化能力好、捕捉奇异性能强等特性.然后利用该变换对多源遥感影像进行多尺度、多方向、多分辨率分解,在不同的分解水平上利用基于区域能量和基于区域的轮廓波对比度方法进行融合.实验结果表明,利用该变换进行遥感影像融合时,能在不降低空间分辨率的情况下有效保留源影像的光谱信息.     

抗混叠轮廓波变换及其在图像融合中的应用

研究了原始轮廓波变换的频谱混叠问题,设计出能抑制混叠的多尺度分解方案,结合方向滤波器组,实现了一种抗混叠的轮廓波变换.在此基础上,提出了新颖的基于抗混叠轮廓波变换的图像融合算法.该算法通过邻域一致性测度的计算,实现了变换系数的局部自适应融合.实验结果表明,所提出的方法在视觉质量及定量指标上都优于基于小波变换和轮廓波变换的传统方法.     

Joint use of time-domain and windowed method for design of modulated DFT filter banks

A novel and efficient technique to design modulated discrete Fourier transform （DFT） filter banks is introduced in this paper. The proposed method first relaxes the limits that the synthesis filters are the time-reversed version of the analysis filters and then adopts the time domain formula of the perfect reconstruction property as the solution to design the synthesis filters. The prototype filter in analysis filter banks is designed based on Fourier-Kaiser window approach. Simulation results show that the designed filter banks approximately satisfy the perfect reconstruction with controllable reconstruction errors.     

Directional multiscale modeling of images using the contourlet transform.

The contourlet transform is a new two-dimensional extension of the wavelet transform using multiscale and directional filter banks. The contourlet expansion is composed of basis images oriented at various directions in multiple scales, with flexible aspect ratios. Given this rich set of basis images, the contourlet transform effectively captures smooth contours that are the dominant feature in natural images. We begin with a detailed study on the statistics of the contourlet coefficients of natural images: using histograms to estimate the marginal and joint distributions and mutual information to measure the dependencies between coefficients. This study reveals the highly non-Gaussian marginal statistics and strong interlocation, interscale, and interdirection dependencies of contourlet coefficients. We also find that conditioned on the magnitudes of their generalized neighborhood coefficients, contourlet coefficients can be approximately modeled as Gaussian random variables. Based on these findings, we model contourlet coefficients using a hidden Markov tree (HMT) model with Gaussian mixtures that can capture all interscale, interdirection, and interlocation dependencies. We present experimental results using this model in image denoising and texture retrieval applications. In denoising, the contourlet HMT outperforms other wavelet methods in terms of visual quality, especially around edges. In texture retrieval, it shows improvements in performance for various oriented textures.     

Least squares approximation of perfect reconstruction filter banks

Designing good causal filters for perfect reconstruction (PR) filter banks is a challenging task due to the unusual nature of the design constraints. We present a new least squares (LS) design methodology for approximating PRFBs that avoids most of these difficult constraints. The designer first selects a set of subband analysis filters from an almost unrestricted class of rational filters. Then, given some desired reconstruction delay, this design procedure produces the causal and rational synthesis filters that result in the best least squares approximation to a PRFB. This technique is built on a multi-input multi-output (MIMO) system model for filter banks derived from the filter bank polyphase representation. Using this model, we frame the LS approximation problem for PRFBs as a causal LS equalization problem for MIMO systems. We derive the causal LS solution to this design problem and present an algorithm for computing this solution. The resulting algorithm includes a MIMO spectral factorization that accounts for most of the complexity and computational cost for this design technique. Finally, we consider some design examples and evaluate their performance     

Discrete Lagrangian Methods for Designing Multiplierless Two-Channel PR-LP Filter Banks

In this paper, we present a new search method based on the theory of discrete Lagrange multipliers for designing multiplierless PR (perfect reconstruction) LP (linear phase) filter banks. To satisfy the PR constraints, we choose a lattice structure that, under certain conditions, can guarantee the resulting two filters to be a PR pair. Unlike the design of multiplierless QMF filter banks that represents filter coefficients directly using PO2 (powers-of-two) form (also called Canonical Signed Digit or CSD representation), we use PO2 forms to represent the parameters associated with the lattice structure. By representing these parameters as sums or differences of powers of two, multiplications can be carried out as additions, subtractions, and shifts. Using the lattice representation, we decompose the design problem into a sequence of four subproblems. The first two subproblems find a good starting point with continuous parameters using a single-objective, multi-constraint formulation. The last two subproblems first transform the continuous solution found by the second subproblem into a PO2 form, then search for a design in a mixed-integer space. We propose a new search method based on the theory of discrete Lagrange multipliers for finding good designs, and study methods to improve its convergence speed by adjusting dynamically the relative weights between the objective and the Lagrangian part. We show that our method can find good designs using at most four terms in PO2 form in each lattice parameter. Our approach is unique because our results are the first successful designs of multiplierless PR-LP filter banks. It is general because it is applicable to the design of other types of multiplierless filter banks.     

基于非抽样复轮廓波变换的图像去噪算法研究

将二维双树复小波变换(DT-CWT)与非抽样方向滤波器组(NSDFB)相结合,构造一种新的非抽样复轮廓波变换(NSCCT),并对其平移不变性作了相应证明。同时利用对称的正态逆高斯(NIG)分布先验概率模型和贝叶斯最小均方算法,提出一种基于NSCCT的图像去噪算法。实验结果表明,本文构造的NSCCT能够有效地抑制伪Gibbs现象,并且具有更丰富的方向分量,因而在图像的细节和纹理表现方面有一定的优势。